Full-scale measurement of wind pressure on the surfaceof an oscillating circular cylinders

Delong Zuo n

Department of Civil and Environmental Engineering, Texas Tech University, Mail Box 41023, Lubbock, TX, USA

a r t i c l e i n f o

Article history:Received 9 August 2013Received in revised form29 July 2014Accepted 1 August 2014Available online 23 August 2014

Keywords:Circular cylinderTurbulenceCritical transitionVortex sheddingWind-induced vibrationFull-scale pressure measurement

a b s t r a c t

Under wind excitation, many slender structural members with circular cross sections have exhibitedlarge-amplitude vibrations. The nature of some problematic vibrations remains to be fully understood.To investigate the excitation mechanisms that can cause the vibrations, an experimental campaign wasconducted to measure simultaneously the wind pressure on the surface of a circular cylinder in theatmospheric boundary layer and the acceleration of this cylinder. The pressure and accelerationmeasurements were used to investigate the interaction between the cylinder and the turbulent windin subcritical and critical Reynolds number ranges. The study revealed several effects of turbulence inwind in the atmospheric boundary layer on the critical transition, including the promotion of earlycritical transition, the attenuation of the single separation bubble, and the early cessation of the coherentvortex shedding. A coherent fluctuating axial flow component in the wake of circular cylinders yawed tothe flow, which has been previously observed in wind tunnel tests in smooth flow and postulated to becritical for the onset of dry cylinder vibration at high reduced velocity, was not observed in the presentexperiment.

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1. Introduction

Circular cylinders are among the simplest shaped bluff bodies.However, the interaction between circular cylinders and fluid flowis very complex primarily due to the fact that both where and howthe flow separates from the cylinder surface depend on not onlythe mean and turbulent nature of the free-stream flow, but alsothe characteristics of the cylinder, such as its size, orientationrelative to the flow, and elastic property. Numerous experiments,most of which being laboratory-based, have been conducted tostudy the flow around circular cylinders. In a two-volume book,Zdravkovich (1997, 2003) comprehensively reviewed many ofthese studies, detailing the observed nature of the flow around acircular cylinder and the corresponding characteristics of theloading on the cylinder over ranges of Reynolds numbers (Re) thatare associated with a succession of transitions of the flow in thewake, the free shear layers, and the boundary layers around thecylinder from laminar to turbulent.

For many engineering applications involving the flow aroundcircular cylinders, the Reynolds number is high, approaching orexceeding those at which the critical transition of the boundary

layers begins (e.g., at ReE2�105 for uniform smooth free-streamflow perpendicular to the cylinder axis). Due to this, and also theperceived drastic change of the loading on the cylinder at thecritical transition, many classical studies (e.g., Almosnino andMcAlister, 1984; Bearman, 1969; Eisner, 1925; Fage, 1929; Farelland Blessmann, 1983; Güven et al., 1980; Humphreys, 1960;Schewe, 1983) have focused on the flow at high Reynolds numbers.The results from these studies have led to advances in funda-mental knowledge of the evolution of the flow and the resultantcharacteristics of the force acting on the cylinder with increasingReynolds number. Most notably, it was revealed that when thefree-stream flow is uniform, smooth and perpendicular to thecylinder axis, the transition of the boundary layers from laminar toturbulent causes a drastic decrease of the drag coefficient, acondition known as the “drag crisis”. It was also observed thatas the Reynolds number increases, the critical transition occurs onone side of the cylinder first, creating a separation bubble on thisside and resulting in a net mean lift force, and then on both sidesof the cylinder, forming two symmetric separation bubbles andgenerating zero mean lift. The previous studies also suggests thatas the Reynolds number further increases, the flow enters thesupercritical regime, over which the separation bubbles are dis-rupted and fragmented, resulting in irregular separation linesand the cessation of periodic vortex shedding. Subsequently, theflow enters the postcritical range (e.g., Re44�106), over which

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Journal of Wind Engineeringand Industrial Aerodynamics

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J. Wind Eng. Ind. Aerodyn. 133 (2014) 65–79

straight separation lines are reestablished and periodic vortexshedding reappears (e.g., Bearman, 1969; Cincotta et al., 1966;Roshko, 1961). The Stouhal number (St) in the postcritical regionwas estimated to be greater than the nominal value over theprecritical Reynolds number regime (i.e., StE0.2).

Previous studies have also suggested that the flow aroundcircular cylinders can be significantly influenced by turbulence andshear in the free-stream flow as well as by the roughness of thecylinder surface. It was observed that increasing the turbulence inthe free-stream causes the laminar to turbulent transition in the freeand boundary layers to occur at progressively lower Reynoldsnumbers (e.g., ESDU, 1980; Fage and Warsap, 1929; Kiya et al.,1982; Zasso et al., 2005), and that increasing surface roughness has asimilar effect on the critical transition (e.g., ESDU, 1980; Fage andWarsap, 1929; Zasso et al., 2005). In particular, one group ofresearchers provided formulas (ESDU, 1980) that can be used toquantify the effects of the surface roughness and the free-streamturbulence (in terms of the turbulence intensity and the lateralintegral length scale of the longitudinal turbulence) on the criticaltransition. Further, Blackburn and Melbourne (1996) revealed thatfor free-stream flow of low turbulence intensity (e.g., for a long-itudinal turbulence intensity, Iu, of 4.6%, as in Blackburn andMelbourne, 1996), periodic vortex shedding occurs in the precriticaland critical Reynolds number regimes, with a Strouhal number of0.18, but ceases to exist in the supercritical Reynolds number regime.The same researchers also suggested that for free stream flow ofhigh turbulence intensity (e.g., Iu ¼ 18%, as in Blackburn andMelbourne, 1996), organized vortex shedding exists beyond thecritical Reynolds number regimes, with a Strouhal number of 0.23.

In addition, previous studies have indicated that although shearalong the cylinder axis in the free-stream flow does not significantlyaffect the critical transition (Davies, 1975), it does create secondaryflows along the cylinder axis on both the windward and the leewardsides which cause the drag coefficient to vary along the cylinder axis(e.g., Masch and Moore, 1963; Shaw and Starr, 1972). It also has beenobserved that for this type of free-stream flow, vortex sheddingoccurs in a “cellular” pattern along the cylinder axis, with theshedding frequency being constant within each cell (Maull andYoung, 1973). On the other hand, a limited number of studies (e.g.,Kiya et al., 1980) have suggested that shear across the cylinder in thefree-stream flow results in asymmetric pressure distribution on thecylinder surface. However, none of these studies were conducted athigh Reynolds numbers. As a result, the effect of shear across thecylinder for flows at high Reynolds numbers is unclear.

Despite the extensive fundamental understandings gained fromprevious studies, several types of large-amplitude wind-inducedcircular cylinder vibration still cannot be adequately explained. Forexample, stay cables of many cable-stayed bridges have beenobserved to vibrate at excessively large amplitudes (i.e., of the orderof multiple diameters of a cable) under the excitation of wind withsimultaneous occurrence of rain (e.g., Hikami and Shiraishi, 1988;Matsumoto et al., 1998). Full-scale measurements (e.g., Hikami andShiraishi, 1988; Matsumoto et al., 2003; Zuo and Jones, 2010) haverevealed that these large-amplitude vibrations occur over arestricted range of reduced velocities that is significantly higherthan that over which circular cylinders exhibit lock-in vortex-induced vibration. The same studies have also suggested that staycables declining in the direction of the wind are more susceptible tothis type of vibration than are cables of the opposite orientation.Initially, it was believed that the occurrence of rainfall is necessaryfor the onset of this type of vibration. However, a recent full-scalestudy has suggested that the characteristics of the large-amplitudevibrations occurring with rainfall, and the correlation of thesecharacteristics with the wind characteristics, are similar to thecorresponding characteristics and correlation of a class of dry staycable vibration (Zuo and Jones, 2010). This indicates that the

vibrations occurring with rainfall are likely related to the aerody-namics of dry circular cylinders.

