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AN INVESTIGATION ON THE EFFECT OF CURRENT DIRECTIONALITY

ON RISER VORTEX-INDUCED VIBRATION

S. Manayankath, Lloyd’s Register, UK  

S. Huang, University of Strathclyde, UK  

ABSTRACT

The paper presents the results from a preliminary study on the influence of current direction ondeepwater riser VIV. The theoretical investigation was carried out using SHEAR7 and the VIV analysiscodes within Orcaflex. It was observed that compared to a unidirectional current over the full riser length,

in a multidirectional inflow the fatigue damage reduced significantly. The reduction in fatigue damagewas noted over the complete riser length though the current direction was varied only in the lower half of

the riser. Based upon the results, it appears that we can conclude that using a unidirectional current inVIV analysis would lead to results which are likely to be highly conservative and this needs to beconsidered and studied further in future VIV modeling and prediction.

1. INTRODUCTION

Fatigue damage due to vortex-induced vibration

(VIV) is an important issue in deepwater riser

design. The mechanism of VIV is complex and not

fully understood. Apart from risers, other offshore

installations like tethers, pipelines, members of

 jacketed structures and even deepwater pile

installations are affected by problems arising from

alternating vortex shedding. VIV suppression

devices such as helical strakes are used to suppressVIV. Though these devices do improve the VIV

 performance to some extent, it comes at additional

 penalties such as drag increase and costs in

fabrication and handling.

 Notwithstanding its complexity, progress has been

made both numerically and experimentally in

understanding the fundamentals of marine riser

VIV. Numerous papers have been published on

this topic in the last decade as the offshore

engineering industry relentlessly pushes into everdeeper waters. A number of papers such as

Sarpkaya (2004), Vandiver (1993), Pantazopoulos

(1994), and Gabbai & Benaroya (2005) are

excellent sources of information that trace the

developments in this field over the years and

 provide a comprehensive review.

Along with numerous efforts to investigate various

aspects of marine riser VIV, a great deal of work

has been carried out to synthesise these results to

yield theoretical VIV prediction models and codes.SHEAR7 (Vandiver and Li, 2005) is an example

of these models and codes and is probably the

most commonly used design tool in the industry

for riser VIV analysis at the moment.

In the recent years, as the riser monitoring devices

 become better understood and more and more

reliable, efforts have been made to calibrate the

riser field-monitoring data with the SHEAR7

 predictions (Tognarelli et al, 2009). Many

technical issues and fundamental questions

however arise in this calibration effort. For

example, SHEAR7 is based upon some empiricalinput data which are derived in low Reynolds

number model tests. These data are not necessarily

applicable to full-scale risers (Huang and Kitney,

2009).

Another issue relates to the key assumption used

in SHEAR7, i.e. the current profile is

unidirectional across the water column. In the real

ocean environment, particularly in deepwater,

however, a riser will be subjected to multi

directional currents along its length. In calibratingSHEAR7 by the use of riser field-monitoring data,

this issue of discrepancy between the modeling

assumption and the reality has yet to be addressed

and its effects quantified.

Most of the model tests on VIV are carried out

with rigid or flexible cylinders placed in a

unidirectional flow due to practical limitations.

There is very little published data on the effect of

current directionality on VIV. It is generally

considered that a unidirectional inflow would leadto conservative results, but with further research

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on VIV in multidirectional currents it is hoped that

the design conservatism could be reduced in the

future.

The paper presents the preliminary results from a

theoretical investigation into the effect of currentdirection on riser VIV. The currently popular

theoretical models were used for the investigation.

It was believed that such a study would provide

some insight, however limited it may be, on the

riser VIV response in a multi directional current

environment. It was also felt that such a theoretical

study would draw attention and R&D efforts to

this so-far largely ignored issue.

2. INVESTIGATION METHODOLOGY

A top tensioned riser was analysed using Orcaflex

with its associated VIV analysis tools and

SHEAR7 programs in different flow conditions as

described below with a view to make a qualitative

assessment of the influence of current direction on

riser VIV. The inflow conditions were as given

 below.

•  Uniform flow over the full length of the

riser.

•  Flow direction in the riser lower half at

different angles of incidence with respect

to the uniform flow on the upper half.

SHEAR7 is a program widely used in the industry

for VIV analysis which uses a modal analysis

technique and iteratively calculates the lift and

damping coefficients to attain a balance of power

input from lift force and power output throughdamping (Vandiver and Li, 2005).

