Usteady Characteristics of Aerodynamic Forces on Circular cylinders in the Critical ... · 2019-05-23 · 15th International Conference on Fluid Control, Measurements and Visualization

15th International Conference on Fluid Control, Measurements and Visualization

27-30 May 2019, Naples, Italy

Paper ID:203 1

Usteady Characteristics of Aerodynamic Forces on Circular cylinders in the

Critical Reynolds Number Range

Wenyong Ma1,2,*, Bocheng Huang2, Qingkuan Liu1, Deqian Zheng3

1 Innovation Center for Wind Engineering and Wind Energy Technology of Hebei Province, Hebei, 050043, China

2 School of Civil Engineering, Shijiazhuang Tiedao University, Hebei, 050043, China 3 School of Civil Engineering and Architecture, Henan University of Technology, Henan province, 450001,China

*corresponding author: [email protected]

Abstract The excitation mechanism of vibrations of circular cylinders in the critical Reynolds number range

remains unclear. It is related to the complicated aerodynamic force in the critical regimes, in which the three-

dimensional and unsteady characteristics are worthy of studying. In the present study, the wind pressure on a

circular cylinder in the entire critical Reynolds number range is measured. Aerodynamic force and wind pressure

distribution along the length of the cylinder and on circumference are discussed to reflect the three dimensional

characteristics. Meanwhile, the unsteadiness also revealed by variation of aerodynamic force and pressure in time.

Keywords: Circular cylinder, Critical Reynolds number, Wind tunnel test, Aerodynamic forces, Unsteadiness

characteristics

1 Introduction

In wind engineering, dry galloping was reported as a large amplitude vibration for a cable in cable-stay bridge

in dry condition[1]. The phenomena have been reproduced in wind tunnel tests by different research groups[2-

8], and they believe these vibrations strongly depend on the specific flow state in the critical Reynolds number

range.

The flow around a circular cylinder in the critical Reynolds number range is complicated due to the sensitivity

of the flow state to small disturbances or uncertainties[9]. In the critical range, the precritical regime (TrBL0),

one-bubble regime (TrBL1) and two-bubble regime successively occur in a narrow Reynolds number range.

Therefore, the transition of the flow states significantly influence the variation of aerodynamic forces in time

and space[10]. Moreover, the prediction of aerodynamic forces on the imperfect circular cylinder is very

difficult because the flow in the critical regime is very sensitive to even the subtle disturbances[11-13].

In the present study, the wind pressure on a circular cylinder in the critical Reynolds number range is measured

by a rigid sectional model in a wind tunnel to reveal the three-dimensional unsteady characteristics of

aerodynamic forces. The pressure distribution along the length of the cylinder and on the circumference are

discussed to show its three-dimensionalities. The variation of aerodynamic forces and stagnation point with

time are also presented to illustrate the unsteadiness of the flow state.

2 Experimental setup

Tests were carried out in a wind tunnel with a working section of 5 m (length) × 2.2 m (width)×2 m (height). The wind

velocity was up to 80 m/s in the working section. When the wind velocity is approximately 63 m/s, the turbulence intensity

was lower than 0.5%, and the difference in the wind velocity distribution over the section is less than 1%.

In the present study, the circular cylinder model was a custom-made plexiglass pipe with a length L=2 m and diameter

D=150 mm, as shown in Fig. 1 (a),. The blockage ratio was approximately 7.5%. A total of 312 pressure taps were

arranged in four lines along the length and on five rings around the circumference. As shown in Fig. 1 (b), the five rings

were termed A, B, C, D and E. Ring C was in the middle of the cylinder, and rings B and D were 300 mm and 150 mm

from ring C on both sides. Rings A and E were 270 mm and 300 mm from ring B and ring D, respectively. On each ring,

40 pressure taps were uniformly distributed, and each tap was indicated by the angular position θ, as shown in Fig. 1

(c). The four lines were at θ=0°, 90°, 180°, and 270°, respectively. Twenty-eight pressure taps were arranged to start from

28 mm from the end of the cylinder and uniformly distributed with a spacing of 72 mm.