Motivated by the observations in the field, many wind tunneltests have been conducted to expressly study the wind loading ofyawed or inclined circular cylinders (e.g., Cheng et al., 2008;Cosentino et al., 2003; Hikami and Shiraishi, 1988; Matsumotoet al., 1992, 2001; Zuo and Jones, 2009). However, the findingsfrom these studies have varied. The tests that simulated rainfall orused solid strips to simulate the water rivulets on the cylindersurface during rainfall (e.g., Cosentino et al., 2003; Hikami andShiraishi, 1988; Matsumoto et al., 1992) suggest that these rivuletsplay an important role in the onset of large-amplitude rain-wind-induced vibration, either by interacting with the oscillation of thecylinder or by aerodynamically modifying the cylinder surface. Thestudies that tested dry circular cylinders without artificial rivuletsindicated that yawed or inclined dry circular cylinders can besusceptible to galloping over the critical Reynolds number range(Cheng et al., 2008), as well as a type of vortex-shedding relatedexcitation at high reduced velocity due to the presence of an axialflow component (e.g., Cheng et al., 2008; Matsumoto et al., 2001;Zuo and Jones, 2009). Based on these studies, it has beensuggested that the mechanisms which caused significant drycircular cylinder vibrations in the wind tunnels are also likely tobe the causes for the large-amplitude stay cable vibrations.

In addition to the experimental work, numerical investigationsbased on computational fluid dynamics (e.g., Hoftyzer andDragomirescu, 2010; Kawamura and Hayashi, 1994; Lucor andKarniadakis, 2003; Yeo and Jones, 2008) have also been conductedto study the wind flow around yawed circular cylinders. Somerecent studies (Hoftyzer and Dragomirescu, 2010; Yeo and Jones,2008) have particularly focused on the characteristics of an axialflow component in the wake of the cylinder, and it has beenindicated that the interaction between this axial wind componentand the vortex shedding into the wake of the cylinder can excitethe cylinder to vibrate at large amplitudes.

Despite the extensive field, laboratory and computationalstudies that have been completed, the complex interactionsbetween circular cylinders and wind that induce large-amplitudevibrations are still not adequately understood. In particular, sincemost of the wind tunnel and numerical studies were conductedbased on uniform smooth flow, the effects of the wind shear andturbulence in the atmospheric boundary layer on the interactionare mostly unclear. Also, in the experiments in which the windpressure on the surface of a circular cylinder was measured, withfew exceptions (e.g., Jakobsen et al., 2012), the cylinder was heldstationary. As a result, the interaction between the cylinderoscillation and the flow could not be fully assessed.

This paper presents the findings from a field experimentalcampaign conducted to measure simultaneously wind pressure onthe surface of a slender circular cylinder and the resulting vibra-tion of this cylinder. As a first step, the cylinder was orientedhorizontally to facilitate an investigation of the effects of theturbulence and shear in the atmospheric boundary layer winds aswell as the yaw angle of the cylinder on the cylinder-windinteraction. This paper details the characteristics of the windpressures and the resultant forces acting on the cylinder in windregimes of various mean and turbulent characteristics, as well asthose of the corresponding cylinder response. The implications ofobservations on the excitation mechanism of large-amplitude drycircular cylinder vibration are also presented.

2. Experimental configuration

The experiment was conducted at the full-scale test facilityat Texas Tech University in Lubbock, Texas, USA. This facility is

D. Zuo / J. Wind Eng. Ind. Aerodyn. 133 (2014) 65–7966

situated on flat, homogeneous terrain with minimal obstruction.The specimen used in the study was a 7.62 m long circular cylinderconsisting of a 6.40 m long steel pipe and a 1.22 m long PVC pipeboth of 0.224 m outer diameter and 0.8 cm wall thickness.As shown in Fig. 1, the steel pipe was mounted horizontallyat a height of 6 m above ground level near the top of a taperedcircular steel pole, which was 30.5 cm and 36.8 cm in diameter atthe top and the base, respectively. The wall thickness of the polewas 1 cm.

The monitoring system consisted of 36 pressure taps to measurethe wind pressures at selected locations on the surface of thecylinder, and an accelerometer to measure the cylinder oscillation,while site meteorological conditions were monitored by an ultra-sonic anemometer, a temperature and relative humidity sensor anda barometric pressure sensor. As schematically depicted in Fig. 2,the pressure measurement system consisted of a ring of 32 pressuretaps (numbered 1 to 32) evenly spaced at 11.251 intervals, and fourmore additional pressure taps (numbered 33 to 36) on the ring’ssides. The pressure tap ring was located at 2.1 m from the free endof the cylinder, thus all the taps were at least eight cylinderdiameters from the free end of the cylinder and 23 cylinderdiameters from the fixed end of the cylinder. To further minimizethe influence of the free end of the cylinder on the flow near thepressure taps, a half spherical cap was installed at this end. Due tothe inability of the pressure measurement system to functionproperly in rain, the taps were covered in advance wheneverrainfall was anticipated. Each pressure tap was connected to apressure transducer (Setra System, model 265) with a range of71.245 kPa through a tubing system of 0.91 m in length and 0.6 cmin diameter. The tri-axial accelerometer (Memsic Inc., modelCXL04LP3 with a measurement range of 74 g) used to monitorthe oscillation of the cylinder was located immediately adjacent tothe pressure tap ring. The ultrasonic anemometer (R.M. Young,

Company, model 81000) was mounted on the top of the verticalpole, providing wind measurements at a height of 1.5 m above theaxis of the horizontal circular cylinder. The other meteorologicalsensors were located at the base of the vertical pole.

The data acquisition system sampled each instrumentedchannel at a rate of 32 Hz and recorded data files of 10 min inlength. Two additional 10-s records were also sampled immedi-ately before and after each 10-min record for calibration of thepressure transducers. The monitoring program lasted fivemonths.

It is worth noting that the specimen used in the experimentwas a cantilevered cylinder supported by a circular pole and thatthe flow around the cylinder can be affected by its end conditions.The end connected to the pole was not likely to have affected thepressures at the locations of the pressure taps since the taps weremore than 20 cylinder diameters from this end. Also, since thewind-induced forces on the segment of the cylinder close to thepole contributed insignificantly to the generalized forces, anyeffects by the end condition were inconsequential for the oscilla-tion of the cylinder.

