1

Proceedings of the 3rd

International Deepwater Offshore Specialty Symposium

DOSS 2013

July 26-28, 2013, Harbin, China

On experimental method of VIV scaled test of circle cylinders

based on Re similarity

Zhou Yang1 and Huang Weiping

2

1Shandong Provincial Key Laboratory of Ocean Engineering, Ocean University of China, Qingdao, China, 266100,

E-mail:edit502@126.com 2Shandong Provincial Key Laboratory of Ocean Engineering, Ocean University of China, Qingdao China,266100,

E-mail:wphuang@ouc.edu.cn

Abstract

An experimental method, based on Reynolds number

similitude, of the vortex-induced vibration (VIV) of circle

cylinder is proposed to achieve VIV similarity between

prototype and tested model. The VIV response of a circle

cylinder is closely related to Reynolds number because the

mode of vortex shedding is highly depend on Re. However,

the scaled model test of circle cylinder’s VIV is nowadays

designed based on Froude number similarity but Reynolds

number not similar under the same fluid for both model

and prototype. Therefore, the VIV response of tested model

is not similar to that of the prototype modeled by the model

because they have different vortex shedding modes. It

means that the test results can not be used to predict the

VIV response of the prototype according to the scaling law

based on Froude number similarity. In this paper, four

experiments with different schemes have been simulated

using CFD to validate the method. The results show that

the similarity between prototype and model is satisfied by

the Reynolds number similarity and both Froude number

and Reynolds number similarity. But the similarity

between prototype and model is not satisfied by Froude

number similarity.

Keywords: voertex-induced vibration(VIV); Cylinder;

CFD; Reynolds number similarity; Froude number

similarity

1 Introduction

The phenomenon of vortex induced vibration (VIV)

is well-known in the engineering field.. Objects immersed

in fluid will oscillate under certain velocity because of the

alternate pressure generated by the alternate wake vortex.

At the current, the investigation of vortex induced

vibration on marine risers is prominent. Many illustrious

scholars do the research on vortex induced vibration of

marine risers and subsea pipelines in high slenderness ratio

through different methods[1-2]. Furthermore, the relevant

investigation focusing on engineering application about

forecasting for global vortex induced vibration of ocean

platforms and the mechanism research on the complex

turbulence[3-4], the generation of vortex and the vortex

shedding around non-streamline cylinders are also

studied[5-6].

Three main analysis methods are applied in vortex

induced vibration including model experiment, numerical

simulation and theoretical analysis. In the past, model

experiment and numerical simulation about vortex induced

vibration are designed based on Froude number similarity

to realise the scale model test[7-8]. Nevertheless vortex

shedding is closely related to Reynolds number, and the

dynamic characteristics forecasted based on Froude

number similarity is somewhat deficient and unscientific.

In the research of vortex induced vibration, Reynolds

number similarity has its own significance. However, due

to the limit of experimental condition, the viscosity of fluid

is hard to change to realise the Reynlods number similarity.

Ansys-CFX is a simulation software of computational fluid

dynamics (CFD), which can regulate the viscosity unlike

many model experiments. In this paper, the vortex induced

vibration of a cylinder is discussed with the help of

Ansys-CFX. Four experimental models, the prototype

model, the Froude number similarity model, the both

Froude number and Reynolds number similarity model and

the Reynolds number similarity model, have been

simulated to investigate the lift coefficient, the drag

coefficient and the period in order to figure out the

feasibility of similarity theory in VIV.

2 Introduction of model test

2.1 Similarity Theory

Due to the large scale of offshore structures, when

designing model experiments and numerical simulation,

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scale models are usually used in order to save material and

improve calculation efficiency. Similarity theory will be

applied in the scale models so that the models can reflect

the property of the prototype correctly.

When gravity is dominated in the research, the scale

model will be designed based on Froude number similarity

which means that the Froude number of the scale model

should be the same as that of the prototype. The Froude

number is given by

gl

V 2

Fr (1)

Here V is the velocity, g is the gravity and l is the

length. The corresponding scale ratio is obtained

1g

2

l

V

(2)

Here V is the scale ratio of velocity, g is the scale

ratio of gravity and l is the scale ratio of length. In this

paper g is a fixed value 1, and so the equation above is

turned to be

12

l

V

or 2

1

lV (3)

The corresponding scale ratio of time is obtained

2

1

t l

V

l

(4)

In this scale model, the scale ratio of the density is 1

the same as the the sacle ratio of the viscosity .

When viscosity is dominated in the research, the scale

model will be designed based on Reynolds number

similarity which means that the Reynolds number of the

scale model should be the same as that of the prototype.

