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Virginia Tech Vortex-Induced Vibrations Project

A. H. Nayfeh, M.R. Hajj, and S. A. Ragab Department of Engineering Science and Mechanics,

Virginia Polytechnic Institute and State University, Blacksburg, VA 24061-0219

e-mail: anayfeh@vt.edu

R. M. SextonStarmark Offshore Inc.

Danville, VAe-mail: sexton@starmark.net

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Vortex-Induced VibrationsIntroduction

• Offshore Drilling, Production, and Export Riser Systems

• Interaction Between Fluid Forces and Riser Motions

• Ultimate Solution

– Numerical simulation of the fluid flow and riser’s response

– Fluid and riser are treated as a single dynamical system

– Formidable task, high Reynolds number and long riser

• Reduced-Order Model

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Objectives

• Develop a practical and reliable engineering method for the prediction of Vortex-Induced Vibrations (VIV) on offshore slender structures• Develop technical breakthrough in the basic understanding and calculation of VIV and Fluid-Structure Interaction (FSI) for offshore slender structures, such as vertical risers, flexible risers, steel catenary risers, tendons, mooring lines, pipelines, etc• Develop software modules to calculate and simulate VIV on marine slender structures, including hydrodynamic coefficients and fatigue damage • Calibrate theoretical calculations with (a) existing data from participants, (b) new laboratory measurements, and (c) offshore measurement programs • Stimulate worldwide academic and industry research in the VIV area • Train a new cadre of undergraduate and graduate students in the VIV area for possible research and employment

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Deliverables

• Software modules to calculate and simulate VIV on marine slender structures, including hydrodynamic coefficients and fatigue damage

• Technical papers and documents

• Short courses, seminars, and discussion of the project results

• Consulting expertise

• Hold international conferences on VIV

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Project Philosophy

• Focus recent breakthroughs in – CFD: RANS, LES, DNS – Laboratory and field measurements– Nonlinear dynamics and control – Generation of design models using identification techniques – Structural dynamics – High-order spectral methodsto understand and quantify the VIV problem

• Execute the project in phases that are dependent on participants’ technical input and funding levels • Encourage VIV experts to participate and to share knowledge in an effort to stimulate worldwide research

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Organization

• The project will be directed by the Virginia Tech Nonlinear Vibrations and Fluid Mechanics Laboratories

• An advisory/steering committee representing participating organizations

• Joint-Industry Project (JIP) participants • The project liaison is Starmark Offshore Inc. (SOI)

• Other experts and specialists

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Approach

• Use detailed fluid-structure-control simulations to generate a database that will be used to develop and calibrate finite-degree-of- freedom models for the design and analysis of VIV problems• Combine

– Time Histories of Lift, Drag, Motion Obtained by• CFD (RANS, LES, DNS)

• Finite Elements

• Full scale and model scale experiments

• Field Measurements

– Nonlinear Dynamics– Higher-Order Spectral Methods– Nonlinear Identification Techniques

• Validation - Physics

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Example of Methodology Lift and Drag Models

• Lift-wake oscillator model – Hartlen and Currie (1970)

– Lift represented by the Rayleigh equation

• Currie and Turnball (1987)

– Drag represented by the Rayleigh equation

• Kim and Perkins (2002)

– Coupled van der Pol Equations for both lift and drag

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Lift and Drag Model for a Stationary Cylinder in a Uniform Flow

• RANS solutions of the flow field

• Higher-Order Spectral Moments

– Amplitude and phase Information

• Perturbation Techniques

– Approximate solutions

• Parameter identification in the governing equations

• Validation-Physics

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Numerical Simulation - Velocity Vectors

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Numerical Simulation - Velocity Vectors

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Numerical Simulation - Vorticity

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Lift and Drag Spectra

•Lift frequency at vortex shedding•3f in lift spectra•2f and 4f in drag spectra

Flutter

Lift Drag

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Lift Modeling & Approximate Solution

Rayleigh equation:

Van der Pol equation:

2 2 0s v vl l l l l

32

1cos( ) cos(3 3 )

32 2v

s ss

l a a

2 3 0s r rl l l l

3 1cos( ) cos(3 3 )

32 2r s

s sl a t a t

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Phase Measurement with Auto-Trispectrum

*1lim ( ) ( )xx T

P E X f X fT

• Auto-Power Spectrum:

• Auto-Trispectrum:

Phase of auto-trispectrum can be used to determine whether the Rayleigh or the van der Pol equation should be used to model the lift.

