VIV of Flexible Riser Conveying Internal Fluid Subjected to Uniform Current

Min Li, Di Deng, Decheng Wan*

Computational Marine Hydrodynamics Lab (CMHL), State Key Laboratory of Ocean Engineering,

School of Naval Architecture, Ocean and Civil Engineering, Shanghai Jiao Tong University, Shanghai, China *Corresponding author

ABSTRACT

Vortex-induced vibration (VIV) of a riser in consideration of both

internal and external flows is numerically studied based on the in-house

CFD solver viv-FOAM-SJTU. The main objective of the study is to

investigate effects of the internal flow on VIV responses of the riser,

when the velocity ratio of internal flow against external current varies.

The results from dynamic analysis indicate that the internal flow does

play a greatly important part in determining the typical VIV

characteristics of the riser including vibration amplitude, vibration

frequency and the dominant mode in both CF and IL directions. In

addition, multi-modal vibration and mode transition phenomenon may

occur when the internal flow velocity is relatively high.

KEY WORDS: Vortex-induced vibration; internal flow; viv-FOAM-

SJTU; velocity ratio.

INTRODUCTION

The flexible riser is an important part of the structure of deep-sea oil

exploitation system. When a circular cylinder is exposed to a flowing

fluid, it is easy to excite the vortex-induced vibration (VIV). When the

vortex shedding frequency is close to the natural frequency of the riser,

the phenomenon of "lock-in" (Yang and Li, 2009) will occur. Under

this circumstance, the vibration of the riser is significantly amplified

and the vortex shedding frequency becomes very close to the vibration

frequency, which may cause structural fatigue damage of the riser.

Therefore, it is of great significance to accurately predict the VIV

response of the marine risers for the practical design of deep-sea

structures.

Since the past decades, researchers have extensively studied the vortex-

induced vibration of flexible risers. Systematic experimental studies

were conducted, such as Chaplin (2005), Trim (2004) and Huera-

Huarte (2009). These experimental data provided reliable references for

later studies. In addition, massive numerical studies on VIV problems

of both rigid and flexible cylinders can be found such as Yamamoto et

al. (2004), Kaja et al. (2016) and Willden et al. (2001).

In practical engineering, the flexible riser works in the complex

environment, where external environment loads such as wind, wave

and current interact with the structure. Meanwhile, marine risers are

usually utilized for oil gas transportation. Though there exist massive

works carried out for VIV of the riser subjected to external current, the

VIV dynamic behavior of the flexible riser with internal flow has rarely

been studied relatively. When the internal fluid travels along the curved

pipe, it will generate Centrifugal acceleration and Coriolis acceleration,

so that the fluid dynamic pressure will periodically affect the dynamic

response of the riser and excite the additional vibration. It has been

proved that complicated phenomenon can emerge due to both internal

and external flows (Modarres and Paidoussis, 2013). Housner (1952)

concluded that the fluid inside the riser could cause the reduction of

natural frequency of the riser. The results indicate that when the

internal flow velocity increases to a certain critical velocity, the

dynamic dissipation and instability will occur in the riser. Paidoussis et

al. (1974) studied the dynamic characteristics of vertical pipes

transporting fluid through physical experiments as well as mathematical

models, and then analyzed the influence of Coriolis force and

Centrifugal force on the whole vibration system.

Empirical methods such as Van Der Pol wake oscillator model have

been used to calculate VIV of the riser with internal flow. Duan et al.

(2018) investigated VIV of a riser numerically considering both

internal and external flows based on the semi-empirical method

proposed by Thorsen et al. (2014). Typical VIV characteristics such as

the dominate mode and frequency in both IL and CF directions are

analyzed, as well as the Root Mean Square (RMS) of the amplitudes,

standing and traveling waves for the IL and CF responses. By using a

CAE technology which combines structural software with the CFD

technology, Chen et al. (2012) performed the numerical study about

VIV of a flexible riser model in consideration of internal flow

progressing inside. According to the result from dynamic analysis, it

has been found that the existence of upward-progressing internal flow

plays an important part in determining the dynamic behaviors of VIV.

