MARINE TECHNOLOGY Tecnologia por uma sociedade melhor

2013 – November – 11

Marcelo Caire

Pedro Henrique Affonso Nobrega

Instituto S INTEF do Brasil

Free span VIV Capabilities of numerical methods - VIVANA

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Presentation outline

i. Introduction

ii. Our semi-empirical code: VIVANA

iii. Free span analysis with VIVANA

i. Combined frequency and nonlinear time domain analysis

ii. Multiple span pipeline interaction

iv. Future investigations at ISdB

v. Final remarks

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Introduction Prediction methods

Three main groups of prediction methods

1. Wake-oscillator models

2. Computational fluid dynamics (CFD)

3. Semi-empirical force coefficient methods

• Combine a linear frequency domain structural solution method (finite differences,

finite element methods) with an empirical hydrodynamic model

• Still the technique mostly used in the analysis/verification

• Codes: VIVANA (MARINTEK/NTNU), VIVA and SHEAR7 (MIT), ABAVIV (TECHNIP)

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Introduction Free span pipelines

Free span VIV model challenges

− Pipeline / seafloor interaction

Nonlinear stiffness and damping including friction for in-line oscillations

− Multispan pipeline interaction

Dynamic interaction between adjacent spans

− Oscillations close to seafloor

Hydrodynamic coeff. for a pipe that oscillates in a current close to wall

− Interaction between In-line and Cross-flow response

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Our semi-empirical code: VIVANA Main characteristics

− Static condition found from a general 3D non-linear finite element method (RIFLEX) that

allows very large displacements

− Frequency response method (linear) to calculate the dynamic VIV response

Iteration to ensure consistency between response amplitude and excitation coefficients

− Default hydrodynamic coeff. for pure CF or user-defined

Recent features

− Pure IL

− Combined CF + IL response

i. Same CF coefficients

ii. Modified IL coeff. Larger IL amplitudes for IL+CF than for pure IL. IL frequency = 2 times CF frequency

− Current may have an arbitrary variation in speed and direction along the structure

− Additional analysis options

i. Updated static analysis by a second use of STAMOD where magnified drag forces are introduced

ii. Improved dynamic analysis by using intermediate results from VIVANA in a non-linear time domain model

(DYNMOD).

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Our semi-empirical code: VIVANA Analysis procedure step by step

1. Perform static analysis with RIFLEX

2. Solve eigenvalue problem with prescribed added mass (still water)

3. Identify cross-flow and in-line modes

4. Identify possibly active frequencies

5. For each possible frequency, repeat until convergence is achieved:

1. Compute new added mass (moving cylinder)

2. Update the mass matrix and solve the new eigenvalue problem

3. Obtain a new estimate for the oscillation frequency

6. Rank active frequencies (time-sharing or space-sharing methods)

7. Find the response shape and amplitude

8. Calculate of fatigue damage

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Our semi-empirical code: VIVANA Strouhal number and kinematic viscosity

Kinematic viscosity x Temperature

(Faltinsen, 1990)

Strouhal x Reynolds

(Bleivins, 1990)

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- Solve eigenvalue problem with prescribed added mass (still water)

𝐌0 − 𝜔𝑖2𝐊0 𝜑𝑖 = 0

- Identify cross-flow and in-line modes

• 𝜑𝑖 is decomposed in 𝜑𝑖,𝐶𝐹 and 𝜑𝑖,𝐼𝐿 in the local coordinate system

• norms are calculated to define if the i-th eigenvector is CF or IL

𝑪𝑭 𝒊 = 𝜳𝒊,𝒋,𝑪𝑭, 𝜳𝒊,𝒋,𝑪𝑭𝒋 𝑳𝒋

𝑰𝑳 𝒊 = 𝜳𝒊,𝒋,𝑰𝑳, 𝜳𝒊,𝒋,𝑰𝑳

𝒋

𝑳𝒋

Our semi-empirical code: VIVANA Eigenvalue calculation (still water)

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Our semi-empirical code: VIVANA Identifying possible active eigenfrequencies

Based on Gopalkrishnan's tests (1993) with forced CF motions of a rygid cylinder

and Aronsen's (2007) tests with forced IL motions

Excitation coefficients obtained by Gopalkrishnan

0.125 ≤ 𝑓 ≤ 0.3 3.33 ≤ 𝑈𝑅 ≤ 8

(0.2 ≤ 𝑓 ≤ 0.9 for IL)

Range where the excitation

coefficient is positive

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Our semi-empirical code: VIVANA Added mass coefficients and oscillation frequency

For each possible frequency, repeat until convergence is achieved:

1. Compute new added mass (moving cylinder)

2. Update the mass matrix and solve the new eigenvalue problem

3. Obtain a new estimate for the oscillation frequency

Added mass coefficients for IL Added mass coefficients for CF

Added mass is weakly dependent on the oscillation amplitude

VIVANA adopts a amplitude independet model

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Our semi-empirical code: VIVANA Excitation force

Default or user-defined coefficients for pure IL, pure CF and combined CF+IL

𝑭𝒆,𝑪𝑭/𝑰𝑳 = 𝟏

𝟐𝝆𝑪𝒆,𝑪𝑭/𝑰𝑳𝑫𝑯𝑼𝑵

𝟐∆𝑳

Defaut parameters for CF excitation coefficients CF excitation coefficients approximated curve

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Our semi-empirical code: VIVANA Hydrodynamic damping

1. Outside the excitation zone

Venugopal's (1996) model for damping coefficients: still water, low and high velocity zones

