Transcript Time Series - Starmark Offshore, Inc.

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: [email protected]
R. M. Sexton
Starmark Offshore Inc.
Danville, VA
e-mail: [email protected]
1
Vortex-Induced Vibrations
Introduction
• 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
2
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
3
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
4
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 methods
to 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
5
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
6
Approach
• Use detailed fluid-structure-control simulations
to generate a database that will be used to
develop and calibrate finite-degree-offreedom 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
7
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
8
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
9
Numerical Simulation - Velocity Vectors
10
Numerical Simulation - Velocity Vectors
11
Numerical Simulation - Vorticity
12
Lift and Drag Spectra
Drag
Lift
Flutter
•Lift frequency at vortex shedding
•3f in lift spectra
•2f and 4f in drag spectra
13
Lift Modeling & Approximate Solution
Rayleigh equation:
l   l  r l   r l  0
2
s
3
rs
1
l  a cos(s t   ) 
a cos(3st  3   )
32
2
3
Van der Pol equation:
l   l  v l  v l l  0
2
s
2
v 3
1
l  a cos( s   ) 
a cos(3 s  3   )
2
32 s
2
14
Phase Measurement with Auto-Trispectrum
• Auto-Power Spectrum:
1
Pxx  lim E  X ( f ) X * ( f ) 
T  T
• Auto-Trispectrum:
1
Txxxx  lim E  X ( f l ) X * ( f k ) X * ( f i ) X * ( f j ) 
T  T
where f l  f k  f i  f j
for f k  f i  f j  f
Phase of auto-trispectrum   (3s )  3 (s )
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.
15
Lift CFD Solution
Trispectrum representation of the steady-state lift
l  a1 cos(s )  a3 cos(3 s   )
where
1
   (3s )  3 (s )  
2
Therefore, the lift should be modeled with the van der Pol equation
l   l  v l  v l l  0
2
s
2
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Approximate Solution of the
van der Pol Equation
Van der Pol Equation
l  s2l  v l  v l 2l  0
Solution
v 3
1
l  a cos( s   ) 
a cos(3 s  3   )
2
32 s
2
where
1
1
3
a  v a   v a
2
8
Then
4 v
v
a 
a2
 v ( t  c )
v  e
v
2
17
Identification
CFD
l  a1 cos(s )  a3 cos(3 s   )
Approximate Solution of van der Pol Equation
v 3
1
l  a cos( s   ) 
a cos(3 s  3   )
2
32 s
2
Therefore
v
a1  a  2
v
v a 3
and a3 
32 s2
Solving these equations yields
32 s2 a3
v 
a13
1
and v   v a12
4
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Trispectrum of CFD Steady-State Lift
Table 1: Lift parameters as a function of the Reynolds Number.
Re
200
1,000
2,000
10,000
20,000
40,000
100,000
1,000,000
f
0.193
0.2295
0.2368
0.2391
0.2368
0.2510
0.2538
0.2550
a1
0.6184
1.205
1.394
1.793
1.728
1.465
1.056
1.321
a3
0.0044
0.039
0.052
0.049
0.055
0.040
0.021
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
20
Drag Modeling
Drag Spectra have components at 2 f and 4 f and a very
small component at f
Therefore
2
2
d is proportional toeither l or l or ll
Cross-Bispectrum
1
Bdll  lim E  D(2 f ) L* ( f ) L* ( f ) 
T  T
Because the phase of the cross-bispectrum is
therefore
3

2
2k1 2
d  d m  k1  2 l  k 2 l
a1
where k2 is verysmall
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Identified Drag Parameters
Table 2: Drag parameters as a function of Re
Re
dm
k1
200 1.1896 0.0389
k2
-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
-0.0068
0.067
40000 1.3200 0.0786
0.00000
100000 0.9650 0.0696
-0.0053
1000000 0.9708 0.0871
-0.0000
22
Drag Modeling
2k1 2
d  d m  k1  2 l  k 2 l
a1
Re = 20000
Re = 100000
23
Validation - Physics
Lift Spectra
CFD
Model
24
Validation - Physics
Drag Spectra
CFD
Model
25
Validation - Physics
Lift - Drag Linear Coherence
CFD
Model
26
Validation - Physics
Lift - Drag Cross-Bicoherence
CFD
 in lift  2 (drag)
Model
27
Validation - Physics
Lift Auto-Tricoherence
CFD
Model
   in lift  3
28
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
29
An Infinite Cylinder Oscillating Transversely to a
Uniform Flow
• Specify a transverse harmonic motion of the form
y  A cos(t )
• Modified van der Pol oscillator
l   l  v l   v l l  F ( y, y, y )
2
s
2
• Select the Reynolds number, A, and 
• 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
30
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
l  s2l  vl   vl 2l  F ( y, y, y)
• 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
31
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
32
Summary of Tasks
33
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.
34
Terascale Images - G5s in Racks
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