Vedeld 2 - VIV Fatigue Calculation

7/31/2019 Vedeld 2 - VIV Fatigue Calculation

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VIV Fatigue Calculation


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Slide 2

Vortex Induced Vibrations (VIV)

Let us try to calculate the fatigue life of a span!


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Slide 3

Fatigue - overview

Strength

Probability

2-Design criteria

2-Resistance

S

N

4,5-Load effects

(cyclic stresses)

6, 7-

Structural response

3-Environment

WavesCurrent


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0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0

Reduced Velocity VR

Normalised

vibrationamplitudeA/D

IN-LINE

CROSS-FLOW

U/f0D

Summary Response Model Basic Concepts

CF induced

IN-LINE


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Slide 5

Exercise

Calculate the fatigue life of a 40m long free span at 300m water depth.

0 m

75 m

500 m

500 m

100 m


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Slide 6

Basic data

Pipe dimensionsOutside diameter D 500 mm

Wall thickness t 13.2 mm

Operational parameters

Operational pressure Pop 100 barg @ +30m

Operational temperature Top ambient

Content density cont 153 kg/m3

Residual lay tension Heff 200 kN

Design life Tlife 25 years

Environment

Weibull parameter - Shape 1.718

Weibull parameter - Scale 0.133 m/s

Weibull parameter - Location 0.005 m/s

Current reference height zr

3.0 m

Current to pipe angle 90

Incoming turbulence Ic 5 %

Water depth d 300 m

Seabed

Medium sand

Corrosion coating asphalt

Thickness tcorr 6.0 mmDensity corr 1900 kg/m

3

Concrete coating

Thickness tcon 50.0 mm

Density con 2240 kg/m3

Structural damping 0.5 %

SN curve F1 free corrosion

Slope parameter m 3

Fatigue constant Log(C) 11.222


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Slide 7

Practical information

The presented information should be used for allexercises during day 1


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Slide 8

VIV Load and Response

Let us start look at the loading mechanism


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Slide 9

CR

OSS-FLOW

In-line and Cross-flow VIV

Flow

IN-LINE

IN-LINE

CROSS-FLOW


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Slide 10

Vortex shedding frequency- Strouhal number

D

UStfs =

The frequency at which the

vortices are shed from a

fixed cylinder

Oscillations in the lift force

occur at the Strouhal

frequency

Oscillations in the drag

force occur at twice the

Strouhal frequency


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Slide 11

Response Model - example

Provides amplitude versus loading

Swing different lengths

or Pendulum


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Slide 12

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0

Reduced Velocity VR

VibrationamplitudeA/D

IN-LINE

CROSS-FLOW

U/f0D

widthelmod

cycleperlength

Df

UV

0

R ==

Response Models

CF induced

IN-LINE


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Slide 13

Lock-in phenomena - cross-flow

the vortex shedding locks-on

to the natural frequency

St

1

Df

U

Df

Uff

s0

s0

==

=


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Slide 14

Exercise Calculate Amplitude

Given:

- Current velocity, U = 0.6 m/s

- Natural frequency, f0

= 0.773 Hz

- Reduced frequency should be used for

calculation of reduced velocity

- In-line Response Model (next sheet)

Use Response Model to estimate vibration

amplitude, A/D and fill value into spreadsheet

1.1,0,0 == ff

d

ff


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Slide 15

In-line Response Model

0.00

0.02

0.04

0.06

0.08

0.10

0.12

0.14

0.0 1.0 2.0 3.0 4.0 5.0

VR

(A

y/D)


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Slide 16

Calculation sheet

UC

p(UC

) VR,d

AY

/D SIL

Ni

=a/Sm ni

=Tyear

p(UC

)f1

ni

/Ni

0

0,1

0,2

0,3

0,4

0,5

0,6

0,7


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Slide 17

Challenge

Break a wire by hand


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Slide 18

Reflection

Fatigue failure

Relation between Stress Range and Number of cycles to failure


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Slide 19

Fatigue Calculation

Damage accumulation by Miner-Palmgren:

Number of stress cycles:

Number of cycles to failure by SN curve:

=i

ifat

NnD

Tf)(Pn vi =

mii SaN

=

1

10

100

1000

1.E+03 1.E+04 1.E+05 1.E+06 1.E+07 1.E+08 1.E+09 1.E+10

No of cycles, N

StressR

ange,

S

NSW

SSW

(a1;m1)

(a2;m2)


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Slide 20

SN curve (F1 free corrosion)

