The document discusses Vortex Induced Vibration (VIV) and the Milan Wake Oscillator Model for modeling VIV in the time domain. It provides background on VIV, including the physics behind it and characteristics. It then describes empirical oscillator models used to model VIV and focuses on explaining the Milan Wake Oscillator Model, which models the wake zone and its effect on a cylinder's oscillation using masses, springs, and dashpots. The model equations are presented and test results comparing it to experiments are discussed, noting some limitations. In conclusion, the document states that VIV analysis has uncertainties and multiple models should be used for load cases.

1. Vortex Induced Vibration (VIV)
Milan Wake Oscillator Model
(Empirical Model - Time Domain)
Alberto Alvino
September 2018

2. Agenda
• Introduction
• Physics behind the VIV
• Main Characteristics of VIV
• VIV Empirical Models – Oscillator Models
• Milan Wake Oscillator Model
• Conclusions

3. INTRODUCTION

4. Introduction
• What is VIV ? VIV are motion induced on
bodies interacting with external fluid flow,
produced by the periodical irregularities on
this flow;
• Why do we need to model VIV? It has been a
primary challenge in the design of deepwater
projects. It can represent around 10% of multi
million dollar project;

5. Introduction
• How is VIV modeled? It can be modeled in the
time and frequency domain. Both option has
its advantage/un-advantage. This presentation
will focus VIV model based on time domain;
• Normally those models require experimental
data, either as input data or to its verification;

6. Introduction
• Some parameters comparison between VIV
models in frequency and time domain:
Domain Type
Comparison Parameters
Analysis
type
Analysis
Time
Consuming
Condition
Type
Experimental
Input Data?
Results
Software
Example
Frequency Linear Short Static Yes
Very
Conservative
Shear 7
Time
Computational
Nonlinear
Long
Dynamic
Not (Require
Validation)
Require
Validation
CFD
Empirical Medium Yes
Less
Conservative/
some time
Under
Conservative
Milan Wake
Oscillator

7. Introduction
• This presentation will focus in the Milan
Wake Oscillator (MWO);
• MWO model is already implemented in the
commercial software Orcaflex;

8. PHYSICS BEHIND VIV

9. Flow Around Static Cylinders
A
B
C

10. Flow Around Static Cylinders
• The flow of a perfect fluid past a cylinder
bifurcates at the front edge of the cylinder
(Point A), where static pressure is a maximum;
• Accelerates to the pressure minimum (Point
B), and decelerates in the presence of the
adverse pressure gradient (Point C);
• The viscous force in the boundary layer, close
to the surface, are the main factor of the
adverse pressure gradient;

11. Flow Around Static Cylinders
• The negative pressure separates the boundary
layer from the surface, generating: 1) vortex in
both side of the body (cylinder) and 2) the
wake zone;

12. Flow Around Static Cylinders
• Those vortex appears in alternate (oscillatory)
way after the destabilization of the flow due
mainly to the surface roughness of the
cylinder;
• In fluid dynamics, a wake is the region of
disturbed flow (usually turbulent) downstream
of a cylinder moving through a fluid, caused
by the flow of the fluid around the cylinder;

13. Force Around Cross Flow Static
Cylinder
• The vortex, generated in oscillatory way
following the shedding frequency, makes the
pipes move in in-line (IL) and cross flow (CF)
direction to the current;

14. • Total Force = Drag Force (FD)+
Force Around Cross Flow Static
Cylinder

15. Force Around Static Cross Flow
Cylinder
• The FD and FL are
i n f l u e n c e d b y t h e
behavior of the wake
zone;
• The oscillation of lift
force occur at the vortex
shedding frequency and
oscillation in drag force
occur at twice the vortex
shedding frequency;

16. MAIN CHARACTERISTIC OF VIV

17. VIV – Main Definitions
• This presentation will not cover in detail VIV
theory, therefore, it assume the reader has the
knowledge of the basic VIV concepts such as:
• Reynolds number
• Reduced velocity
• Shedding frequency
• Natural frequency
• Amplitude oscillation
• Strouhal number
• Lift coefficient

18. Simplified VIV Models Test for
Complex Systems
• Reproduce real VIV
phenomenon on test
laboratory is a challenger
task, due the complexity
of the phenomenon;
• To o v e r c o m e t h i s
complexity, simplified
VIV model test has been
used to simulate complex
systems;

19. Complication on Experimental VIV
Test
• Deepwater riser can have a length-to-diameter
ration greater than 5000, Spar and semi-
submersible platform operate in the Reynolds
number regime 107 or greater;
• These massive sizes, and the non-dimensional
parameter associated with it, make it difficult
to build and test models that effectively
represent the actual structure;

20. Complication on Experimental VIV
Test
• Those simplified test models bring first insight
about the VIV phenomenon, helping in the
decision to carry out more complex/realistic
test;
• In the following slides, experimental results of
simplified VIV tests models will be showed, in
order to see the main characteristics of the VIV
phenomenon;

21. Some VIV Experiments Results

22. Some VIV Experiments Results

23. U1*
Self Limiting
U2*
Main Characteristics of VIV
• The nature of
self-exited;
• Self-limiting;
• Oscillatory
nature;