To reduce the free end effects on the flow state, a circular end plate was used at the two ends at distances of 1910mm.



Paper ID:203 2

The aspect ratio is approximately 12.73. The diameter of the end plate was chosen as 600 mm, four times the diameter of

the cylinder, De=4D.

The approaching wind faced the pressure tap with θ=0°. The wind velocity varied from 4.55 m/s to 49.02 m/s at various

intervals, corresponding to Reynolds numbers Re=0.47×105-5.07×105 which cover the entire range of the critical

Reynolds numbers. The wind pressure was measured instantaneously by pressure sensors (ESP-64Hd, Measurement

Specialties (formerly PSI), Hampton, VA, USA), which were located inside of the cylinder to reduce the length of the

pressure tubes. In the present study, the tubes were 530mm, 780mm, 930mm, 790mm and 620mm in length for rings A,

B, C, D and E, and 930mm in length for the pressure taps along the four lines. The recorded wind pressure was corrected

by the theoretical frequency response function of each tube to eliminate the distortion induced by the pressure tube

systems. In the present study, the aerodynamic forces were estimated by integrating the wind pressures.

Fig. 1 Schematics of the wind tunnel arrangement and the model with the main parameters indicated: (a) model and

pressure tap arrangement, (b) the definition of parameters.

3 Results

3.1 Variation of aerodynamic forces with Reynolds number

To clarify the flow states, the variation of average drag and lift coefficients at the middle of the cylinder (Ring

C) with Reynolds number are shown in Fig.2 (a) and (b). The shadow in Fig.2 also shows a range of mean

value plus and minus the standard deviation, which reflects the fluctuation. As can be seen in Fig.2 (a), the

drag coefficients decrease with the increasing Reynolds number until a plateau from Re=4.0×105, which

presents the flow reattaches as both sides of the cylinder. More clearly, when flow reattachs at one side of the

cylinder (TrBL1 regime), an average non-zero lift coefficient occurs, as shown in Fig.2 (b) from Re=2.6×105-

4.0×105. The variation of average aerodynamic force coefficients with Reynolds number indicates clearly that

the flow experience sub-critical (TrSL), pre-critical (TrBL0),one-bubble (TrBL1) and two-bubble (TrBL2)

regimes. Fig.2 (a) and (b) also show the fluctuation of drag and lift coefficients reduce with increasing

Reynolds number except at the beginning of TrBL1.

Fig 2. (c) shows the variation of base pressure coefficients at leeward of Ring C (θ=180°). The increases of

base pressure coefficient with Reynolds number reflect that the wake becomes weaker at higher Reynolds

number. The motion of stagnation point varies with flow states. Average, maximum and minimum position of

stagnation point in 60 seconds is shown in Fig. 2 (d) at various Reynolds number to show the influence of flow

states on stagnation point. As expected, the average stagnation points move approximately 3° non-reattach side

in TrBL1 regime. This means that that flow keeps asymmetric from windward to leeward in TrBL1 regime.

Fig.2 (d) also reflects that stagnation points swings in larger range from approximately -6° to 6° in the subcritical regime and narrower range from around -2° to 1° in TrBL2 regime.

2.2m

2m

Le=1.91m

L=2m

1m

570mm

A B C D E

Wind tunnel Walls

End plate De=4DModel D=150mm

Pressure taps

θ

θ =0º

θ =90º

θ =180º

θ =270º

CD

CL

40 pressure taps at each ring for ring A, B, C, D and E

28 pressure taps at each line at θ =0º, 90º, 180º and 270º

(b) (a)



Paper ID:203 3

Fig. 2 Effects of Reynolds number on (a) drag coefficients, (b) lift coefficients, (c) Base pressure coefficients, and (d)

stagnation points.

