Presentation for Vortex Induced Vibration under Viscoelastic support

1. OUTLINE
1
3.
Conclusions
and Future
Work
2.
Experimental
viv on a SLS
viscoelastic
arrangement
1.
Transverse
VIV of a
circular
cylinder on
nonlinear
viscoelastic
support

2.  Motivation and literature gap
 Problem Formulation
 Validation
 Results and discussion
 Conclusion
2
Transverse VIV of a circular cylinder on a non linear viscoelastic support
1

3. 3
• Electromagnetic energy harvesting
• Marine risers
• Buildings
• Heat exchangers
Dejong et al. 2014
• Most work involves VIV on kelvin –voigt base
• Structural equation is second order ode
• Amplitude decreases with structural damping
• VIV on spring damper arrangement similar to standard linear solid (SLS)
with one spring non linear is rare
• Structural equation is third order ode
• Amplitude non-monotonic with structural damping

4.  Re=150, D =1
 Incompressible fluid
 Spectral element technique for spatial discretisation with element
resolution 6 × 6
 Time step = ∆𝑡=0.0125
4
VIV under non linear spring damper
base

5.  Reduced mass = 2.546
 𝑅 =
𝑘𝑛
𝑘
, ξ=
𝑐
2 𝑘𝑚
, 𝜆 = −𝐷/ −𝑘/𝑎
 The ode defining structural motion
 For linear 𝜆 = 0
5

6. 6
Case 1 𝜁 = 0 or R =0, 𝜆 = 0
𝑋 + 4𝜋2
𝑓𝑛
2
𝑋 =
2 𝐹
𝜋𝑚
𝑓𝑛 = 1/𝑈𝑟, (𝑈𝑟 = 𝑈𝑟𝑒𝑓/𝐷𝑓𝑛)
Case 2 ζ = ∞ , R =1, 𝜆 = 0
𝑋 + 4𝜋2( 2𝑓𝑛)2𝑋 =
2 𝐹
𝜋𝑚
Freq 𝑓2𝑛 = 2𝑓𝑛

7. 7
 Re = 150
 𝜁 = 0
 Reduced mass = 2.546
 Natural frequency of linear
spring = 0.222

8. 8
(a) Amplitude, (b) Peak lift coefficient, (c) Normalized frequency
Location of peak amplitude
non-monotonic with damping
𝜁 = 0.001, 𝑈𝑟 = 8.4
𝜁 = 1, 𝑈𝑟 = 7.2
𝜁 = 10, 𝑈𝑟 = 8.0
Range of nearly constant
peak lift non-monotonic with
𝜁
𝜁 = 0.001, 4.6 < 𝑈𝑟 < 8.4
𝜁 = 1, 5.3 < 𝑈𝑟 < 6.2
𝜁 = 10, 4.4 < 𝑈𝑟 < 6.8
Lock-in range and
frequency is non
monotonic
𝜁 = 0.001, 𝑓∗
≈ 0.7
𝜁 = 0.1, 𝑓∗ ≈ 1
𝜁 = 10, 𝑓∗
≈ 0.8

9. 9
Based on the actual frequency
of non linear system
Based on the natural frequency of
linear spring, 𝑈𝑟 =
𝑈∞
𝐷𝑓𝑛
 Effective non linearity non
monotonically vary with
damping
 Effect of damping more
prominent for high value of 𝜆

10. 10
characteristics similar to linear system
Hardening is more effective

11. 11
 Softening spring collapse to
linear system
 Hardening spring effective non-
linearity starts at 𝑈𝑟 = 3.2, end
shifted right with 𝜆
 Higher the amplitude more the
nonlinearity

12. 12
Increasing strength of softening,
decreases amplitude
 Increasing strength of hardening,
increases the amplitude
 The peak amplitude shifted right

13. 13
Initial: 2 < 𝑈𝑟< 3.2
𝜆 = 0, 𝑈𝑝𝑝𝑒𝑟: 3.3 < 𝑈𝑟 <3.9
Lower: 4.0 < 𝑈𝑟 < 7.5
desynchronization: 𝑈𝑟 > 7.5

14. 14
No upper branch as missing
multiple frequency in the spectra
of vibration frequency
𝝀 = −𝟏
𝝀 = −𝟏. 𝟔

15. 15
Upper: 3.6 ≤ 𝑈𝑟≤ 4.2
𝝀 = 𝟏
𝝀 = 𝟏
Upper: 3.6 ≤ 𝑈𝑟≤ 4.8

16. 16
Upper: 3.6 ≤ 𝑈𝑟≤ 5.2
𝝀 = 𝟐
Upper: 3.6 ≤ 𝑈𝑟≤ 5.4
𝝀 = 𝟒

17. 17
Stronger the hardening of spring wider the reduced velocity range for peak lift
coefficient