Dai et al. (2013) focused on the VIV dynamic response of a hinged–

hinged pipe with internal fluid velocities ranging from the subcritical to

the supercritical regions.

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Proceedings of the Thirtieth (2020) International Ocean and Polar Engineering ConferenceShanghai, China, October 11-16, 2020Copyright © 2020 by the International Society of Offshore and Polar Engineers (ISOPE)ISBN 978-1-880653-84-5; ISSN 1098-6189

www.isope.org

In this paper, in order to investigate the dynamic response of the

flexible riser with internal flow, a series of numerical simulations are

conducted considering both internal and external flow with various

velocity combinations based on the in-house fluid-structure coupling

solver viv-FOAM-SJTU, and the reliability of the solver has been

effectively verified (Duan and Fu, 2016). In the following section, the

numerical method is introduced firstly. Then the structural modal is set

up based on the classical model test and numerically verified by

comparing with the experimental results in section 3. In section 4, the

numerical results of VIV response with different internal velocities of

the riser is analyzed and discussed. Finally, conclusions are given in

section 5.

NUMERICAL METHOD

Hydrodynamic governing equations

In this paper, the fluid is supposed to be incompressible. The governing

equations of the fluid domain are the Reynolds-averaged Navier-Stokes

(RANS) equations. In cartesian coordinate system, the governing

equations are described as follows:

0i

i

u

x

(1)

2i i j ij j i

j i j

pu u u S u u

t x x x

(2)

where 1

2

jiij

j i

uuS

x x

is the time-averaged rate of strain tensor,

ij= j iu u is regarded as the Reynolds stress resulted from the

fluctuating velocity field, representing the turbulence effect. For the

sake of turbulence closure, the SST k-ω turbulence model is used to

compute the Reynolds stresses in this paper.

Structural governing equations

The riser is regarded as a Euler-Bernoulli beam pinned at both ends.

The dynamical behavior of the riser caused by both external and

internal flows is taken into account. According to the design standards

of ocean risers and relevant studies (DNV, 2004), the effect of internal

flow including Centrifugal and Coriolis forces on the dynamic of the

riser is reflected in the following dynamic equation of the structure:

4 2 2

4 2

, , , , ,2 +m ) ,e i s i x

x z t x z t x z t x z t x z tEI T z mV m c f z t

z z z z t t t

（ (3)

4 2 2

4 2

, , y , , ,2 +m ) ,e i s i y

y z t y z t z t y z t y z tEI T z mV m c f z t

z z z z t t t

（ (4)

where L is the length of the riser, sm is the structural mass per unit

length of the riser, im is the internal fluid mass inside per unit length of

the riser, c is structural damping coefficient, eT z is the effective

tension of the riser. The axial tension of the riser varies along the riser

because of the influence of gravity, regardless of the variation of

tension with time. Referring to the analysis of internal flow by the

Norwegian design standard DNV-OS-F201 (2004), the effective

tension of the riser is influenced by both internal flow velocity and

internal fluid mass. The equations are expressed as follows:

t sT z T L z (5)

2

0 0e i i i iT z T z PA P A AV (6)

where T z is the axial tension, tT is the invariable applied top tension,

s is the weight per unit length of the riser submerged in water in

consideration of the effect of buoyancy, iP and 0P are the internal and

external pressures of the riser respectively, iA and 0A are the internal

and external cross-sectional area of the riser, i is the density of the

internal fluid, V is the internal flow velocity.

Based on the Finite Element Method (FEM), the differential equations

of motions in Eqs.3~4 for the riser can be expressed as follows:

xx x x F M C K (7)

yy y y F M C K (8)

where M is the mass matrix, C is the damping matrix, K is the

stiffness matrix, xF and yF represent the hydrodynamic forces

acting on the structure in the in-line and cross-flow direction

respectively. Moreover, the Newmark-beta method (Clough and

Penzien, 2001) is utilized to solve the structural dynamics equation.