24. VIV EMPIRICAL MODELS
OSCILLATOR MODELS

25. VIV Empirical Model
• Empirical model does not reproduce the
physical phenomenon, instead try to reproduce
the main characteristics of VIV: self-limiting,
self-excited and oscillatory;
• Model based on experimental results, mainly
based on static or oscillating cylinder;

26. VIV - Oscillation Model
• The one-dimensional VIV in the cross flow
direction is modeled a simple linear oscillator,
(spring and dash pot);

27. VIV - Oscillation Model
• Due to the action of the flow fluid, the cylinder
(m) will move in oscillate way according the
values of stiffness (k) and dashpot (c);
• The quantification of k and c is based on
experimental test results;

28. VIV - Oscillation Model
• The 2 key quantities to characterize VIV are
Amax and lock-in range

29. Oscillation Model Types
• Oscillation model can be classified based how
the fluid force (Ffluid), from the wake zone, is
applied on the cylinder in the lift direction;
• Mainly, it consider the part of the fluid force
(F) that exceeds the conventional inviscid
added mass effect:

30. Oscillation Model Types
• Type A: where F is independent of y, and
therefore only depends on time, F (t);
• Type B: Fluidelastic system models , where F
depends on y, denoted as F [y(t), t];

31. Oscillation Model Types
• Type A and Type B formulation model have
not relation to the physics of wake as global
modes;
• Force in VIV are results of the wake dynamics
that follow specific rules;
• Those limitation have led to the development
of models whereby the fluid force is the results
od the wake dynamic, itself influenced by the
cylinder motion;

32. Wake Oscillator Model
Type C: Coupled system models, where F depends
on another variable related to the wake dynamics,
say q, the evolution of which depends on y. Here,
we have F [q(t), t] and the effect of y on the
evolution of q is taken in the most general form
G[y(t), t];

33. Wake Oscillator Model
• The Wake Oscillator model formulation may be
represented by two equations, one for the cylinder
variable y(t):

34. Wake Oscillator Model
• Where F(q) define the effect of the wake on
the cylinder, and another equation for the wake
variable q(t):
Where, W[q(t)] defines the dynamic of the
free wake and G(y,…) defines the effect of the
cylinder on the wake;

35. Wake Oscillator Model
• Several formulation exists for F(q), G(y,…),
W[q(t)] and q(t):
• Bishop & Hassan
• Hartlen and Currie
• Facchinetti, de Langre & Biolley
• Tamura and G. Matsui
• Milan Model (Falco, Fossati and Resta)
• Iwan and Blevins

36. MILAN WAKE OSCILLATOR
MODEL

37. Milan Wake Oscillator (MWO)
• Based on work of Falco, Fossati and Resta
(from Politecnico di Milano), 1999;
• At each node, the MWO models the effect of
vortex shedding (wake zone) on a cylinder
(ms) oscillating in cross flow direction by the
action of a mass connected (mo) to the cylinder
with a system of non-linear spring (ki) and
dash pots (ci);

38. Milan Wake Oscillator
x
y
Structure
Interface
Oscillator
k, c: cylinder linear
stiffness and damping
ko, co: Oscillator non-linear
stiffness and damping
ki, ci: Interaction cylinder-
oscillator non-linear
stiffness and damping

39. x
y
Structure
Interface
Oscillator
Scheme at
one FE node Scheme at global FE nodes
Milan Wake Oscillator

40. Milan Wake Oscillator
x
y
Structure
Interface
Oscillator
y, x: displacement of
cylinder and oscillator
with respect to their rest
position;
The equation of motion,
deducted from Newton’s
second law:

41. Milan Wake Oscillator
x
y
Structure
Interface
Oscillator
Fm is the transverse
component of Morrinson
type force;
Fi is the resultant of
forces on the cylinder at
its interface with the
oscillator (wake zone);
Fo is the force on the
oscillator

42. x
y
Structure
Interface
Oscillator
Milan Wake Oscillator
The non-linearities in Fi
and Fo are introduced by
a third order model in the
stiffness and damping
term:
Where o: oscillator l: linear
i: interface n: Non-linear

43. x
y
Structure
Interface
Oscillator
Milan Wake Oscillator
T h e m a s s o f t h e
oscillator (mo) is chosen
such as its frequency
c o r r e s p o n d t o t h e
Strouhal frequency, fs,
when the cylinder is not
moving:

44. x
y
Structure
Interface
Oscillator
Milan Wake Oscillator
The stiffness and damping
coefficients are made non-
dimensional:

45. x
y
Structure
Interface
Oscillator
Milan Wake Oscillator
Falco at al. carried out
experimental test of the
transverse VIV linearly-
supported cylinder;
They found the values of
t h e n o n - d i m e n s i o n a l
stiffness and damping
coefficients:

46. Milan Wake Oscillator
Comparison Results
The oscillation frequency
does not lock onto the
natural frequency;
Do not predict the lower
branch of the cross flow
displacement;

47. Milan Wake Oscillator
Comparison Results

48. (*)
Milan Wake Oscillator
Comparison Results
(*) “An Investigation on the Effect of Current Directionality on Riser Vortex –Induced
Vibration”, Satheesh Manavankath and Shan Huang, 1st International Conference on Floating
Structures for Deepwater Operation

49. CONCLUSION
• VIV analysis is not a well-developed field, so
some spread in results is not uncommon;
• All models have their own weaknesses and
strengths;
• Recommend running more than one model
for any given load case;