𝑐𝑖𝑗 = 𝑅𝐿

𝑥 𝑁𝑖 𝑥 𝑁𝑗 𝑥 𝑑𝑠

i. Damping in still water

ii. Damping in low velocity regions

iii. Damping in high velocity regions

𝑅𝑠𝑤 =𝜔𝜋𝜌𝐷𝐻

2

2

2 2

𝑅𝑒𝜔+ 𝑘

𝐴

𝐷𝐻

2

, 𝑈𝑁 = 0

𝑅𝑙𝑣 = 𝑅𝑠𝑤 +1

2𝜌𝐷𝐻 𝑈𝑁𝐶𝑣𝑙 , 𝑓 ≥ 𝑓 𝑢𝑝𝑝𝑒𝑟

𝑅ℎ𝑣 =1

2𝜌𝑈𝑁

2𝐶𝑣ℎ , 𝑓 ≤ 𝑓 𝑙𝑜𝑤𝑒𝑟

2. Inside the excitation zone

- Free spans -> constant flow velocity along length

- If oscillation amplitude > (A/D)CL=0 the lift coef.

become negative leading to damping

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Our semi-empirical code: VIVANA Frequency response

−𝜔2(𝐌𝑠 + 𝐌𝐻)𝐱 + 𝑖𝜔(𝐂𝑠+𝐂𝐻)𝐱 + 𝐊𝐱 = 𝐗

𝐌𝑠, 𝐂𝑠 : structural mass and damping matrices

𝐌𝐻 , 𝐂𝐻 : hydrodynamic mass and damping matrices

𝐊 : stiffness matrix

𝐗 : external load vector

𝐂𝑯, 𝐗 and 𝐱 unknown: iterations needed!

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Concurrent response frequencies

Space sharing

𝐸𝑖 = 𝑈𝑁3

𝐿𝑒,𝑖

𝑠 𝐷𝐻2 𝑠

𝐴

𝐷𝐶𝑒=0

𝑑𝑠

Consecutive response frequencies

Time sharing − 𝑃 𝜔 𝑡 = 𝜔𝑖 = 𝐸𝑖 𝐸𝑗𝑗

Our semi-empirical code: VIVANA Frequency ranking

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Our semi-empirical code: VIVANA General coefficient model – Helical strakes

User-defined lift coefficient curves for a

riser with strakes

Easy input of model test results or from CFD

calculations

Amplitude dependent curves for given non-dimensional

frequency (same way as for CF and IL)

Excitation force coefficient as function of amplitude for a

set of non-dimensional frequencies

The section with strakes provides a significant damping

Can handle cases of up to app. 75 % coverage of supression devices -> the

bare pipe controls the VIV response

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Combined frequency and non-linear time domain analysis Nonlinear TD analysis methodology and advantages

1. Nonlinear static analysis with RIFLEX

2. Traditional VIVANA frequency domain

3. Transfer of results from VIVANA to RIFLEX

(response frequency, added mass, damping)

4. Nonlinear time domain analysis with RIFLEX

Improved results for local stresses at the shoulders

Essential for fatigue life prediction and strongly influenced by seaflor interaction

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Combined frequency and non-linear time domain analysis Case study (Larsen et al, 2004)

Bottom stiffness: 400 kN/m2 (hard)

Length: 380 m

External diameter: 0.55 m

Current speed: 0.7 m/s

Similar stresses in the middle and where the pipe remains on the bottom

The nonlinear contact on the shoulders may reduce stresses by app. 15%

Substantial decrease in fatigue damage

Total stress RMS for case 3

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Multispan analysis - VIVANA Case study (Soni & Larsen, 2005)

Springs 2 and 3 stiffness: 50 kN/m

Length: 5.5 m

External diameter: 0.016 m

Energy is transferred from the span with the smallest

displacement amplitude to the neighboring span with

the highest one

Response amplitude for several current velocities

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Multispan analysis - RIFLEX Case study (Soni & Larsen, 2005)

Bottom stiffness: 400 kN/m2

Length: 5.5 m

External diameter: 0.016 m

Soil profile radius: 1m,0.6m,0.2m

Maximum short/long amplitude ratio for

second mode eigenfrequency, which is linked

to a mode with large amplitude at the short

span Short/Long amplitude ratio for several excitation

frequencies

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Future investigations at ISdB Numerical lab (CFD)

Hydrodynamic coefficients for free span

− Boundary layer effects close to the seafloor

Hydrodynamic coefficients (added mass, lift, drag and damping) affected

Full 3D FSI simulations still have

prohibitive computational costs

for engineering applications

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Near-wall cylinder

(H = 1.0 D)

Free-stream cylinder

Near-wall cylinder – pressure field

Future investigations at ISdB Numerical lab (CFD)

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Conclusions

• Recent improvements in VIVANA:

− Current may have arbitrary variation in speed and direction

− calculation of pure IL and combined IL+CF response

• Further research is required for free span hydrodynamic coefficients and how in-

line and cross-flow vibrations interact

• The combined frequency domain + non-linear time domain analysis methodology

improves the fatigue assessment at free span shoulders (pipe-soil interaction)

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Final remarks

Somme comments from the 26th ITTC (2011) Specialist Committee on VIV:

i. The complex VIV fluid-structure interaction problem has not yet been fully understood

ii. There is no consolidated procedure for its analysis

iii. Semi-empirical models are still the technique currently employed in the design of risers and pipelines

iv. Large scatter between different codes in the fatigue damage prediction is observed

v. Lack of full scale measurement data devoted to the determination/validation of the coefficients used in semi-empirical models

There is a need for a joint effort between the industry, and research academia to tackle the problem more efficiently

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For further discussions please contact:

Marcelo Caire, DSc

Marine Technology group leader

marcelo.caire@sintefbrasil.org.br

(21) 9185-3012

(21) 2025-1811