Fluid-structure interaction

Because of the large scale of the flexible riser in deep water, the three-

dimensional numerical simulation will consume a huge amount of

computational resources. Therefore, the strip method which is widely

used to simplify the flow field is adopted to simulate the VIV dynamics

of the flexible riser, and the coupling iterative program developed by

our group can realize the coupling solution of structural dynamics and

fluid dynamics. The main idea of this method is to calculate the

hydrodynamic forces at each strip, and then interpolate the forces to

corresponding elements of the structural modal. Fig. 1 shows the

schematic diagram of the coupling process of the strip method.

Fig. 1 The schematic diagram of the strip method

NUMERICAL MODEL VALIDATION

Before applying the modified solver to investigate the dynamic

response of the riser with internal flow, two series of numerical

simulations are carried out to verify its effectiveness of the solution

method in this section.

Firstly, the internal flow is not considered. The experiment carried out

by Lehn (2003) is selected. The test was carried out in MARINTEK,

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Norway. The riser model is placed vertically in the pool and subjected

to the incoming flow, as shown in Fig. 2. The riser is 0.02m in diameter

and 9.63m long, the aspect ratio of which L/D is 481.5. Other key

characteristics of the riser modal are presented in Table 1. Based on the

model, Lehn conducted a series of experiments under uniform and

shear flows.

Fig. 2 Sketch of test rig (Lehn, 2003)

Table 1. Main parameters of the model riser

Parameter Symbol Value

Diameter D 0.02 m

Length L 9.63 m

Aspect ratio L/D 135.4

Top tension Tt 817 N

Bending stiffness EI 135.4 N m2

Mass ratio 2.23

1th eigenfrequency fn1 1.79 Hz

2th eigenfrequency fn2 3.67 Hz

In the validation condition, the riser is subjected to the external uniform

flow U=0.2m/s. In this simulation, 20 strips are set equidistantly along

the span of the cylinder, and the computational domain is set to be -20D

≤x≤40D, -20D ≤y≤20D. The distribution of strips along the span of the

riser is shown in Fig. 3. The boundary conditions and mesh division of

all strips are consistent. Fig. 4 shows the geometry domain and entire

mesh of each strip. It can be found that grids are gradually becoming

sparse from the structure to the outer region.

Fig. 3 Layout of the computational model

Fig. 4 Entire mesh on each strip

Because of the great significance of the grid quality, three different

simulations are carried out by varying strip numbers and mesh density.

Table 2 presents the information of the three meshes and dimensionless

Root Mean Square (RMS) values of the IL and CF displacement

respectively. The present results are compared with the experimental

data and numerical results of Wang (2016) and Wu (2019). It can be

found that the RMS values exported from the three meshes obtain

relatively good agreement with the experimental results. The calculated

result of Mesh 1 is slightly lower than the experimental value while the

RMS values with Mesh 2 and Mesh 3 are extremely close to the

experimental data in the CF direction. Meanwhile, the results all agree

well in the IL direction. The error of RMS values among three

simulations is acceptable. Fig. 5 shows the RMS of vibration

displacement along the span of the whole riser in CF and IL directions.

It can be found that the dominant vibration modes are first order and

second order in the CF and IL direction respectively. The vibration

trajectories along the cylinder calculated by Mesh 3 are shown in Fig.

6(c) and (d). The corresponding experimental results are also given in

Fig. 6 (a) and (b). It can be observed apparently that the vibration

shapes are in good agreement with the experimental results. Slight

disagreement (in magnitude and position) is probably related to some

simplification methods adopted in the process of the convergence

calculation and differences in the selection of sampling time.