The Reynolds number is given by

VlRe (5)

Here is the kinematic coefficient of viscosity. The

corresponding scale ratio is obtained

1

lV (6)

In this scale model, is 1, and so the equation above is

turned to be

1lV or

l

V

1

(7)

The corresponding scale ratio of time is obtained

2

t l

V

l

(8)

In this condition, the ratio of the density is 1.

The two similarity models above can be realized by

numerical simulation in Ansys-CFX, and also can be

realized by model experiments. However, when gravity

and viscosity are both important in the research, the

similarity between prototype and model should be satisfied

by the both Froude number and Reynolds number

similarity. At this moment, the kinematic coefficient of

viscosity have to be changed in order to realize the

Reynolds number similarity, and this can be carried out

with the help of numerical simulation.

When the Froude number of the model should be the

same as that of the prototype, the equation is obtained

12

l

V

(9)

When the Reynolds number of the model should be

the same as that of the prototype, the equation is obtained

1

lV (10)

When the both Froude number and Reynolds number

of the model should be the same as that of the prototype,

the is obtained

2

3

l (11)

The corresponding scale ratio of time is obtained

2

1

t l

V

l

(12)

In this scale model , the scale ratio of the density is

obtained

2

3

l (13)

It can be concluded from the three similarity models

above that nomatter which similarity method is used all

other scale ratios can be obtained from the scale ratio of

length.

2.2 Numerical Models

The prototype cylinder for numerical simulation has a

diameter 0.3m while the size of the fluid domain is 6m

long, 3m wide and 0.6m high. This test is carried out in the

water domain at a current speed 0.02m/s, and the

corresponding Reynolds number is 6000. The length

direction of the cylinder is in the same direction of the

hight direction of the fluid domain, and the center of the

cylinder is 1.5m far from the inlet which is shown in Fig. 1.

The scale ratios of length of the three numerical models are

all 10. Table 1 shows the design parameters in more detail.

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Figure 1: Model of the fluid domain

3 Numerical simulation method

3.1 Theoretical foundation

In this paper, the cylinder is treated as a rigid body to

carry out the global analysis. The lift force, drag force and

period of the cylinder will be discussed. In fact, nomatter

which Similarity method is used, the force coefficient ratio

is always 1. So the comparation between force is replaced

by the comparation between dimensionless force

coefficients. The lift coefficient LC , drag coefficient

DC

can be expressed as following[9]:

DHU

F2C

2

LL

DHU

F2C

2

DD

(14)

Here LF is the total lift force of the cylinder, DF is the

total drag force of the cylinder, is the density of the

fluid, U is the speed of the fluid, D is the diameter of

the cylinder, H is the length of the cylinder.

Via the comparation between force coefficients and

periods, the feasibility of Froude number similarity and

Reynolds number similarity applied in VIV of cylinders

will be discussed.

3.2 Modeling And Mesh

With the help of Ansys-workbench, the prototype, the

Froude number similarity model, the both Froude number

and Reynolds number similarity model and the Reynolds

number similarity model is built respectively. The software

ICEM is used to mesh the fluid domain. In order to avoid

the computational deviation caused by the inconsistent

mesh, the four models are meshed the same. So the mesh

spacing of each model is in accord with its own similarity

method, and all models have the same mesh number as is

shown in Fig. 2.

Figure 2: Mesh of the fluid domain

Table 1: Parameters of the fluid domain

With the help of shear stress transport (SST) turbulence

model in Ansys-CFX, the time-history curves of lift force

and drag force of the cylinders in the fluid domain are

acquired where the computation time, time step and current

speed of the prototype is 3000s, 2s, and 0.02m/s.

4 Resuclts

4.1 Features of vortex shedding

Numerical simulation experiments on Vortex

shedding of the four models were carried out via CFX, and

the data was output every 10 steps. Comparing the vortex

shedding with each other when it is stable. According to

the similarity theory, if the model meets with the selected

similarity theory, its vortex shedding will be according

with the prototype’s.

Fig. 3 shows the vortex shedding condition of each

model. It can be seen that the both Froude number and

Reynolds number similarity model, the Reynolds number

similarity model and the prototype are in accordance on

vortex shedding, and the number of their wake vortexes

at one side is all 5. However, the number of the wake

vortexes at one side of the Froude number similarity model

is 4. It is conceivable that when the model is designed

Wide Length Hight Diameter Density Viscosity Velocity Re

Prototype 3m 6m 0.6m 0.3m 1000 kg/m3 1e-6 m2/s 0.02m/s 6000

Froude number

similarity model 0.3m 0.6m 0.06m 0.03m 1000 kg/m3 1e-6 m2/s 0.00632m/s 189.6

Both Froude number

and Reynolds

number similarity

model

0.3m 0.6m 0.06m 0.03m 31.6 kg/m3 3.16e-8 m2/s 0.00632m/s 6000

Reynolds number

similarity model 0.3m 0.6m 0.06m 0.03m 1000 kg/m3 1e-6 m2/s 0.2m/s 6000

4

based on Froude number similarity, its spacing of the wake

vortexes is not in accord with its similarity ratio. This can

reflect that the Froude number similarity in VIV may not

be suitable, and on the contrary, the Reynolds number

similarity in VIV should be paid attention to.

