1. 1 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. Sexton Starmark Offshore Inc. Danville, VA e-mail: sexton@starmark.net

2. 2 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

3. 3 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

4. 4 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

5. 5 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

6. 6 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

7. 7 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

8. 8 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

9. 9 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

10. 10 Numerical Simulation - Velocity Vectors

11. 11 Numerical Simulation - Velocity Vectors

12. 12 Numerical Simulation - Vorticity

13. 13 Lift and Drag Spectra Lift frequency at vortex shedding 3f in lift spectra 2f and 4f in drag spectra Flutter Lift Drag

14. 14 Lift Modeling & Approximate Solution Rayleigh equation: Van der Pol equation:

15. 15 Phase Measurement with Auto-Trispectrum 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.

16. 16 Lift CFD Solution Trispectrum representation of the steady-state lift where Therefore, the lift should be modeled with the van der Pol equation

17. 17 Approximate Solution of the van der Pol Equation Van der Pol Equation Solution where Then

18. 18 Identification CFD Approximate Solution of van der Pol Equation Therefore Solving these equations yields

19. 19 Trispectrum of CFD Steady-State Lift

20. 20 Lift Modeling The van der Pol equation gives the right phase relation for modeling the lift Re = 20000 Re = 100000

21. 21 Drag Modeling Drag Spectra have components at 2 f and 4 f and a very small component at f Therefore Cross-Bispectrum therefore Because the phase of the cross-bispectrum is

22. 22 Identified Drag Parameters Re d m k 1 k 2 2001.18960.0389-0.0006 10001.29000.139 0.00000 20001.36000.175 0.00000 100001.56000.060-0.0045 200001.4350.067-0.0068 400001.32000.0786 0.00000 1000000.96500.0696-0.0053 10000000.97080.0871-0.0000 Table 2: Drag parameters as a function of Re

23. 23 Drag Modeling Re = 20000Re = 100000

24. 24 Validation - Physics Lift Spectra CFDModel

25. 25 Validation - Physics Drag Spectra CFDModel

26. 26 Validation - Physics Lift - Drag Linear Coherence CFDModel

27. 27 Validation - Physics Lift - Drag Cross-Bicoherence CFDModel  in lift  drag)

28. 28 Validation - Physics Lift Auto-Tricoherence CFDModel  in lift 

29. 29 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

30. 30 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

31. 31 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

32. 32 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

33. 33 Summary of Tasks

34. 34 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.

35. 35 Terascale Images - G5s in Racks