Table 2. the details of three-meshes and simulation results

Case Strip

number

Number

of Cells

max

xrmsA / D max

yrmsA / D

Experiment - - 0.103 0.401

Wang (2016) - - 0.125 0.395

Wu (2019) 20 811000 0.114 0.404

Mesh 1 10 366720 0.102 0.368

Mesh 2 20 733440 0.110 0.398

Mesh 3 20 1026000 0.123 0.410

(a) (b)

Fig. 5 Comparation of RMS of the vibration displacement along the

cylinder span with three meshes: (a) CF direction and (b) IL direction

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(a) (b)

(c) (d)

Fig. 6 The comparison of the vibration trajectories along the cylinder:

(a) the CF direction (Lehn, 2003) (b) the IL direction (Lehn, 2003) (c)

the CF direction (Mesh 3) (d) IL direction (Mesh 3)

Moreover, a series of numerical simulations have been carried out in

consideration of internal flow, the results of which are compared with

the empirical results by Li (2010). The numerical simulation model

follows the experiment by Chaplin et al.(2005a) in which the riser is

subjected to a stepped flow. Fig. 7 shows the comparison between the

empirical result of vibration displacement concerning three different

internal flow velocities in the CF direction and the present

corresponding numerical results, shown in Fig.7 (a) and (b) respectively.

Although there exists a certain error in the vibration amplitude, which

is due to the considerable difference in two methods. It is known that

CFD method is more accurate, especially at the nodes along the span of

riser. And the trend of the vibration response affected by internal flow

calculated by the CFD method agrees well with the empirical results.

Therefore, the effectiveness of the method is verified.

(a) (b)

Fig. 7 The comparison of the RSM displacement with internal flow

velocities in the CF direction: (a) empirical result (Li, 2010) (b)

numerical result

RESULT AND DISSCUSION

Set up of simulation conditions

Aiming at investigating effects of internal flow on the dynamic

response of the riser under external current, the VIV dynamics with

different internal flow velocities V are investigated based on the above

test model by Lehn in this section. Ten simulation cases of various

combination of internal flow velocities (V=0 m/s, 1 m/s, 2 m/s, 5 m/s,

10 m/s) and external flow velocities (U=0.2 m/s, 0.36 m/s) are

performed respectively, as shown in Table 3. Here, the expression V =0

m/s means the water inside the riser being in still state.

According to the "lock-in" region of the first-order vibration mode and

the second-order vibration mode of the riser model, the above two

corresponding external flow velocities are chosen. It is generally

believed that 0 9 1 4s nf . . f is the " lock-in " resonance region

(Carberry and Sheridan, 2001).

ts

S Uf

D (9)

where sf is the vortex shedding frequency, tS is the Strouhal number.

Table 3. Set up of simulation conditions

Case External flow velocity Internal flow velocity

1 0.2 m/s 0 m/s

2 0.2 m/s 1 m/s

3 0.2 m/s 2 m/s

4 0.2 m/s 5 m/s

5 0.2 m/s 10 m/s

6 0.36 m/s 0 m/s

7 0.36 m/s 1 m/s

8 0.36 m/s 2 m/s

9 0.36 m/s 5 m/s

10 0.36 m/s 10 m/s

Dynamic analysis of flexible riser

Fig. 8 shows the dimensionless RMS value of the IL and CF

displacement concerning different velocities of internal flow (V) under

the external flow velocity U=0.2 m/s. The results show that when V=0

m/s, the vibration amplitude of the riser in both directions is close to

that of the riser without internal flow by comparison of the results in

the preceding section. The modal power spectral densities of the riser

subjected to the external flow U=0.2 m/s in the CF and IL directions are

presented in Fig. 9 and Fig. 10, respectively. The VIV dynamic

response of the riser influenced by the internal flow including vibration

displacement, vibration frequency and dominant mode will be analyzed

as follows:

As shown in Fig. 8, with lower increasing internal velocity (case 2 and

3), it can be found that the vibration amplitude of the riser decreases

slightly. And in cases 1~3, the riser vibrates at a single frequency, and

the main vibration frequency is relatively close in the CF direction as

shown in Fig. 9 (a), (b) and (c). The coverage range of the dominant

frequency in case 2 and 3 is slightly wider than that in case 1,

indicating that the vortex shedding frequency in case 1 is closer to the

first mode "lock-in" frequency, so that the vibration energy of the VIV

processes is highly concentrated, regarding as “narrow-band”. It can be

known that it is in the very range of locking vibration region and "lock-

in" phenomenon occurs. When the internal flow velocity increases, the

reduction of the natural frequency of the riser causes that the whole

riser gradually leaves the first order "lock-in" region. That is why the

vibration amplitude of the riser decreases. However, the vibration mode

remains the same and the vibration intensity is comparative in case 1~3

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as shown in subplot (a)~ (c) of Fig. 9 and Fig. 10. With the increase of