3.2 Pressure distribution in space

Mean wind pressure distribution along the length of the cylinder at four lines, θ=0°(windward), 90°(downside), 180° (leeward) and 270°(upside), are shown in Fig.3. Meanwhile, the wind pressure distribution on the circumference at different rings at various Reynolds numbers are shown in Fig. 4, in which the shadow represents mean pressure coefficients plus and minus the standard deviation. In the subcritical Reynolds number, as shown in Fig.3 (a) at Re=2.01×105, pressure coefficients at four lines are

uniformly distributed along the length of the cylinder except for approximately 0.05L next to the end plates. This

implies a two-dimensional flow state in the subcritical regime. The corresponding wind pressure distribution on

circumferences at ring C is shown in Fig.4, first at first line. With the increase of the Reynolds number, the difference

of wind pressure along the length of the cylinder at both sides (θ=90° and 270°) occurs, as shown in Fig. 3 (b). The

onset of stronger negative pressure at θ=90°or 270° in certain ranges reveals that flow in these ranges may enter TrBL1 regime. An example is shown in Fig.4, second at first line. The flow reattachs at one side of the cylinder and creates a strong negative pressure on this side. With a further increase in Reynolds number, the reattachment occurs at more locations, as shown in Fig. 3 (c). Interestingly, as shown in Fig. 3 (d) and corresponding wind pressure coefficients distribution at ring A and D, the reattachments occur at different sides of the cylinder along the length of the cylinder, such as separation bubble on downside at ring A and upside at ring D. This illustrates strong three-dimensional characteristics of the flow in the critical regime. This may be induced by the difference of oncoming flow or surface condition of the model itself, but we believe it is more likely to be attributed to the unsteadiness of the flow state in the specific regime. The similar phenomena also occur at Re=3.79×105,

as shown in Fig. 3 (e) and Fig. 4 at ring C and E. Once the flow reattaches at both sides for the entire cylinder,

the wind pressure coefficients distribution is like Fig. 3 (f) along the length and Fig.4 at ring A and C. It should

be highlighted that in this regime, the flow is also three dimensional.

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.00.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

CD

CDr

CD

Dra

g c

oef

fici

ents

Re(105)

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0-1.0

-0.8

-0.6

-0.4

-0.2

0.0

0.2

0.4

0.6

0.8

1.0

Lif

t co

effi

cien

ts

Re(105)

CL

CLr

CL

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0-2.0

-1.8

-1.6

-1.4

-1.2

-1.0

-0.8

-0.6

-0.4

-0.2

Bas

e p

ress

ure

co

effi

cien

ts

Re(105)

CPB

CPBr

CPB

1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0-8

-6

-4

-2

0

2

4

6

8

0 ()

Re (105)

Average Maximum Minimum

(a) (b)

(c) (d)



Paper ID:203 4

Fig. 3 Mean wind pressure coefficient distribution along the length of the cylinder at Re= (a) 2.01×105, (b) 3.30×105,

(c) 3.38×105, (d) 3.54×105, (e) 3.79×105, and (f) 4.04×105.

-0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

Rings: EDCBA End plate

CP

x/L

Anglar position 0 90 180 270

End plate

-0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

CP

x/L

End plate Rings: A B C D E End plate


-0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

CP

x/L



End plate

-0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

CP

x/L


CP


End plate

-0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

CP

x/L



End plate

-0.5 -0.4 -0.3 -0.2 -0.1 0.0 0.1 0.2 0.3 0.4 0.5-3.5

-3.0

-2.5

-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

CP

x/L



End plate

Ring C

Re=2.01×105Ring C

Re=3.30×105

Ring A

Re=3.54×105

Ring D

Re=3.54×105

Ring C

Re=3.79×105Ring E

Re=3.79×105

Ring A

Re=4.04×105

Ring C

Re=4.04×105

(a) (b)

(c) (d)

(e) (f)



Paper ID:203 5

Fig. 4 Wind pressure coefficient distribution on circumference at different rings at various Reynonls number.