* * *

s s

1lim ( ) ( ) ( ) ( )

where

for

Phase of auto-trispectrum (3 ) 3 ( )

xxxx l k i jT

l k i j

k i j

T E X f X f X f X fT

f f f f

f f f f

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Lift CFD Solution

1 3cos( ) cos(3 )s sl a a

1(3 ) 3 ( )

2s s

Trispectrum representation of the steady-state lift

where

Therefore, the lift should be modeled with the van der Pol equation

2 2 0s v vl l l l l

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Approximate Solution of the van der Pol Equation

2 2 0s v vl l l l l

32

1cos( ) cos(3 3 )

32 2v

s ss

l a a

31 1

2 8v va a a

Van der Pol Equation

Solution

where

Then

2( )

42

v

v vt c

v v

a ae

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Identification

1 3cos( ) cos(3 )s sl a a

3

1 3 22 and

32v v

v s

aa a a

CFD

Approximate Solution of van der Pol Equation

Therefore

Solving these equations yields2

2313

1

32 1and

4s

v v v

aa

a

32

1cos( ) cos(3 3 )

32 2v

s ss

l a a

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Trispectrum of CFD Steady-State Lift

Table 1: Lift parameters as a function of the Reynolds Number.

Re f a1 a3 200 0.193 0.6184 0.0044

1,000 0.2295 1.205 0.039 2,000 0.2368 1.394 0.052

10,000 0.2391 1.793 0.049 20,000 0.2368 1.728 0.055 40,000 0.2510 1.465 0.040

100,000 0.2538 1.056 0.021 1,000,000 0.2550 1.321 0.033

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Lift Modeling

The van der Pol equation gives the right phase relation for modeling the lift

Re = 20000 Re = 100000

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Drag Modeling

Drag Spectra have components at 2 f and 4 f and a very small component at f

2 2is proportional toeither or ord l l ll

* *1lim (2 ) ( ) ( )dll T

B E D f L f L fT

3

2

Therefore

Cross-Bispectrum

therefore21

1 221

2m

kd d k l k l

a

Because the phase of the cross-bispectrum is

2where is verysmallk

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Identified Drag Parameters

Re dm k1 k2

200 1.1896 0.0389 -0.0006

1000 1.2900 0.139 0.00000

2000 1.3600 0.175 0.00000

10000 1.5600 0.060 -0.0045

20000 1.435 0.067 -0.0068

40000 1.3200 0.0786 0.00000

100000 0.9650 0.0696 -0.0053

1000000 0.9708 0.0871 -0.0000

Table 2: Drag parameters as a function of Re

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Drag Modeling

Re = 20000 Re = 100000

211 22

1

2m

kd d k l k l

a

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Validation - PhysicsLift Spectra

CFD Model

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Validation - PhysicsDrag Spectra

CFD Model

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Validation - PhysicsLift - Drag Linear Coherence

CFD Model

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Validation - PhysicsLift - Drag Cross-Bicoherence

CFD Modelin liftdrag)

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Validation - PhysicsLift Auto-Tricoherence

CFD Model

in lift

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Technical Plan

• A Stationary Cylinder in a Uniform Flow Field– Collect CFD and experimental data for many Reynolds

numbers– Compute the shedding frequency and the amplitudes of the

first and third harmonics using the FFT– Compute the mean and amplitudes of the harmonics in the

drag using the FFT– Use the methodology described earlier to build an

extensive database for • the shedding frequency • the parameters for the van der Pol oscillator• the mean drag• the coefficients in the drag formula

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An Infinite Cylinder Oscillating Transversely to a Uniform Flow

• Specify a transverse harmonic motion of the form

• Modified van der Pol oscillator

• Select the Reynolds number, • Run CFD code, calculate the flow field, including the

pressure• Integrate pressure to calculate lift and drag coefficients• Calculate the spectra of the lift and drag using the FFT• Inspect the spectra to ascertain whether the F is a

linear or a nonlinear function

cos( )y A t

2 2 ( , , )s v vl l l l l F y y y , andA

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An Infinite Cylinder Oscillating Transversely to a Uniform Flow-Continued

• Calculate the different orders of spectral moments between y

and l to determine the function F• Solve the modified van der Pol oscillator

• Compare the results with the CFD results to identify the

coefficients • Compare the spectrum of the drag coefficient with that of the lift

to ascertain how to modify the unforced drag model• Repeat the process for many Reynolds numbers and amplitude

and frequency of the cylinder velocity

2 2 ( , , )s v vl l l l l F y y y

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Technical Plan-Continued

• An infinite cylinder oscillating in-line to a uniform flow• Interaction of transverse motion of a cylinder with a uniform flow• Interaction of in-line motion of a cylinder with a uniform flow• Interaction of transverse and in-line motions of a cylinder with a

uniform flow• Finite-element method analysis coupled with local van der Pol

oscillators • Reduced-order model with local van der Pol models • Correlation of vortices in a sheared flow• Multimode interactions in flexible risers

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Summary of Tasks

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A 96-Node Cluster for Computation and Visualization

• Typically simulations and visualizations are run independently– A simulation run gathers data, which is stored, processed and then

visualized on a target system such as a CAVE facility

– Simulation errors are expensive. Simulation runs last weeks and if the visualization system detects an error, the simulation has to be re-run

• Recommendation: Combine simulation and visualization into a single cluster system– This permits real-time visualization of data from the simulation.

– A human-in-the-loop interface can be used to detect errors and correct them in real-time

– This enables run-time steering of complex software systems as opposed to the “watching a movie” environment presented by current visualization technologies.

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Terascale Images - G5s in Racks