internal flow velocity (case 4 and 5), it is apparent that higher vibration

mode dominates the whole riser system as shown in Fig. 8. Because

when the internal flow velocity is high, the natural vibration frequency

of the riser decreases greatly, and the vortex shedding frequency may

fall into a higher adjacent mode under the same external flow velocity.

Thus, the riser may vibrate with higher vibration mode. In addition, the

maximum RMS value of the displacement of the riser decreases

significantly, with the reduction of 50% in the CF direction and 40% in

the IL direction approximately. From the perspective of the energy

transfer between the outflow and the riser, the high mode with a large

amplitude is difficult to be excited. Because of the higher vibration

mode, the vibration frequency increases correspondingly as shown in

(d)~(e) of Fig. 9 and 10. The vibration frequency is approximately

equal concerning two cases with V=5 m/s and V=10 m/s.

(a) (b)

Fig. 8 The RMS value with different V, when external flow velocity

U=0.2 m/s: (a) CF RMS value and (b) IL RMS value

In comparison of vibration response of two directions, under the

influence of internal flow, the frequency variation trend in the IL

direction is the same as that in the CF direction. In general, the in-line

vibration frequency is exactly twice as that in cross-flow direction, so

does the dominant mode.

In addition, some subordinate frequency components of vibration

modes with considerable vibration intensity emerges in the IL direction

as shown in Fig. 10 (a)~(c). The fourth modes have been excited

around the original second vibration mode and the total vibration

intensity of others is much smaller than the former two. By comparison

of various internal flow velocities, it can be seen that the existence of

internal flow will change the dominant vibration frequency to some

degree by influencing the natural frequency of the riser. It also can be

found that the lower internal flow mainly influences the values of

vibration displacement. However, a higher internal flow velocity may

excite a higher dominant vibration mode.

(a) (b) (c)

(d) (e)

Fig. 9 CF modal power spectral densities with different internal flow

velocities: (a) V=0 m/s, (b) V=1 m/s, (c) V=2 m/s, (d) V=5 m/s and (e)

V=10 m/s, when external flow velocity U=0.2 m/s

(a) (b) (c)

(d) (e)

Fig. 10 IL modal power spectral densities with different internal flow

velocities: (a) V=0 m/s, (b) V=1 m/s, (c) V=2 m/s, (d) V=5 m/s and (e)

V=10 m/s, when external flow velocity U=0.2 m/s

Fig. 11 shows the RMS value of displacement in the IL and CF

direction concerning different velocities of internal flow under the

external flow velocity U=0.36 m/s. The calculation results show that

the vibration mode of the riser increases compared with that of

U=0.2m/s with the same velocity of internal flow. In case 6, the

vibration response is mainly dominated by the 2nd mode in the CF

direction and 5st mode in the IL direction. Therefore, it can be found

that the external flow velocity has a great influence on the modal

response of the riser. The modal power spectral densities of the riser

subjected to the external current U=0.36 m/s in the CF and IL

directions are presented in Fig. 12 and Fig. 13, respectively. Contrary to

2385

the results of the preceding group (U=0.2m/s), when the internal flow

velocity is lower (case 7 and 8), it can be found that the vibration

amplitude of the riser increases in the CF direction, which is consistent

with the conclusion of Guo and Lou (2008). When the internal fluid is

still, it can be seen that the dominant vibration mode is second-order

with slight first mode component as shown in Fig. 12 (a). Therefore, it

is under the transition state from first mode to second mode at the

current velocity of U=0.36m/s which is relatively far from the second

mode "lock-in" region. With the increasing internal flow velocity and

then the decrease of the natural frequency of the riser, the number of

elements with "lock-in" phenomenon increases in this condition so that

the vibration becomes more violent.