4.2 Flow force of different models

Fig. 4 shows the lift coefficient LC and drag

coefficient DC of each model. Fig. 5 shows the spectrum

of lift coefficient of each model in the form of period.

Some fundamental characteristics can be summarized from

Fig. 4 [10]:(1) The period of the lift coefficient is double

that of the dragcoefficient; (2) The average of the lift

coefficient is 0 which is accordding with the symetry of

vortex shedding.

4.3 Comparation of the flow force

(1) Table 2 shows the amplitude of lift coefficient and

the average of the drag coefficient. It can be concluded that

the both Froude number and Reynolds number similarity

model, the Reynolds number similarity model and the

prototype are in accordance on the lift coefficients and drag

coefficients. The amplitudes of the lift coefficients of the

three models are all 0.9 while the corresponding drag

coefficients are all 0.9 too. Different from the previous

three models obviously, the amplitude of the lift coefficient

of the Froude number similarity model is 0.6 while the

corresponding drag coefficient is 1.4.

Figure 3: Vortex shedding of different models

Prototype

-2

-1

0

1

2

800 1000 1200 1400t/s

Coefficient CD CL

Fr Similarity

-1

0

1

2

253 316 380 443t/s

Coefficient CD CL

Re and Fr Similarity

-2

-1

0

1

2

253 316 380 443t/s

Coefficient CD CL

Re Similarity

-2

-1

0

1

2

8 10 12 14t/s

Coefficient CD CL

Figure 4: Time history of

DC and LC

(2) Table 2 shows the period of lift coefficient, the

theoretical period ratio, and the experimental period ratio.

It can be concluded that the both Froude number and

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Reynolds number similarity model, the Reynolds number

similarity model and the prototype are in accordance. The

similarity of the periods among the three models is

satisfied by their own similarity theory: When it comes to

the Reynolds number similarity model, its period of lift

coefficient is 0.549s, 0.0102 of the prototype’s; When it

comes to the both Froude number and Reynolds number

similarity model, its period of lift coefficient is 17.1s,

0.315 of the prototype’s; However , when it comes to the

Froude number similarity model, its period of lift

coefficient is 22.3s, 0.414 of the prototype’s, not according

with the corresponding similarity ratio 0.316.

Figure 5: Spectrum of lift coefficient

Table 2: Results of different models

(3) It can be concluded from the camparation of the

periods and force that when it comes to investigate VIV of

a cylinder, models based on Reynolds number similarity

can reflect the dynamic characteristic of the prototype

objectively. When both Froud number and Reynolds

number similarity are applied in the scale model, the

dynamic characteristic of the prototype can be also

reflected objectively because of the Reynolds number

similarity. On the contrary, when only Froude number

similarity is used in the scale model, the dynamic

characteristic of the prototype can not be reflected correctly.

5 Conclusion

In this paper, similarity experiments of VIV of

cylinders were carried out through Ansys-CFX. Lift

coefficients, drag coefficients and periods of four

similar models were discussed. A conclusion can be drew

that:

(1) Reynolds number is a very important parameter

when studying VIV of a cylinder. It determines the mode

Amplitude of LC Average of DC Period [s]

The theoretical

period ratio, t

The experimental

period ratio '

t

Prototype 0.9 0.9 53.9 1 1

Froude number

similarity model 0.6 1.4 22.3 0.316 0.414

Both Froude number

and Reynolds

number similarity

model

0.9 0.9 17.0 0.316 0.315

Reynolds number

similarity model 0.9 0.9 0.549 0.01 0.0102

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of vortex shedding, the lift coefficient, the drag coefficient

and the period.

(2) The application of Froude number similarity in

VIV of cylinders may not be suitable. The characteristics

between the scale model established by Froude number

similarity and the prototype are not accordant.

(3) At the current many scale experiments about VIV

carried out in water channels are based on Froude number

similarity, and this should be cautious. The VIV of a

cylinder in the current is different from the condition of a

cylinder in the wave, and scale models designed for this

based on Froude number similarity are defective. In the

research of VIV scale models, it is reasonable that the

Reynolds number similarity should be considered first, not

Froude number similarity.

(4) In order to do the theoretical research of VIV of

cylinders, the fluid structure interaction is not considered

in this paper. In the further research, the fluid structure

interaction will be discussed, and physical models will also

be compared with.

Acknowledgements

This study is supported financially by the Natural

Science Foundation of China (NSFC) (No.

51179179,51079136,51239008). The authors would like to

express profound thanks for them.

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