However, according to the results from previous studies(e.g., Fox and Apelt, 1993; Fox and West, 1993a,b; Humphreys,1960; Ramberg, 1983), the presence of the free end can potentiallyconsiderably influence the wind-induced pressure at the locationsof the pressure taps. In particular, it has been suggested (e.g., Foxand West, 1993b; Humphreys, 1960) that when the flow isperpendicular to the cylinder axis, the mean forces acting on thecylinder is minimally affected by the effects of the free end, whilethe fluctuating wind flow, such as vortex shedding from thecylinder, can be significantly influenced at locations that are morethan 5 cylinder diameters away from the free end of a cylinder oflarge aspect ratio. Additionally, previous studies have revealed thatwhen the cylinder is yawed to the flow, the effects of the free enddepends on the yaw angle, which is defined as the angle betweenthe cylinder axis and the normal to the free streamwind direction.In particular, it has been indicated that the region affected by thefree end effects is proportional to the yaw angle (Zdravkovich,2003).

In the present study, the effects of the free end on the interactionbetween the wind and the circular cylinder are not specificallyassessed due to the difficulty in addressing this problem at full-scale, especially with the added complexity by the effects of theReynolds number and the turbulence in the free stream wind.In most cases, however, it is generally accepted that the effects ofthe free end on the flow at the locations of the pressure taps wereinsignificant since the taps were at least eight cylinder diametersaway from the free end with a half spherical cap. Moreover, theflows were of high Reynolds numbers, at which the effects of thefree end are less significant (Humphreys, 1960).Fig. 1. Circular cylinder subjected to monitoring in the experiment.

1 2 3 45

678910

1112

13141516171819

2021

2223

24252627

2829

3031 32

11.25°

0.224 m 0.224 m

1

2

3

4

5

4333

35 36

Fig. 2. Configuration of pressure taps (not to scale).

D. Zuo / J. Wind Eng. Ind. Aerodyn. 133 (2014) 65–79 67

3. Wind characteristics

Fig. 3 shows the distribution of longitudinal mean wind speedand turbulence intensity over wind direction. The wind directionis at 01 when wind approaches along the axis of the cylinder fromthe free end and increases with a clockwise rotation. The turbu-lence intensity presented in this figure is calculated based on the10-min mean wind speed and the standard deviation of theturbulent wind component estimated by subtracting a time-varying mean component from the total wind speed, as illustratedin Fig. 4. The time-varying mean component was estimated bydecomposing the along-wind speed time history using a 10th levelDaubechies wavelet of order 3 (Daubechies, 1992). Therefore, thiscomponent corresponds to the slowly fluctuating component ofwind at frequencies below 0.015 Hz. The turbulence intensitycalculated in this manner is a good measure of the effects of theturbulence on the wind loading on the cylinder because thedynamic loading on this particular cylinder and the correspondingresponse caused by the low frequency wind component isinsignificant.

It is apparent according to Fig. 3 that during the measurements,wind predominantly approached the cylinder from the directions01 to 901. It is also seen that the wind at the height of measure-ment had varying turbulent characteristics, with the along-windturbulence intensity ranging from lower than 0.05 to higher than0.15. According to the measurements by a nearby meteorologicaltower, winds of low turbulence occurred in atmospherically stableboundary layers, (in which the vertical wind speed shear wasmore pronounced due to thermal stratification,) and winds ofhigher turbulence occurred in atmospherically unstable or neutralboundary layers, (in which the low vertical wind speed shear wasprimarily due to the surface friction) (e.g., Zuo and Xiao, 2012).These characteristics of wind in boundary layers of differentstability states are illustrated by the 10-min mean longitudinalwind speed and turbulence intensity profiles shown in Fig. 5.

4. Characteristics of cylinder response

To characterize the vibration of the cylinder, the accelera-tion time histories were numerically integrated to estimate thecorresponding displacement time histories at the location of theaccelerometer. After each integration step, a 5th order high-passButterworth filter with a cut-off frequency of 0.2 Hz was applied toeliminate the spurious effect of low frequency noise. The displace-ments were then band-pass filtered using a 5th order Butterworthfilter to obtain the response in the first two in-plane and out-of-plane modes of the structure. The frequencies of the first two in-plane modes were estimated to be 2.43 Hz and 5.48 Hz, respec-tively, and those of the first two out-of-plane modes wereestimated to be 2.17 Hz and 5.55 Hz, respectively, by identifyingthe peaks in the estimated power spectral density functions of theacceleration measurements. The pass bands of the filter were0.5 Hz frequency bands centered at the estimated natural frequen-cies. Finally, the Hilbert transform was finally applied to individualmodal displacements to assess the evolution of the modal vibra-tion amplitudes and frequencies (Bendat and Piersol, 2010). Thedata suggested that the displacement of the cylinder was pre-dominantly in the first in-plane and out-of-plane modes. There-fore, the vibration in these two modes will be used subsequentlyto represent the response of the cylinder.

Fig. 6 shows the 10-min mean displacement amplitude (A) inthe first in-plane and out-of-plane modes against the correspond-ing mean wind speed (U) and direction (θ). It is evident that thecylinder exhibited significant vibration in the in-plane cross-winddirection over a narrow range of low wind speeds, but for a broadrange of wind directions. This is obvious evidence of classicalvortex-induced vibration. The figure also suggests that at higherwind speeds, the vibration amplitudes in the in-plane and out-of-plane directions both increased with increasing wind speed, whichis typical for vibration due to buffeting.

Fig. 7 shows the 10-min mean in-plane vibration amplitude (Az)against the reduced velocity (Vr) and the longitudinal turbulenceintensity. The reduced velocity is computed based on the windcomponent normal to the cylinder, the in-plane modal vibrationfrequency (f) and the diameter of the cylinder (D) as

Vr ¼ jU sin θjf D

ð1Þ

It can be seen that the vortex-induced vibrations occurred overa narrow reduced velocity range centered at a value greater thanfive, which is equivalent to the nominal Strouhal number of 0.2for a circular cylinder normal to uniform smooth flow in thesubcritical Reynolds number range. This can be primarily

5%

10%

15%

270° 90°

180°

0°

0 - 55 - 1010 - 1515 - 20

5%

10%

15%

270° 90°

180°

0°

0 - 0.050.05 - 0.10.1 - 0.150.15 - 0.2

Fig. 3. Distribution of (a) mean wind speed (in m/s) and (b) longitudinal turbulence intensity.

0 100 200 300 400 500 6000

5

10

Alo

ng-w

ind

spee

d(m

/s)

Time(s)

time historytime varying mean

Fig. 4. Wavelet decomposition of wind speed time history.

D. Zuo / J. Wind Eng. Ind. Aerodyn. 133 (2014) 65–7968

attributed to a number of reasons: first, according to windmeasurements by the adjacent meteorological tower, the windspeed measured by the anemometer (which was 1.5 m above thecylinder axis) can be 1% to 10% higher than that at the height of thecylinder, depending on the stability state of the atmosphericboundary layer; second, according to Fig. 7, the significantvortex-induced vibrations occurred over a broad range of long-itudinal turbulence intensities, which means that the Strouhalnumber associated with the vortex shedding that caused thesevibrations can be considerably lower than 0.2 (Blackburn andMelbourne, 1996).

In addition to revealing the reduced velocity range over whichvortex-induced vibration occurred, Fig. 7 also suggests that nolarge-amplitude vibration occurred at higher reduced velocity,regardless of the wind direction.