As the internal flow velocity continues to rise (case 9 and 10), the

vibration amplitude in the CF direction decreases by about 33% and

20% respectively compared with that in case 6, which is distinctly

lower than that in the preceding group. Moreover, the vibration

displacement and dominant vibration mode in the IL direction become

relatively stable with the increase of the internal flow velocity. On the

whole, from the perspective of the fluctuation of displacement

amplitude and the dominant vibration mode, existence of internal flow

seems to have a less effect on riser’s vibration displacement response

compared with the condition of U=0.2 m/s. It is decided by the velocity

ratio of V/U. The larger the velocity ratio is, the more of its influence

contributes to the dynamic response of the riser in consideration of both

external and internal flow.

In general, the dominant vibration mode of the riser is determined by

the coefficient of the natural frequency and the Strouhal frequency of

flexible riser. The Strouhal frequency reflects the external energy,

while the natural frequency expresses the structural characteristics of

the riser itself. It is known that the corresponding vibration mode with

natural frequency closest to the Strouhal frequency, tends to be an

apparent or dominant vibration mode. When the natural frequency of

the riser changes, there is no doubt that the dominant mode of vibration

changes accordingly. Therefore, the existence of internal flow with

different velocities contributes to the vibration mode of the riser greatly

which should not be negligible. The foresaid analysis of the mode

response is consistent with this conclusion, which verifies the reliability

of the calculated results.

(a) (b)

Fig. 11 The RMS value with different V, when external flow velocity

U=0.36 m/s: (a) CF RMS value and (b) IL RMS value

Single-modal vibration state can still be widely observed in case 6~8,

shown in Fig. 12 (a), (b) and (c) subsequently. Although it seems that

the internal flow has little effect on riser’s frequency response, the extra

effect along the main driving portion of the flexible riser model implies

that it is doomed to be a potential fact to eliminate or excite some

candidate vibration mode in some way (Chen, 2010). Moreover, it can

be seen the transformation process of dominate vibration mode from

the second one to the third one with the increase of the internal flow

velocity, as shown in Fig. 12 (d) and (e). When V=5m/s, the third mode

has been excited and becomes the subordinate vibration mode with

considerable energy. Fig. 12 (e) shows that the vibration intensity of the

subordinate vibration mode has exceeded that of the original dominant

vibration mode. In the IL direction, the phenomenon of multi-modal

vibration response can be widely observed. However, the fifth vibration

mode remains the dominant one and some subordinate modes with

small vibration intensity could be negligible.

On the whole, the dynamic vibration response of the riser is more

complicated when external current U rises from 2 m/s to 3.6 m/s. Even

in the case of V=0 m/s when U=3.6 m/s, subordinate vibration modes

emerge in both directions. The internal flow velocity makes less effect

on the frequency response of the riser when the current velocity is

relatively higher, which is mainly reflected in the dominant vibration

frequency.

(a) (b) (c)

(d) (e)

Fig. 12 CF modal power spectral densities with different internal flow

velocities: (a) V=0 m/s, (b) V=1 m/s, (c) V=2 m/s, (d) V=5 m/s and (e)

V=10 m/s, when external flow velocity U=0.36 m/s

Fig. 14 shows the power spectra densities in case 2 and 9 respectively,

which is made by the CF and IL displacements at nine equidistant

arranged nodes of the riser via FFT. The displacement power spectra of

multiple positions along the span of the riser are easily used to analyze

the distribution characteristics of vibration frequency domain along the

span of the riser. It can be found that the vibration energy distribution

in case 2 is gradually weakened from the middle to both ends of the

riser, shown in Fig.14 (a). From another point of view, it indicates that

the dominant vibration mode is the first order. It is apparent that at a

higher outflow velocity, there exist the multi-frequency components

and multi-mode resonance of the riser as shown in Fig. 14 (c). The VIV

dynamic response is more complicated. Fig. 15 shows the power

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spectrum densities of the cross-flow displacements along the span in

case 6 and 10 subsequently. Multi-mode and mode transition

phenomenon can be more apparently presented.