10

100

1000

1.E+04 1.E+05 1.E+06 1.E+07 1.E+08

N

S(MPa

)


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Slide 21

Vibration mode


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Slide 22

Modal stress

Curvature, , of free span vibratingwith a given mode 2nd derivative

of mode

Modal stress found by curvature

E(D-t)/2

Ain, modal stress for maximum mode

amplitude = OD given by multiplying

modal stress by OD Ain = 445 MPa (given value from FE

analysis)

Vibration stress range:

S = 2 Ain

(Ay

/D)

Safety factor on stress range

3.1, == ssd SS

Exercise Calculate Stress Range & Number


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Slide 23

Ca a S a g &of Cycles to Failure

Calculate Stress Range

Calculate Number of cycles to failure


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Slide 24

Calculation sheet

UC

p(UC

) VR,d

AY

/D SIL,d

Ni

=a/Sm ni

=Tyear

p(UC

)f1

ni

/Ni

0

0,1

0,2

0,3

0,4

0,5

0,6 0,00 1,40 0,05

0,7


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Slide 25

Exercise Fatigue Damage & Life

Estimate number of stress cycles per year, n(Hint : vibration frequency = natural frequency)

Calculate fatigue damage (per year)

Find fatigue life (inverse of fatigue damage per year)

Multiply with utilization factor 0.5


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Slide 26

Calculation sheet

UC

p(UC

) VR,d

AY

/D SIL

Ni

=a/Sm ni

=Tyear

p(UC

)f1

ni

/Ni

0

0,1

0,2

0,3

0,4

0,5

0,6 0,00 1,40 0,05

0,7


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Slide 27

Reflection Current

Will the current be constant over time (years) or vary?

L di ib i f


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Slide 28

Long-term distribution of current

Ui(m/s)

F(Ui) f(Ui)= Pi Exposure

(days/year)

0 0.00000 0 0

0.1 0.42517 0.42517 155

0.2 0.85220 0.42703 156

0.3 0.97972 0.12752 47

0.4 0.99840 0.01868 70.5 0.99992 0.0015199 1

0.6 1.00000 7.3066E-05 0

0.7 1.00000 2.1580E-06 0


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Slide 29

Exercise Fatigue life for current distribution

Use approach for one current flow velocity and calculate for a long-termcurrent distribution

Find fatigue life (in years)

C l l ti h t


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Slide 30

Calculation sheet

UC

p(UC

) VR,d

AY

/D SIL

Ni

=a/Sm ni

=Tyear

p(UC

)f1

ni

/Ni

0

0,1

0,2

0,3

0,4

0,5

0,6 0,000073066 1,40 0,05 56,4 930793 1781 0,001913588

0,7

S


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Slide 31

Summary

This exercise follows the principles of VIV fatigue calculation according toDNV RP-F105

Safety factors are included as specified Normal safety classification

and Well defined span.

In addition:

- Cross-flow VIV (in a similar way)

- Cross-flow induced Inline VIV- Direct wave load

and a lot of details.

R fl ti i l i i t


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Slide 32

Reflection main learning points

.

Fatigue overview


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Slide 33

Fatigue - overview

Strength

Probability

2-Design criteria

2-Resistance

S

N

4,5-Load effects(cyclic stresses)

6, 7-

Structural response

3-Environment

WavesCurrent

S R M d l B i C t


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Slide 34

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0Reduced Velocity VR

Vib

rationamplitude

A/D

IN-LINE

CROSS-FLOW

U/f0D

Summary Response Model Basic Concepts

CF induced

IN-LINE

Calculation sheet Results


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Slide 35

Calculation sheet - Results

UC

p(UC

) VR,d

AY

/D SIL

Ni

=a/Sm ni

=Tyear

p(UC

)f1

ni

/Ni

0 0 0 0 0 inf 0 0

0.1 0.42517 0.2325298 0 0 inf 10364509 0

0.2 0.42703 0.46505961 0 0 inf 10409850 0

0.3 0.12752 0.69758941 0 0 inf 3108597 0

0.4 0.01868 0.93011921 0.002102086 2.44 11511283020 455368 3.95584E-05

0.5 0.0015199 1.16264902 0.025356892 29.40 6558240 37051 0.005649549

0.6 0.000073066 1.39517882 0.048611698 56.37 930793 1781 0.001913588

0.7 0.000002158 1.62770862 0.071866503 83.34 288069 53 0.000182617


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Slide 36
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Vedeld 2 - VIV Fatigue Calculation