The Orcaflex VIV toolbox had two wake oscillator

models, i.e. the Milan model and Iwan & Blevins

model. The Milan model is a wake oscillator

model proposed by a group in Italy and described

in the paper by Falco, Fossati and Resta (1999). In

this model, the effects of VIV are simulated using

a series of equivalent oscillators that are connected

to the structural model nodes. The equivalent

oscillator is a non-linear one degree of freedom

system which transmits to the structure forces

equivalent to vortex shedding mechanisms. The

Iwan & Blevins wake oscillator model uses a Van

der Pol type equation with a flow variable todescribe the effects of vortex shedding. Model

 parameters are determined by curve-fitting

experimental results for stationary and forced

cylinders in the Reynolds number range between

103 and 105 (Blevins, 2001).

A top tensioned drilling riser subjected to a

uniform flow of 1.0 m/s over its full length was

selected as the base case. This base case was

analysed using SHEAR7, a frequency domain

model. The same riser was then analyzed using theOrcaflex VIV tool box with its wake oscillator

models which are time domain methods.

With the differences in modelling techniques and

assumptions, as well as the amount of empiricism

in place, close matching of the results from

different models was not expected. It was hoped

that, in the absence of riser field-monitoring data,

a comparison of the base case in SHEAR7 and

Orcaflex would give a qualitative indication on the

conservativeness of the results, assuming

SHEAR7 results to be the reference case.

The cases with multidirectional current inflows

were analyzed using Orcaflex only, as SHEAR7

can only deal with unidirectional current profiles.

The current speed was again 1.0 m/s, as in the base

case. But the angle of attack in the lower half was

varied with respect to the flow direction in the

upper half. The angles analysed were 30, 45, 60,

75 and 90 degrees.

A schematic diagram of the riser model used for

the study is shown in Figure 1. The riser details

are given in Table 1.

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Figure 1 Riser Model

 NameHeight

[m]Mass/m[kg/m]

OD[m]

ID[m]

Submerg

ed wt/m[kN/m]

Ca  CD 

A Pup in air 19.00 769.4 0.603 0.529 -7.467 1.596 1.516

BPup inwater

4.33 769.4 0.603 0.529 -4.732 1.596 1.516

C Slick 18.29 769.4 0.603 0.529 -4.605 1.596 1.516

D Riser(Buoyant)

310.99 1042.8 1.107 0.529 -0.561 1.176 1.301

E Pup 7.92 769.4 0.603 0.529 -4.532 1.596 1.516

Density of sea water 1.025 tons/m3 

Density of contents 1.138 tons/m3 

Table 1 Main Particulars of the Riser

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3. ANALYSIS PROCEDURE

SHEAR7 is based on frequency domain solution

and the program outputs rms  values of

displacement, acceleration, stress and fatigue life,

all in the cross-flow direction. Orcaflex is a timedomain based program and the results in both the

cross-flow and in-line directions are given. At

every node, the minimum, maximum, mean and

standard deviations of different parameters such as

displacement and acceleration are calculated by

the program along with time histories.

In comparing the results from SHEAR7 and the

wake-oscillator models, only the cross-flow

displacements and accelerations were used.

Standard deviation data from Orcaflex wascompared with SHEAR7 rms  data as the mean

value was close to zero in the cases compared.

In comparing the fatigue damage rate, a simplified

 procedure was used to analyse the data. In the

following equations M  is the mass per unit length,

T   is the tension in the riser,  E   is the Young’s

modulus,  I   is the moment of inertia and r   is the

radius of the extreme fibre.

The dynamic equation of the riser in tension for

free vibration is given by

02

2

2

2

4

4

=∂

∂+

∂

∂−

∂

∂

t 

 y M 

 z

 yT 

 z

 y EI   

Considering the riser as a string in tension, i.e.

ignoring the bending stiffness, the dynamic

equation can be simplified to

 y M 

T  y   ′′=  

where double dots represent differentiation with

respect to time and double dashes represent

differentiation with respect to distance z along the

riser.

Assuming sinusoidal modal shape and applying

simple bending theory, the bending stress may be

approximated as

T 

 MEr  ys   =  

The stress range S  is then given by

T 

 MEr  yS  std 22=

 

where subscript std  denotes standard deviation.

Using the stress range and applying a simplified S-

 N   curve approach the annual fatigue damage and

fatigue life was estimated with a view to obtain a

qualitative comparison of the different empirical

model results.

The number of cycles to failure N  is given by

mS 

 A N   =

 

where A = 1.04x1012 and m = 3 were used in the

calculations. The number of stress cycles n  in a

year is determined from the frequency of vibration

and the damage rate is calculated as n/N  [1/year].

4. UNIFORM CURRENT

The top tensioned riser was subjected to a uniform

current of 1.0 m/s and the analysis was carried out

using both SHEAR7 and Orcaflex Milan and Iwan

& Blevins wake oscillator models. As SHEAR7

only models the transverse response, the

comparisons are only for the transverse (Y)

components and the in-line (X) effects were notconsidered for the study. As can be seen from

Figure 2 the transverse displacements estimated

using both Orcaflex Wake Oscillator models and

SHEAR7 were closely comparable. Both programs

indicated a single mode response though the mode

numbers were different. For the two wake-

oscillator models the results were closely

comparable except for the slightly higher peak in

the Iwan & Blevins model.