(a) (b) (c)

(d) (e)

Fig. 13 IL modal power spectral densities with different internal flow

velocities: (a) V=0 m/s, (b) V=1 m/s, (c) V=2 m/s, (d) V=5 m/s and (e)

V=10 m/s, when external flow velocity U=0.36 m/s

(a) (b)

(c) (d)

Fig. 14 The power spectrum densities of the cross-flow displacements

along the span: (a) case 2 in CF direction, (b) case 2 in IL direction, (c)

case 9 in CF direction and (d) case 9 in IL direction

(a) (b)

Fig. 15 Non-dimensional CF vibration modal weight at the mid-span of

the cylinder: (a) case 6 and (b) case 10

Table 4 concludes the vibration frequency and vibration modes of the

riser according to the magnitude of the modal weight in both CF and IL

directions of ten calculation conditions. In general, it has been found

that the vibration frequencies are comparative concerning different

internal flow velocities when the internal flow velocity is relatively low

and the mode transition phenomenon does not occur. With the increase

of V, the multi-modal vibration and the mode transition phenomenon

will occur.

Table 4. The vibration frequency and vibration modes of the riser in

both CF and IL directions

Case CF IL

frequency modes frequency modes

1 1.7 Hz 1 2.29 Hz 2, 4

2 1.68 Hz 1 2.29 Hz 2, 4

3 1.68 Hz 1 2.28 Hz 2, 4

4 2.67 Hz 2 5.14 Hz 4

5 2.54 Hz 2 4.98 Hz 4

6 3.16 Hz 2, 1 8.41 Hz 5, 4, 1

7 3.14 Hz 2 8.40 Hz 5, 1

8 3.17 Hz 2 8.45 Hz 5, 4, 1

9 2.82 Hz 2, 3, 1 7.37 Hz 5, 1

10 4.1 Hz 3 ,2, 1 7.29 Hz 5, 1, 6

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CONCLUSIONS

Aiming at investigating the effect of internal flow on the VIVs dynamic

of the riser, numerical simulations in consideration of both the internal

flow and the external uniform flow have been carried out in this paper.

Centrifugal and Coriolis forces excited by the internal flow are both

included in the riser’s vibration. By analyzing the simulation results of

a series of cases, the following conclusions are drawn:

With the increase of the outflow velocity, the vibration of the cylinder

in both directions intensifies obviously. In addition, the internal flow

also has a great effect on VIV dynamic response of the flexible riser.

When the internal flow velocity is relatively low, it mainly affects the

vibration displacement as the natural frequency of the riser decreases

due to the increase of the internal flow velocity. However, when the

change of the natural frequency causes that the riser is closer to the

locking vibration region, the increase of the internal flow will

strengthen the vibration. And the comparatively low internal flow

velocity contributes little to the dominant vibration frequency.

When the internal flow velocity continues to increase to some extent,

multi-modal vibration and mode transition of the riser are widely

observed. What’s more, the vibration intensity of the higher dominant

mode may be attenuated and the dominant frequency increases

correspondingly. The complicated VIV dynamic response makes the

riser more prone to fatigue damage. Therefore, the influence of internal

flow should be paid much attention in the practical engineering design

of the pipe.

Compared with the cross-flow vibration response, the in-line

displacement amplitude is much lower, and the influence of internal

flow is relatively insensitive, but its vibration frequency is about twice

than that of in cross-flow. Moreover, the multi-modal vibration

phenomenon is more likely to occur, making the riser in a dangerous

state. Thus, it is necessary to make accurate prediction of vortex-

induced vibration responses in both directions at the same time.

ACKNOWLEDGMENTS

This work is supported by the National Natural Science Foundation of

China (51879159), The National Key Research and Development

Program of China (2019YFB1704200, 2019YFC0312400), Chang

Jiang Scholars Program (T2014099), Shanghai Excellent Academic

Leaders Program (17XD1402300), and Innovative Special Project of

Numerical Tank of Ministry of Industry and Information Technology of

China (2016-23/09), to which the authors are most grateful.

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