18. 18
Phase difference shift left with stronger
softening
Phase difference shift right with stronger
softening

19. 19
Behavior comparable to 𝜁 =
0.001
Behavior comparable to linear
system except for high
nonlinearity strength

20. CONCLUSION
 2D model to study VIV response using circular cylinder
 Cylinder supported by spring damper arrangement similar to SLS
model with one spring cubic nonlinearity
 Hardening is more effective than softening
 Effective nonlinearity is non monotonic with damping ratio
 Amplitude decreases with decrease of 𝜆 (𝑠𝑡𝑟𝑜𝑛𝑔𝑒𝑟 𝑠𝑜𝑓𝑡𝑒𝑛𝑖𝑛𝑔)
 Amplitude increases with increase of 𝜆 (𝑠𝑡𝑟𝑜𝑛𝑔𝑒𝑟 ℎ𝑎𝑟𝑑𝑒𝑛𝑖𝑛𝑔)
 Branching of VIV is affected by nonlinearity
 Stronger the hardening of spring, wider the reduced velocity range
for peak lift
20

21.  Motivation
 Problem Formulation
 Linear viscoelastic parameters
 Validation
 Results and discussion
21
Experimental VIV on a viscoelastic arrangement
2

22. MOTIVATION
Courtesy: Elena Blokhina
 Renewable energy harnessing
Vortex induced vibration aquatic clean
energy
Extending spring damper arrangement similar to standard linear solid
(SLS)model of viscoelasticity
Limited study of SLS arrangement is available in literature
OBJECTIVE
22

23. 23

24. 24
 Three experiments performed corresponding to different
springs arrangement
 Three types of natural frequency generated
1. Lower frequency, 𝑓𝑛 = 0.326, 0.680
2. Medium Frequency, 𝑓𝑛 = 0.555, 0.975
3. Higher frequency, 𝑓𝑛 = 0.555, 1.110
2DOF system:- two natural frequencies: First mode , second mode

25. 25
Lower frequency: 𝒇𝒏 =
𝟎. 𝟑𝟐𝟔, 𝟎. 𝟔𝟖𝟎
 Amplitude of A smaller than B
 A, B: same vibration frequency
 lock-in 6.8 ≤ 𝑈∗
≤
11, 𝑓𝑖𝑟𝑠𝑡 𝑚𝑜𝑑𝑒
 lock-in 𝑈∗
> 12, second mode
 Initial: 4 ≤ 𝑈∗ ≤ 5
 Upper: 5 ≤ 𝑈∗
≤ 11
 Lower: 12 ≤ 𝑈∗ ≤ 18
At 𝑈∗
< 11 , amplitude decreases which again increases at 𝑈∗
≈ 11.5 during
switching of frequency mode.

26. 26
Medium frequency: 𝒇𝒏 = 𝟎. 𝟓𝟓𝟓, 𝟎. 𝟗𝟕𝟓
 Amplitude of A smaller than B
and same as lower frequency
 A, B: same vibration frequency
 lock-in 6.8 ≤ 𝑈∗ ≤ 11, 𝑓𝑖𝑟𝑠𝑡 𝑚𝑜𝑑𝑒
 lock-in 𝑈∗
> 12, second mode
 Initial: 4 ≤ 𝑈∗ ≤ 5
 Upper: 5 ≤ 𝑈∗
≤ 11
 Lower: 12 ≤ 𝑈∗ ≤ 14
 Desynchronisation: 𝑈∗
> 14
 Shortening of lower branch
range

27. 27
Higher frequency: 𝒇𝒏 = 𝟎. 𝟓𝟓𝟓, 𝟏. 𝟏𝟏𝟎
 Amplitude of B is smaller than
previous two cases
 A, B: same vibration frequency
 lock-in 6.8 ≤ 𝑈∗ ≤ 11, 𝑓𝑖𝑟𝑠𝑡 𝑚𝑜𝑑𝑒
 lock-in 𝑈∗
> 12, second mode
 Initial: 2 ≤ 𝑈∗ ≤ 5
 Upper: 5 ≤ 𝑈∗
≤ 11
 Lower: 12 ≤ 𝑈∗ ≤ 14
 Desynchronisation: 𝑈∗
> 14.4
 Shortening of lower branch
range

28. 28
 During switching of mode of natural
frequency, phase difference shows bump
 At desynchronization region phase difference
decreases

29. CONCLUSION
 2DOF with two masses (A,B)
 One mass (A) inside fluid flow
 SLS model arrangement for spring damper
system
 Amplitude of A same for different value of
natural frequency
 Amplitude of B is greater than A
 For lower frequency, desynchronization was
missing
 For medium frequency early arrival of
desynchronization
 Results indicate the behavior of a 2DOF VIV
can be tuned by modifying the damping
29

30. THANK
YOU
30