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Figure 2 Transverse displacements in uniform current

Figure 3 Transverse accelerations in uniform current

Figure 4 Maximum fatigue damage in uniform current

The accelerations using the two programs are

compared in Figure 3. It may be seen that the

accelerations estimated by SHEAR7 was almost

twice that determined using both models ofOrcaflex. This implies that, the bending stress,

which is directly proportional to acceleration

would have a similar distribution, which in turn

would affect the fatigue damage calculations.

Once again the results from Milan and Blevins

models were closely matching except for the peak

magnitude estimated by Blevins model beingslightly higher than that by Milan model.

Max Fatigue Damage (Uniform Current)

0 50 100 150 200 250

Shear7

Blevins

Milan

Damage [1/year]

 

0 . 0

0 . 2

0 . 4

0 . 6

0 . 8

1 . 0

1 . 2

1 . 4

1 . 6

1 . 8

2 . 0

0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 3 5 0

R i s e r l e n g t h [ m ]

   Y  -   A  c  c   [  m   /  s  q .  s

   ]

S h e a r 7 - Y - a c c - 0 d e g

M il a n - Y - a c c - 0 d e g

B l e v in s - Y - A c c - 0 d e g

 

0 .0 0

0 .2 0

0 .4 0

0 .6 0

0 .8 0

1 .0 0

1 .2 0

0 5 0 1 0 0 1 5 0 2 0 0 2 5 0 3 0 0 3 5 0

R i s e r l e n g t h [ m ]

   Y   [  m   ]

S h e a r 7 - Y - d i s p - 0 d e g

M il a n - Y - d is p - 0 d e g

B l e v in s - Y - d is p - 0 d e g

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The maximum fatigue damage anywhere on the

riser estimated from SHEAR7 and Orcaflex data

are presented in Figure 4. As fatigue damage

depends on both frequency and stress range,

SHEAR7 predicted the peak damage to be almost

four times that estimated by the Blevins model andeight times as estimated by the Milan model.

5. MULTIDIRECTIONAL CURRENTS

For the multidirectional current case the analysis

was carried out using Orcaflex wake oscillator

models, with the angle of attack on the riser lower

half varying from 0 to 90 degrees with respect to

the current direction on the upper half. The anglesconsidered were 0 (i.e. entire riser subjected to

unidirectional current), 30, 45, 60, 75 and 90

degrees. The flow speed was 1.0 m/s throughout.

The results presented here are for the direction

 perpendicular to the current direction on the riser

upper half.

The results from the Milan wake oscillator model

are plotted in Figures 5 to 7. It may be seen from

the displacements given in Figure 5 that the

displacements over the full riser length

 progressively decreased as the angle of attack inthe riser lower half increased from 0 to 90. This

decrease was seen over the full length of the riser.

The transverse accelerations are plotted in Figure

6. The trends shown in displacements were

repeated here. The calculated fatigue damage over

the riser length is plotted in Figure 7. As expected

the maximum damage in the Y  direction is for the

case of fully unidirectional flow. As the angle of

attack in the lower half increased, the damage in

the Y  direction decreased all along the riser.

The riser in multidirectional current analysed in

the foregoing was further analysed using Iwan &

Blevins wake oscillator model implemented in

Orcaflex. The transverse displacements and

accelerations from the Blevins model are plotted

in Figures 8 and 9 respectively. It can be seen thatthe trends seen from Milan model results repeated

here as well. Consistent trends were shown for all

of the angles analysed.

It was felt that it would be interesting to have a

comparison of the two wake oscillator models and

so the acceleration results from the two models are

compared as shown in Figure 10. In general it can

 be said that the displacements and accelerations

computed by the two models at different angles of

attack are reasonably close except when the angleof attack was 90 deg.

The maximum fatigue damage anywhere on the

riser length at different angles of attack predicted

 by the two models is given in Figure 11. As

discussed earlier the damage progressively

reduced with increase in the angle of attack. It may

 be noted that a current direction of 45 degrees in

the lower half reduced the annual fatigue damage

 by more than half, relative to the fully

unidirectional inflow case. In the cases considered

here the riser fatigue damage reduced over the

complete length though the attack angle was

varied in the lower half only.

The results indicate that the current direction does

influence the overall riser response and so it needs

to be taken into account during the design stage.

The results also seem to suggest that assuming a

unidirectional current in the riser design may

result in highly conservative designs.