5. Interpretation of pressure measurements in the contextof acceleration measurements

A close study of the measurements by the pressure transducersand the accelerometer has revealed some distinct characteristics of

0 2 4 6 8 100

5

10

15

20

Mean wind speed (m/s)

Hei

ght (

m)

0 0.05 0.1 0.15 0.2 0.25

Longitudinal turbulence intensity

0 2 4 6 8 100

5

10

15

20

Mean wind speed (m/s)

Hei

ght (

m)

0 0.05 0.1 0.15 0.2 0.25

Longitudinal turbulence intensity

Fig. 5. Example mean longitudinal wind speed and turbulence intensity profiles in (a) stable and (b) unstable atmospheric boundary layers.

0 2.5 5 7.5 10 12.5 15 17.5 200

0.05

0.1

0.15

0.2

U (m/s)

A/D

In-PlaneOut-of-Plane

0 45 90 135 180 225 270 315 3600

0.05

0.1

0.15

0.2

θ (°)

A/D

In-PlaneOut-of-Plane

Fig. 6. Mean displacement amplitudes in the first in-plane and out-of-plane modes vs. mean wind speed and direction.

0 0.1 0.2 0.3 0.4 0.50

0.05

0.1

0.15

0.2

Iu

Az/D

0 6 12 18 24 300

0.05

0.1

0.15

0.2 Vr=Usinθ/(fD)

Vr

Az/D

Fig. 7. Mean in-plane displacement amplitude vs. reduced velocity and longitudinal turbulence intensity.

D. Zuo / J. Wind Eng. Ind. Aerodyn. 133 (2014) 65–79 69

wind loading on the circular cylinder in different wind regimes.The nature of the wind-cylinder interaction will be illustratedsubsequently for the two cases of wind normal and significantlyoblique to the cylinder.

5.1. Wind normal to the cylinder axis

Fig. 8 shows the estimated 10-min mean drag (CD) and lift (CL)coefficients of the cylinder against the mean longitudinal windspeeds and the corresponding Reynolds numbers when the windswere approximately normal to the cylinder axis (i.e., 851rθr951or 2651rθr2751). Only records with wind direction variation notexceeding 601 are presented herein. The drag and lift coefficientsare defined as

CD ¼ 2FDρU2; CL ¼

2FLρU2 ð2Þ

where FD and FL are the drag and the lift forces, respectively, and ρis the air density calculated based on the temperature, relativehumidity, and barometric pressure measurements. The Reynoldsnumber is computed based on the mean wind speed, an assumedkinematic viscosity (ν) value of 1.5�10�5 m2/s, and the cylinderdiameter as the reference dimension

Re¼ UDν

ð3Þ

It can be seen in Fig. 8 that when the wind was nominallyperpendicular to the cylinder, the transition from the subcriticalto the critical Reynolds number range, which is characterized bythe steady decrease of the mean drag coefficient with increasingReynolds number, starts at a mean wind speed between 5 m/s and7.5 m/s, corresponding to a Reynolds number range of 0.75�105

to 1.12�105. This Reynolds number range is much lower than theReynolds numbers at which the transition occurs in uniformsmooth flow (approximately 2�105, e.g., Zdravkovich, 1997). Suchearly occurrence of the critical transition is expected due to thepresence of turbulence in the free stream flow (e.g., ESDU, 1980).

Fig. 9 shows the mean drag coefficients against the so-calledequivalent Reynolds numbers (Ree) defined in ESDU (1980) forthree groups of data based on three ranges of in-plane vibrationamplitude. The equivalent Reynolds number is expressed as(ESDU, 1980)

Ree ¼ λRλTRe ð4Þin which λR is a factor accounting for the roughness of the Cylindersurface and λT is a factor representing the effect of the free-streamturbulence. According to ESDU (1980), λR is unity for an idealsmooth surface and increases with increasing surface roughness.For the data presented, λR was taken as 1.25 for the paintedsteel pipe (ESDU, 1980), with the understanding that significant

uncertainty in this parameter is inevitable, especially given thefact that the cylinder was exposed in the open environment formultiple months. The values of λT were calculated using theformulas given in ESDU (1980) based on the estimated turbulenceintensities and lateral integral scales of the longitudinal turbu-lence. For comparison purposes, Fig. 9 also shows the dragcoefficients predicted by ESDU (1980) for the ranges of equivalentReynolds numbers of interest. It is apparent that ESDU signifi-cantly overestimates the effect of the free-stream turbulence onthe critical transition. This is true even when the uncertainty in λRis considered, as λR is greater than unity. A similar conclusion wasreached in a previous study based on wind tunnel tests ofstationary circular cylinders in turbulent flow (Zasso et al.,2005). Also, Fig. 9 indicates that due to the free stream turbulence,the rate at which the mean drag coefficient decreases withincreasing equivalent Reynolds number over the beginning partof the drag crisis (starting from ReeE5�105) was slower thanwhat is predicted by ESDU (1980). While the portion of the dragcrisis at higher equivalent Reynolds numbers was not encounteredin the present study, Zasso et al. (2005) did make a similarobservation for the entirety of the drag crisis.

In addition, Fig. 9 suggests that the mean drag coefficient tendsto be larger for larger in-plane vibration amplitude over thesubcritical Reynolds number range. The general scatter of themean drag coefficient over this Reynolds number range canpotentially be attributed to the effects of the different levels ofvertical wind speed shear as well as the turbulence in the wind.Nevertheless, it can be seen in Figs. 8 and 9 that the estimatedmean drag coefficients are lower than those predicted by ESDU(1980) over the subcritical Reynolds number range. A similarobservation was made by Zasso et al. (2005) in a series of windtunnel tests in which stationary circular cylinders with their freeends fitted with half spherical caps were tested in turbulent flow.

Fig. 8 also shows the evolution of the mean lift coefficient inthe subcritical and critical Reynolds number ranges: when theflow is in the subcritical Reynolds number range, with a limitednumber of exceptions, the mean lift coefficient is close to zero;

0 2.5 5 7.5 10 12.5 15 17.5 20

U (m/s)

0 0.37 0.75 1.12 1.49 1.87 2.24 2.61 2.99

0

0.3

0.6

0.9

1.2

1.5

Re (x105)

Mea

n C

D

0 2.5 5 7.5 12.5 15 17.5 2010

U (m/s)

0 0.37 0.75 1.12 1.49 1.87 2.24 2.61 2.99

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

Re (x105)

Mea

n C

L

Fig. 8. Mean drag and lift coefficients vs. mean wind speed and Reynolds number for nominal winds perpendicular to the cylinder axis.

0 2 4 6 8 100

0.3

0.6

0.9

1.2

1.5

Ree (x105)

Mea

n C

D

Az<0.25 cm

0.25 cm ≤Az<1 cm

Az≥1 cm

ESDU

Fig. 9. Mean drag coefficient vs. equivalent Reynolds number for nominal windsperpendicular to the cylinder axis.

D. Zuo / J. Wind Eng. Ind. Aerodyn. 133 (2014) 65–7970

when the flow transitions into the critical Reynolds number range,the mean lift coefficient deviates significantly from zero withincreasing Reynolds number before becoming close to zero again,suggesting a likely successive appearance of a single separationbubble followed by two separation bubbles during the criticaltransition. It is noteworthy, however, that in this case of a cylinderin turbulent wind over the one-bubble critical Reynolds numberrange, the absolute value of the mean lift coefficient did notexceed 0.2, while previous studies based on wind tunnel testing inuniform smooth flow have reported that the absolute mean liftcoefficient can reach as high as 1.3 (Bearman, 1969). Such differ-ence between the mean lift coefficients of a circular cylinder insmooth and turbulent flows over the one-bubble-regime was alsoobserved in a previous wind tunnel study (Zasso et al., 2005).