3.3 Variation of aerodynamics in time

Fig. 5 shows the time history of lift coefficient (Fig.5 (a) and (c)) at ring C at Re=2.71×105 and the

corresponding Morlet wavelets (Fig.5 (b)) and instantanouse wind pressure coefficients distribution (Fig. 5

(d)).

Fig. 5 Variation of aerodynamic at ring C at Re=2.71×105 in time for (a) lift coefficient in 60 seconds, (b) Complex

Morlet wavelets of lift coefficient, (c) lift coefficients in 10 seconds and (d) instantanous pressure coefficients

distribution at nine time points.

In Fig. 5 (a), the lift coefficients sudden change with them. These jumps reflect a quick change of the flow

states. In this case, the non-zero mean lift coefficients from 0s to 12.6s present at reattachment at the upside of

(a)

(b)

(c)

(d)



Paper ID:203 6

the cylinder. The return of lift coefficients to zero implies the disattachement. These sudden change of flow

state also can be revealed in Fig. 5 (b) by Morler wavelets. As can be seen, dominate reduced frequency induced

by vortex shedding becomes weak when the flow reattaches because the reattachment stops the communication

of separated flow at both sides of the cylinder in the wake. Fig. 5 (c) and (d) show the details of the change in

lift coefficient in 19.6s to 20.6s. The wind pressure changes on the whole circumference when the flow is

controlled by vortex shedding, as shown in t1, t2, and t3. Once the flow reattaches the pressure fluctuates at

the separation region instead of the whole circumference.

3.3 Swing of the stagnation points in time

Similar to a variation of life coefficients, the stagnation points also reflect the unsteadiness of flow states, as

shown in Fig. (6). The strong fluctuation of lift coefficient reflects large range swing of stagnation point.

Meanwhile, mean lift coefficients correspond to the average move of stagnation point.

Fig. 6 Variation of stagnation points at ring C at Re= (a) 1.45×105, (b) 2.71×105, (c) 2.71×105, (d) 3.54×105, (e)

3.71×105, and (f) 4.04×105.

4 Conclusions

The aerodynamic forces on a circular cylinder in the critical Reynolds number range are three dimensional in

space and unsteady in time. Flow reattaches firstly in a certain range of the cylinder on one side instead of at

the entire length of the cylinder, which means TrBL1 regime can only occur in a certain range. Moreover, the

flow can also attach on the other side of the cylinder at another range of the cylinder. Once the separation

bubble is formed, it will extend along the cylinder with increasing Reynolds number. Flow finally reattaches

at both sides of the cylinder for different location of the cylinder at different Reynolds numbers in the TrBL2

regime. The aerodynamic forces jump with time when the flow state changes from TrBL0 to TrBL1 or TrBL1

10 11 12 13 14 15-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

CL

Time(s)

CL

At ring C, Re=1.45105

-10

-8

-6

-4

-2

0

2

4

6

8

10

()

10 11 12 13 14 15-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

CL

Time(s)

CL

-10

-8

-6

-4

-2

0

2

4

6

8

10

()


18 19 20 21 22 23-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

CL

Time(s)

CL

-10

-8

-6

-4

-2

0

2

4

6

8

10

()


45 46 47 48 49 50-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

CL

Time(s)

CL

-10

-8

-6

-4

-2

0

2

4

6

8

10

()


10 11 12 13 14 15-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

CL

Time(s)

CL

-10

-8

-6

-4

-2

0

2

4

6

8

10

()


10 11 12 13 14 15-2.0

-1.5

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

CL

Time(s)

CL

-10

-8

-6

-4

-2

0

2

4

6

8

10


()



Paper ID:203 7

to TrBL2 which correspond to the formation of two separation bubbles. These jumps reflect strong

unsteadiness in aerodynamic forces because the reattachments are intermittent during the formation of a stable

separation bubble.