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0

0.2

0.4

0.6

0.8

1

1.2

0 50 100 150 200 250 300 350

Riser length [m]

   Y   [  m   ]

Y-disp-0deg

Y-disp-30deg

Y-disp-45deg

Y-disp-60deg

Y-disp-75deg

Y-disp-90deg

 

Figure 5 Transverse displacements at different angles of attack

00.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 50 100 150 200 250 300 350

Riser length [m]

   Y  -   A  c  c   [  m   /  s  q .  s

   ]

Y-acc-0deg

Y-acc-30deg

Y-acc-45deg

Y-acc-60deg

Y-acc-75deg

Y-acc-90deg

 

Figure 6 Transverse accelerations at different angles of attack

-5

0

5

10

15

20

25

30

50 100 150 200 250 300 350

Riser length [m]

   D  a  m  a  g  e   [   1   /  y  e  a  r   ]

Y-damage-0deg

Y-damage-30deg

Y-damage-45deg

Y-damage-60deg

Y-damage-75deg

Y-damage-90deg

 

Figure 7 Fatigue damage at different angles of attack

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0

0.2

0.4

0.6

0.8

1

1.2

0 50 100 150 200 250 300 350

Riser length [m]

   Y

   [  m   ]

Y-disp-0degY-disp-45deg

Y-disp-60deg

Y-disp-75deg

Y-disp-90deg

 

Figure 8 Transverse displacements at different angles of attack (I & B model)

0

0.2

0.4

0.6

0.8

1

1.2

0 50 100 150 200 250 300 350

Riser length [m]

   Y  -   A  c  c   [  m   /  s  q .  s

   ]   Y-acc-0deg

Y-acc-45deg

Y-acc-60deg

Y-acc-75deg

Y-acc-90deg

 

Figure 9 Transverse accelerations at different angle of attack (I & B Model)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0 50 100 150 200 250 300 350

Riser length [m]

   Y  -   A  c  c   [  m   /  s  q .  s

   ]

Milan-Y-acc-45degMilan-Y-acc-90deg

Blevins-Y-acc-45degBlevins-Y-acc-90deg

 

Figure 10 Transverse accelerations (Milan vs. I&B)

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Max Fatigue Dam age( Diff angles of attack on r iser low er

half)

0 20 40 60 80 100

0 deg

30 deg

45 deg

60 deg

75 deg

90 deg

Damage [1/year]

Blevins

Milan

 

Figure 11 Maximum fatigue damage at different angles of attack

6. CONCLUSIONS

Based upon the preliminary results presented in

this paper, the following conclusions can be drawn.

•  For the unidirectional current, all models

 predicted a single mode response for the

uniform flow condition. However there

were differences in the mode number and

magnitude of the accelerations. The fatigue

damage calculated from SHEAR7 outputs

 by assuming a sinusoidal modal response

of the riser was four to eight times larger

than that calculated from Orcaflex wake

oscillator models’ results.

•  The investigation revealed that compared

to the case of unidirectional current inflow

over the full riser length, in amultidirectional inflow the fatigue damage

was significantly reduced. It was found

from the study that a current direction of

45 degrees in the lower half reduced the

annual fatigue damage by a factor of two to

five relative to the fully unidirectional

inflow case. The reduction in fatigue

damage was observed over the complete

riser length even though the angle of attack

was varied only in the riser lower half.

•  The study appears to indicate that using a

unidirectional current in VIV analysis

would lead to results which are likely to be

highly conservative. Future VIV model

developments and calibrations need to

consider this issue.

ACKNOWLEDGEMENTS

The authors wish to acknowledge the support fromDr. Dave Thomas and Mr. David Heffernan of

Orcina and Dr. Richard James of BP Exploration.

DISCLAIMER

The views expressed in this paper are those of the

authors alone.

REFERENCES

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Florida, USA.

Falco, M., Fossati, F.,Resta, F., 1999. On the

vortex-induced vibration on submarine cables:

design optimization of wrapped cables for

controlling vibrations. 3rd international

Symposium on Cable Dynamcs, Trondheim,

 Norway.

Gabbai,R.D., Benaroya, H., 2005. An overview ofmodeling and experiments of vortex-induced

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vibration of circular cylinders. Journal of Sound

and Vibration, 282, pp. 575-616.

Huang, S and Kitney, N, 2009. Dependence of Lift

Coefficient Clv on Reynolds Number and Surface

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Pantazopoulos, M.S., 1994. Vortex-induced

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Sarpkaya, T., 2004. A critical review of the

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Tognarelli, M. et al, 2009. Benchmarking of

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Vandiver, J.K., 1993. Dimensionless parameters

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currents. Journal of Fluids and Structures, 7, pp.

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Vandiver, J.K. and Li, L., 2005. SHEAR7

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