Fig. 10 shows the mean lift coefficient against both the meanwind speed and the longitudinal turbulence intensity, and it isclear that the few points in Fig. 8 showing significantly non-zerolift coefficient at low Reynolds numbers (i.e., approximately0.35�105) were associated with winds of very low turbulenceintensity (i.e., approximately 0.03). As indicated earlier, this type ofwind of low turbulence intensity is also characterized by pro-nounced speed shear across the cylinder. Thus, it could be arguedthat the significantly non-zero mean lift force coefficients over thesubcritical Reynolds number range are related to vertical windspeed shear, which can cause asymmetric wind pressure on thecylinder surface.

In the following, four representative records with wind char-acteristics and associated mean drag and lift coefficients listed inTable 1 are used to illustrate the interaction between the cylinderand winds in various regimes, for the case of wind direction beingnominally perpendicular to the cylinder.

Record one illustrates the nature of the interaction between thelow-amplitude cylinder vibration and the wind in the subcriticalReynolds number range. Fig. 11 shows the estimated drag and liftcoefficients of the cylinder based on the wind and pressuremeasurements in record one, as well as the correspondingestimated power spectral density functions. Here, it can be seenthat the lift force was dominated by a component at 2.19 Hz, which

corresponds to a reduced velocity of five. This frequency compo-nent, therefore, was a result of vortex shedding from the cylinder.It also can be seen that for this particular record, the dragcoefficient had a significant component at 4.36 Hz, which isapproximately twice the dominant frequency of the lift coefficient.This is an expected result due to alternating vortex shedding at theupper and lower surface of the cylinder.

Fig. 12 shows the accelerations of the cylinder in the in-plane(az) and out-of-plane (ax) directions for record one, as well as thecorresponding estimated power spectral density functions. It isapparent that both the in-plane and out-of-plane vibrations wereprimarily in the first modes at 2.45 Hz and 2.18 Hz, respectively.The vibration amplitudes were very low because the dominantvortex shedding frequency (2.19 Hz) was considerably differentfrom the natural frequencies of the cylinder in the out-of-planedirection. Such interaction between the full-scale cylinder andturbulent wind in this particular wind regime is fundamentallysimilar to the corresponding observations from wind tunnel testsin uniform smooth flow (e.g., Goswami et al., 1993).

Record two is a representative record where vortex sheddingwas locked in with the cylinder vibration. Fig. 13 shows theestimated drag and lift coefficients of the cylinder, as well as thecorresponding estimated power spectral density functions. It isevident that the lift coefficient was dominated by a narrow-bandcomponent at 2.43 Hz, indicating coherent vortex shedding fromthe cylinder at this frequency. However, the Strouhal numbercalculated based on this dominant frequency and the correspond-ing mean wind speed listed in Table 1 is 0.15, which is significantlylower than that of a circular cylinder subjected to uniform smoothflow in the wind tunnel.

In Fig. 13, it is also of interest to see that the dominantfrequency of the drag coefficient was 2.43 Hz, which was thesame as rather than twice the dominant frequency of the liftcoefficient. This is believed to be caused by the oscillation of thecylinder, which, as it will be seen subsequently, was dominated bythe first in-plane mode at 2.43 Hz. Fig. 13 also shows, however,that the drag coefficient indeed had a frequency component of4.86 Hz resulting from the alternating shedding of vortices fromthe top and from the bottom of the cylinder.

Fig. 14 shows the cross-correlation coefficients of the pressuresat five taps along two axial lines on the leeward side of thecylinder over a time lag of five seconds. The subscripts indicate thetap numbers. The measurement by tap number 36 is not usedbecause this tap malfunctioned. The cross-correlation functionsshown are clearly those of narrow band processes with the samecenter frequency. The fact that the local maxima of the correlationcoefficients are all close to unity for short time lags indicates thatthe vortex shedding from the cylinder was coherent over the axiallengths separating the pressure taps.

Fig. 15 shows the acceleration of the cylinder at the location ofthe pressure tap ring, as well as the corresponding estimatedpower spectral density functions. The steady primarily in-planevibration (az) was predominantly in the first in-plane mode of thecylinder at 2.43 Hz, which was also the shedding frequency of thevortices as indicated by the pressure measurements. This clearlysuggests that the vortex shedding was locked-in with the vibrationof the structure.

It is also noteworthy that, in addition to the dominantfrequency component at 2.43 Hz, the in-plane vibration also hada component at 4.86 Hz, which is twice the vortex-sheddingfrequency, despite the fact that this frequency is neither a naturalfrequency of the structure nor the vortex-shedding frequency inthe cross-wind direction. This is an indication that the in-planevibration at 4.86 Hz was due to a super-harmonic of the excitationat 2.43 Hz, which further suggests that the excitation was periodicbut non-sinusoidal. Since the drag coefficient had a significant

05

1015

20 00.05

0.10.15

0.2-0.6-0.4-0.2

00.20.40.6

IuU (m/s)

Mea

n C

L

Fig. 10. Variation of mean lift coefficient with mean wind speed and longitudinalturbulence intensity for nominal winds perpendicular to the cylinder axis.

Table 1Characteristics of example records of nominal winds normal to the cylinder axis.

Record number U (m/s) Re (�105) θ (1) Iu Mean CD Mean CL

1 2.47 0.37 88.9 0.029 0.80 0.112 3.7 0.55 85.5 0.086 1.02 0.013 8.15 1.22 93.9 0.128 0.85 0.174 14.50 2.17 88.5 0.118 0.60 0.09

D. Zuo / J. Wind Eng. Ind. Aerodyn. 133 (2014) 65–79 71

frequency component at 2.43 Hz, it is also of interest to notice thatthe insignificant out-of-plane vibration also consisted of a notice-able component at this frequency, in addition to the modalcomponents at 2.17 Hz and 5.55 Hz, etc.

By comparing the lift coefficient time history shown in Fig. 13and the in-plane acceleration time histories shown in Fig. 15, it isapparent that for this particular record, although the response ofthe structure was steady, the lift force acting at the location of thepressure tap ring was not. This is further illustrated in Fig. 16,

0 120 240 360 480 6000

2

4

CC

D0 2 4 6 8 10 12 14 16

10-4

10-3

10-2

S DD

(1/H

z)

4.36Hz

0 120 240 360 480 600-4-2024

L

Time (s)0 2 4 6 8 10 12 14 16

10-4

10-2

100

S LL (1

/Hz)

Frequency (Hz)

2.19Hz

Fig. 11. Drag and lift coefficients of the cylinder and the corresponding spectra: record one, subcritical Reynolds number range, U¼2.47 m/s, θ¼88.91, Iu¼0.029,Re¼0.37�105.

0 120 240 360 480 600-1

-0.50

0.51

a z (g)

0 2 4 6 8 10 12 14 16

10-6

10-4

10-2

S zz (g

2 /Hz) 2.45Hz

2.19Hz

0 120 240 360 480 600-1

-0.50

0.51

a x (g)

Time (s)0 2 4 6 8 10 12 14 16

10-6

10-4

S xx (g

2 /Hz)

Frequency (Hz)

2.18Hz

2.45Hz

Fig. 12. Acceleration time histories and the corresponding spectra: record one, subcritical Reynolds number range, U¼2.47 m/s, θ¼88.91, Iu¼0.029, Re¼0.37�105.