Acknowledgments

The authors gratefully acknowledge the support of the National Natural Science Foundation of China (Grant

No. 51778381 and 51408196), Natural Science Foundation of Hebei Province (Grant No. E2017210107 and

ZD2018063) and Collaborative Innovation Centre of Preventing Disasters and Reducing Damages for Large

Infrastructures in Hebei Province.

References

[1] Matsumoto, M., T. Yagi, H. Hatsuda, T. Shima, M. Tanaka,H. Naito (2010), Dry galloping characteristics

and its mechanism of inclined/yawed cables. Journal of Wind Engineering and Industrial Aerodynamics.

vol. 98 pp 317-327.

[2] Ma, W., Q. Liu,M. Matsumoto (2019), Excitation of the large-amplitude vibrations of a circular cylinder

under normal wind conditions in the critical Reynolds number range. Journal of fluids and structures. vol.

84 pp 318-328.

[3] Nikitas, N.,J.H.G. Macdonald (2015), Aerodynamic Forcing Characteristics of Dry Cable Galloping at

Critical Reynolds Number. European Journal of Mechanics - B/Fluids. vol. 49 pp 243-249.

[4] Nikitas, N., J.H.G. Macdonald, J.B. Jakobsen,T.L. Andersen (2012), Critical Reynolds number and

galloping instabilities: experiments on circular cylinders. Exp Fluids. vol. 52 pp 1295-1306.

[5] Jakobsen, J.B., T.L. Andersen, J.H.G. Macdonald, N. Nikitas, G.L. Larose, M.G. Savage,B.R. McAuliffe

(2012), Wind-induced response and excitation characteristics of an inclined cable model in the critical

Reynolds number range. Journal of Wind Engineering and Industrial Aerodynamics. vol. 110 pp 100-112.

[6] Zuo, D.,N.P. Jones (2009), Wind tunnel testing of yawed and inclined circular cylinders in the context of

field observations of stay-cable vibrations. Journal of Wind Engineering and Industrial Aerodynamics.

vol. 97 pp 219-227.

[7] Cheng, S., G.L. Larose, M.G. Savage, H. Tanaka,P.A. Irwin (2008), Experimental study on the wind-

induced vibration of a dry inclined cable Part I: Phenomena. Journal of Wind Engineering and Industrial

Aerodynamics. vol. 96 pp 2231-2253.

[8] Cheng, S., P.A. Irwin,H. Tanaka (2008), Experimental study on the wind-induced vibration of a dry

inclined cable Part II: Proposed mechanisms. Journal of Wind Engineering and Industrial Aerodynamics.

vol. 96 pp 2254-2272.

[9] Ma, W., Q. Liu, J.H.G. Macdonald, X. Yan,Y. Zheng (2019), The effect of surface roughness on

aerodynamic forces and vibrations for a circular cylinder in the critical Reynolds number range. Journal

of Wind Engineering & Industrial Aerodynamics. vol. 187 pp 61-72.

[10] Zdravkovich, M.M. (1997), Flow Around Circular Cylinders Vol 1: Fundamentals[M]. Vol. I., New York:

Oxford University Press.

[11] Bearman, P.W. (1969), On vortex shedding from a circular cylinder in the critical Reynolds number

region. Journal of fluid Mechanics. vol. 37 pp 577-587.

[12] Matteoni, G.,C.T. Georgakis (2012), Effects of bridge cable surface roughness and cross-sectional

distortion on aerodynamic force coefficients. Journal of Wind Engineering and Industrial Aerodynamics.

vol. 104–106 pp 176-187.

[13] Matteoni, G.,C.T. Georgakis (2015), Effects of surface roughness and cross-sectional distortion on the

wind-induced response of bridge cables in dry conditions. Journal of Wind Engineering and Industrial

Aerodynamics. vol. 136 pp 89-100.

Documents

Usteady Characteristics of Aerodynamic Forces on Circular cylinders in the Critical ... · 2019-05-23 · 15th International Conference on Fluid Control, Measurements and Visualization