0 120 240 360 480 6000

2

4

CD

0 2 4 6 8 10 12 14 1610-4

10-2

100

S DD

(1/H

z) 2.43Hz4.86Hz

0 120 240 360 480 600-4-2024

CL

Time (s)0 2 4 6 8 10 12 14 16

10-4

10-2

100

S LL (1

/Hz)

Frequency (Hz)

2.43Hz

Fig. 13. Drag and lift coefficients of the cylinder and the corresponding spectra: record two, subcritical Reynolds number range, U¼3.7 m/s, θ¼85.51, Iu¼0.086,Re¼0.55�105.

-5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50.6

0.8

1

Time lag (s)

Cro

ss-c

orre

latio

n

R33,34 R33,2 R2,34 R35,4

Fig. 14. Cross-correlation coefficients of pressure measured along the axial direc-tion on the leeward side of the cylinder: record two, subcritical Reynolds numberrange, U¼3.7 m/s, θ¼85.51, Iu¼0.086, Re¼0.55�105.

D. Zuo / J. Wind Eng. Ind. Aerodyn. 133 (2014) 65–7972

0 120 240 360 480 600-1

-0.50

0.51

a z (g)

0 2 4 6 8 10 12 14 1610-6

10-3

100

S zz (g

2 /Hz)

2.43Hz

4.86Hz5.46Hz

0 120 240 360 480 600-1

-0.50

0.51

a x (g)

Time (s)0 2 4 6 8 10 12 14 16

10-6

10-4

10-2

S xx (g

2 /Hz)

Frequency (Hz)

2.43Hz2.17Hz

5.55Hz

Fig. 15. Acceleration time histories and the corresponding spectra: record two, subcritical Reynolds number range, U¼3.7 m/s, θ¼85.51, Iu¼0.086, Re¼0.55�105.

120 240 360 480-4-2024

d (c

m)

Time (s)

-4-2024

CL

330 332 334 336 338 340-4-2024

d (c

m)

Time (s)

-4-2024

CL

Fig. 16. Cylinder displacement and lift coefficient at location of pressure tap ring: record two, subcritical Reynolds number range, U¼3.7 m/s, θ¼85.51, Iu¼0.086,Re¼0.55�105.

Fig. 17. Synchronization of vortex-shedding with cylinder vibration: record two, subcritical Reynolds number range, U¼3.7 m/s, θ¼85.51, Iu¼0.086, Re¼0.55�105.

0°

90°

180°

270°

0 22.5 45 67.5 90 112.5 135 157.5 180 202.5 225 247.5 270 292.5 315 337.5 360-2.5

-2-1.5

-1-0.5

00.5

11.5

CP

Angular position (°)

CD = 1.015; CL= 0.006

Fig. 18. Mean pressure distribution at the pressure tap ring: record two, subcritical Reynolds number range, U¼3.7 m/s, θ¼85.51, Iu¼0.086, Re¼0.55�105.

0 120 240 360 480 6000

2

4

CD

0 2 4 6 8 10 12 14 1610-4

10-2

100

S DD

(1/H

z)

0 120 240 360 480 600-4-2024

CL

Time (s)0 2 4 6 8 10 12 14 16

10-4

10-2

100

S LL (1

/Hz)

Frequency (Hz)

Fig. 19. Drag and lift coefficients of the cylinder and the corresponding spectra: record three, critical Reynolds number range, U¼8.15 m/s, θ¼93.91, Iu¼0.128, Re¼1.22�105.

D. Zuo / J. Wind Eng. Ind. Aerodyn. 133 (2014) 65–79 73

which shows the lift coefficient and displacement time histories.It can be seen that the lift force and the displacement at thelocation of the pressure tap ring were only intermittently syn-chronized likely due to the turbulence in the wind.

Fig. 17 illustrates approximately one cycle of vibration at thepressure tap ring location and the corresponding pressure dis-tribution on the surface of the cylinder, when the vibration andthe lift force were nearly synchronized. It is apparent that whenthe cylinder was at symmetrical positions during upward anddownward movements, the pressure distribution on the ring wasquite different, indicating different vortex shedding patterns fromthe upper and lower surface primarily due to the existence ofturbulence.

Fig. 18 depicts the distribution of the mean pressure coeffi-cients (Cp) over the 10-min duration. It can be seen that for thisparticular record, the distribution of the mean pressure was quitesymmetric about the horizontal plane through the centerline ofthe cylinder. Figs. 17 and 18 together, therefore, show that theturbulence affects the wind-cylinder interaction only at a shorttime scale.

Records three and four illustrate the wind-cylinder interactionwhen the mean wind direction is nominally perpendicular to thecylinder axis and when the mean wind speed is in the criticalReynolds number range. According to Fig. 19, when the windspeed was near the lower end of the critical Reynolds numberrange (record three), neither the drag force nor the lift force atthe location of the pressure tap ring had a dominant frequencycomponent, but the lift force did have considerable contributionsfrom components across a broad frequency band centered betweenapproximately 6 Hz and 8 Hz. This frequency band represents that ofincoherent vortex-shedding from the cylinder.

Fig. 20 shows the cross correlation coefficients of the pressuresat five taps along two axial lines on the leeward side of thecylinder over a time lag of five seconds. These correlation coeffi-cients are typical for random processes of quite broad bandwidths.The ripples at small time lags indicate the existence of thefrequency band centered between 6 Hz and 8 Hz, which, as

indicated by Fig. 19, was due to incoherent vortex shedding. Thegraph also suggests that the pressures at the tap locations werewell correlated for a small time lag, indicating cohesive large-scaleflow structure extending over the distance covered by the pressuretaps in the axial direction. However, the cross-correlations appar-ently decay much faster than in the case of record two, where thevortex-shedding was locked in with the cylinder vibration.

The data suggests that when the wind speed increases towardthe higher end of the critical Reynolds number range, even theincoherent vortex shedding disappears. This can be seen in Fig. 21,which shows the drag and lift coefficients for record four and thecorresponding power spectra. The spectra show no sign of coher-ent vortex-shedding, suggesting complete turbulent separation ofthe flow from the cylinder surface.

Fig. 22 shows the cross-correlation coefficients of the pressuresat five taps along two axial lines on the leeward side of thecylinder over a time lag of five seconds for record four. These aresimilar to the cross-correlation functions shown in Fig. 20 forrecord three. The difference is that the pressures at the locationsalong the axial direction were less correlated for record four thanfor record three.

Records 3 and 4 collectively also suggest that when the wind issignificantly turbulent, the disappearance of coherent vortexshedding occurs at much lower Reynolds numbers than whenthe wind is smooth (i.e., Re¼4�105 to 5�105; Shih et al., 1993).

Due to the disappearance of coherent vortex shedding, theresponse of the cylinder to the wind in the critical Reynoldsnumber range was fundamentally similar. For example, Fig. 23shows the acceleration response of the cylinder for record four.It can be seen that the accelerations in both the in-plane and theout-of-plane directions were at fairly small amplitudes and domi-nated by the first two modes in these directions. It is alsonoteworthy that the vibration in the out-of-plane direction alsohad a component at a frequency of 5.48 Hz, which is the frequencyof the second in-plane mode, due to the coupling between thesecond in-plane and out-of-plane modes of similar frequencies.However, the pressure measurement shown in Fig. 21 and the

-5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50.6

0.8

1

Time lag (s)

Cro

ss-c

orre

latio

n

R33,34 R33,2 R2,34 R35,4

Fig. 20. Cross-correlation coefficients of pressure measured along the axial direc-tion on the leeward side of the cylinder: record three, critical Reynolds numberrange, U¼8.15 m/s, θ¼93.91, Iu¼0.128, Re¼1.22�105.

0 120 240 360 480 6000

2

4

CD

0 2 4 6 8 10 12 14 1610-4

10-2

100

S DD

(1/H

z)

0 120 240 360 480 600-4-2024

CL

Time (s)0 2 4 6 8 10 12 14 16

10-3

10-2

10-1

S LL (1

/Hz)

Frequency (Hz)

Fig. 21. Drag and lift coefficients of the cylinder and the corresponding spectra: record four, critical Reynolds number range, U¼14.50 m/s, θ¼88.51, Iu¼0.118, Re¼2.17�105.

-5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50.6

0.8

1

Time lag (s)

Cro

ss-c

orre

latio

n

R33,34 R33,2 R2,34 R35,4

Fig. 22. Cross-correlation coefficients of pressure measured along the axial direc-tion on the leeward side of the cylinder: record four, critical Reynolds numberrange, U¼14.50 m/s, θ¼88.51, Iu¼0.118, Re¼2.17�105.

D. Zuo / J. Wind Eng. Ind. Aerodyn. 133 (2014) 65–7974

acceleration measurement shown in Fig. 23 do not indicate anysignificant aeroelastic interaction between the cylinder andthe wind.

5.2. Wind oblique to the cylinder axis

The wind loadings on the cylinder by oblique and normalwinds show quite similar fundamental characteristics except forsome details. As an illustration, Fig. 24 shows the mean drag andlift coefficients against the mean wind speed and the correspond-ing Reynolds number for winds of yaw angle between 251 and 351(i.e., when the mean wind direction, θ, was between 551 and 651,or 1151 and 1251, or 2351 and 2451, or 2951 and 3051). The meandrag coefficient shows large scatter over low Reynolds numbers,which can be attributed to the same factors (i.e., shear and

turbulence in the free-stream wind) that have resulted in thescatter of the drag coefficient in this Reynolds number range forthe case of wind nominally normal to the cylinder. The data doshow, however, that the drag coefficient decreases as a trend withincreasing wind speed when the wind speed is higher than about7.5 m/s, which corresponds to a Reynolds number of 1.12�105,indicating the transition from the subcritical to the critical Rey-nolds number range at about this wind speed. However, this doesnot exclude winds of lower speed but high turbulence from alsobeing in the critical Reynolds number range.

Fig. 24 also suggests that when the wind yaw angle wasbetween 251 and 351, the estimated mean lift coefficient candeviate significantly from zero starting from a Reynolds numberof approximately 0.5�105, which is much lower than the valuestarting from which significant net mean lift force develops for asimilarly yawed circular cylinder in uniform smooth flow(Jakobsen et al., 2012). This is due to the inclusion of records oflow wind speed but high turbulence in Fig. 24. Indeed, as it can beseen in Fig. 25, the mean lift coefficient remains close to zero forlow wind speed and low turbulence intensity, but deviatessignificantly from zero when the turbulence intensity is high,even when the mean wind speed is low.

In the following, the three representative records with thewind characteristics and the corresponding mean characteristicsof the loading listed in Table 2 are used to illustrate the nature ofthe interaction between the cylinder and oblique winds in differ-ent regimes.

Record five illustrates the interaction between the cylinder andoblique winds when the vortex shedding locked in with the cylin-der vibration. Fig. 26 shows the time histories and the correspondingpower spectral density functions of the force coefficients at the

0 120 240 360 480 600-1

-0.50

0.51

a z (g)

0 2 4 6 8 10 12 14 1610-6

10-3

100

S zz (g

2 /Hz) 2.42Hz 5.45Hz

0 120 240 360 480 600-1

-0.50

0.51

a x (g)

Time (s)0 2 4 6 8 10 12 14 16

10-6

10-3

100

S xx (g

2 /Hz)

Frequency (Hz)

2.17Hz 5.53Hz5.45Hz

Fig. 23. Acceleration time histories and the corresponding spectra: record four, critical Reynolds number range, U¼14.50 m/s, θ¼88.51, Iu¼0.118, Re¼2.17�105.

0 2.5 5 7.5 10 12.5 15 17.5 20U (m/s)

0 0.37 0.75 1.12 1.49 1.87 2.24 2.61 2.99

0

0.3

0.6

0.9

1.2

1.5

Re (x105)

Mea

n C

D

0 2.5 5 7.5 10 12.5 15 17.5 20U (m/s)

0 0.37 0.75 1.12 1.49 1.87 2.24 2.61 2.99

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

Re (x105)

Mea

n C

L

Fig. 24. Mean drag and lift coefficients associated wind of yaw angle between 251 and 351.

0 5 10 15 20 00.05

0.10.15

0.2-0.6-0.4-0.2

00.20.40.6

IuU (m/s)

Mea

n C

L

Fig. 25. Dependence of lift coefficient on mean wind speed and longitudinalturbulence intensity for winds of yaw angle between 251 and 351.

D. Zuo / J. Wind Eng. Ind. Aerodyn. 133 (2014) 65–79 75

pressure tap ring, and Fig. 27 shows the acceleration response of thecylinder at this location and the corresponding estimated powerspectral density functions. By comparing these graphs with thecounterparts for record two, it is apparent that the characteristicsof the loading and the response of the cylinder were fundamentallysimilar for both normal and oblique winds when the vortex-shedding was locked in with the vibration.

Fig. 28 depicts the cross-correlation coefficient functions of thepressures at the taps along the axial direction on the leeward sideof the cylinder, and it is evident that the pressures at theselocations were narrowband and well correlated, indicating coher-ent vortex shedding from the cylinder surface. This is similar to thecase illustrated by record two, when the wind was nominallynormal to the cylinder axis.

Records six and seven illustrate the characteristics of thecylinder-wind interaction for significantly oblique winds whenthe wind speed is near the lower and upper ends in the criticalReynolds number range. Figs. 29 and 30 show the time historiesand the corresponding estimated spectra of the drag and lift

coefficients at the pressure tap ring for these two records. Thespectra indicate that for both cases, the separation of the flow wasturbulent without the presence of coherent vortex shedding. Thissuggests that for this cylinder yawed to the turbulent flow,coherent vortex shedding disappears from the lower end of thecritical Reynolds number range. The component at 5.48 Hz shownin the spectrum of the drag coefficient in Fig. 29 was a result of thecylinder vibration in the second out-of-plane mode.

The cross-correlations between the pressures measured alongthe axial lines on the leeward side of the cylinder for records sixand seven are also fundamentally similar. For example, Fig. 31shows these cross-correlation coefficients for record seven. Theseare typical for quite well correlated broad band processes. Thisindicates that although the flows at the locations along these twolines were turbulent, they were also quite coherent over the twolines. It is particularly noteworthy that the maximum values ofthe cross-correlation functions for records five to seven are allassociated with zero time lag, which indicates that there is no

0 120 240 360 480 6000

2

4

CD

0 2 4 6 8 10 12 14 16

10-4

10-2

100

S DD

(1/H

z)

2.44Hz4.88Hz

0 120 240 360 480 600-4-2024

CL

Time (s)0 2 4 6 8 10 12 14 16

10-4

10-2

100

S LL (1

/Hz)

Frequency (Hz)

2.44Hz

Fig. 26. Drag and lift coefficients of the cylinder and the corresponding spectra: record five, subcritical Reynolds number range, U¼3.94 m/s, θ¼116.21, Iu¼0.022,Re¼0.59�105.

0 120 240 360 480 600-1

-0.50

0.51

a z (g)

0 2 4 6 8 10 12 14 1610-6

10-3

100

S zz (g

2 /Hz)

2.44Hz

4.88Hz

0 120 240 360 480 600-1

-0.50

0.51

a x (g)

Time (s)0 2 4 6 8 10 12 14 16

10-6

10-3

100

S xx (g

2 /Hz)

Frequency (Hz)

2.44Hz

2.18Hz 5.57Hz

Fig. 27. Acceleration time histories and the corresponding spectra: record five, subcritical Reynolds number range, U¼3.94 m/s, θ¼116.21, Iu¼0.022, Re¼0.59�105.

-5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50.6

0.8

1

Time lag (s)

Cro

ss-c

orre

latio

nR33,34 R33,2 R2,34 R35,4

Fig. 28. Cross-correlation coefficients of pressure measured along the axial direc-tion on the leeward side of the cylinder: record five, subcritical Reynolds numberrange, U¼3.94 m/s, θ¼116.21, Iu¼0.022, Re¼0.59�105.

Table 2Characteristics of wind and mean loading of example records with mean wind yawangle between 251 and 351.

Record number U (m/s) Re (�105) θ (1) Iu Mean CD Mean CL

5 3.94 0.59 116.2 0.022 1.08 0.046 8.14 1.22 64.0 0.121 0.77 0.117 13.3 1.99 120.1 0.129 0.59 �0.02

D. Zuo / J. Wind Eng. Ind. Aerodyn. 133 (2014) 65–7976

coherent fluctuating flow structure in the axial direction at thelocations of the pressure taps. As a contrast, a previous studybased on wind tunnel tests of yawed cylinders in smooth wind hasrevealed the presence of a coherent axial flow component (Chenget al., 2004). The findings from the present study suggest thatsignificant turbulence in the free-stream wind can prohibit theformation of a coherent axial flow component.

The characteristics of the cylinder response are also fundamen-tally the same for records six and seven. For this reason, only thein-plane and out-of-plane responses of the cylinder for recordseven are shown in Fig. 32 for illustration purposes. According tothis figure, the low-amplitude acceleration of the cylinder wasdominated by its first two modes in the in-plane and out-of-planedirections due to buffeting of the wind. The coupled motion in thesecond in-plane and out-of-plane directions of the cylinder issimilar to those of the cylinder response for records three and four,in which the wind was nominally perpendicular to the cylinder.

6. Conclusions

A full-scale experimental campaign was conducted to study thedynamic interaction between wind and a circular cylinder.An interpretation of the pressures measured on the surface ofthe cylinder suggested that turbulence in the free-stream windcauses the critical transition to occur at Reynolds numbers that aremuch lower than those at which the transition occurs in smoothfree stream wind. While this agrees qualitatively with the resultsfrom previous wind tunnel studies, the present study also suggeststhat this effect of the free stream turbulence has been over-estimated by a previous comprehensive study (ESDU, 1980). Usingboth the pressure measurements and the measured motions of thecylinder, the nature of the wind loading and the correspondingresponse of the cylinder was also investigated. It was revealed thatfor both normal and oblique winds, the significant cylindervibrations were due to vortex-shedding locked in with thecylinder oscillation. It was also observed that when the wind issignificantly turbulent, coherent vortex shedding from the cylin-der disappears at much lower Reynolds numbers than those atwhich coherent vortex shedding stops for circular cylinders insmooth flow. In addition, the study suggests that strong turbu-lence in the wind can prohibit the formation of a coherentfluctuating axial flow component in the wake of the cylinder,which has been indicated in previous studies to be critical for theonset of large-amplitude dry circular cylinder vibration at highreduced velocity. Since neither large-amplitude vibration nor flowstructures that could potentially induce large-amplitude vibrationsof the horizontal cylinder was observed at high reduced velocity,

0 120 240 360 480 6000

2

4

CD

0 2 4 6 8 10 12 14 1610-4

10-2

100

S DD

(1/H

z)

0 120 240 360 480 600-4-2024

CL

Time (s)0 2 4 6 8 10 12 14 16

10-3

10-2

10-1

S LL (1

/Hz)

Frequency (Hz)

Fig. 30. Drag and lift coefficients of the cylinder and the corresponding spectra: Record 7, critical Reynolds number range, U¼13.3 m/s, θ¼120.01, Iu¼0.129, Re¼1.99�105.

-5 -4.5 -4 -3.5 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50.6

0.8

1

Time lag (s)

Cro

ss-c

orre

latio

n

R33,34 R33,2 R2,34 R35,4

Fig. 31. Cross-correlation coefficients of pressure measured along the axial direc-tion in the leeward side of the cylinder: record 7, critical Reynolds number range,U¼13.3 m/s, θ¼120.01, Iu¼0.129, Re¼1.99�105.

0 120 240 360 480 6000

2

4

CD

0 2 4 6 8 10 12 14 1610-4

10-2

100

S DD

(1/H

z)

5.47Hz

0 120 240 360 480 600-4-2024

CL

Time (s)0 2 4 6 8 10 12 14 16

10-4

10-2

100

S LL (1

/Hz)

Frequency (Hz)

Fig. 29. Drag and lift coefficients of the cylinder and the corresponding spectra: Record 6, critical Reynolds number range, U¼8.14 m/s, θ¼64.01, Iu¼0.121, Re¼1.22�105.

D. Zuo / J. Wind Eng. Ind. Aerodyn. 133 (2014) 65–79 77

this study also indicates that the inclination of circular cylinders insheared boundary layer flow potentially plays an important role inthe onset of large-amplitude dry circular cylinder vibration at highreduced velocity.

Acknowledgements

This study was sponsored by the National Science Foundationof the United States through award number 0900643. Any opi-nions, findings, conclusions or recommendations expressed in thisstudy are those of the authors and do not necessarily reflect theviews of the National Science Foundation.

References

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Bendat, J.S., Piersol, A.G., 2010. Random Data. John Wiley & Sons, Hoboken, NewJersey.

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0 120 240 360 480 600-1

-0.50

0.51

a z (g)

0 2 4 6 8 10 12 14 16

10-6

10-3

100

(Sa) zz

(g2 /H

z) 2.44Hz 5.48Hz5.56Hz

0 120 240 360 480 600-1

-0.50

0.51

a x (g)

Time (s)0 2 4 6 8 10 12 14 16

10-6

10-3

100

(Sa) xx

(g2 /H

z)

Frequency (Hz)

2.17Hz 5.55Hz5.48Hz

Fig. 32. Acceleration time histories of and the corresponding spectra: record 7, critical Reynolds number range, U¼13.3 m/s, θ¼120.01, Iu¼0.129, Re¼1.99�105.

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