Reading Digest -VIV

1.1 2019 Bin Qin,JFM, Free vibrations of two tandem elastically mounted cylinders in crossflow

Questions:

how does the initial state of a cylinder affect the vibration of the the other?

under what conditions does the vibration amplitude of a cylinder exceed that of the other?

how are the vibrations of the cylinders sustained?

is there any difference in the characteristics of vortices originating from different cylinders?

how do they contribute to the work done on the cylinders?

vibration constraint: only laterally

methods: exp, Laser vibrometer, hotwire, pressure scanner, PIV

quantities of interest:

cylinder vibration, frequency responces,

surface pressures, shedding frequencies, flow fields

variables spacing ratio L/D = 1.2-6.0 where L is cylinder centre-to-centre distance D is the cylinder diameter

f _v: vortex frequency, which is obtained from

the power spectral density function of the streamwise velocity obtained at (X/D, y/D, z/D) = (4,1,0)

reduced velocity, U_r = 3.8 -47.8

results

Four vibration regimes
increasing or spreading rapidly
a higher reduced velocity, U_r, than that at which the vortex

excitation occurs

excitation: [n] 1. (technical) the application of energy to a particle, objects, or physical system.
(no term): (physics) the process in which an atom or other particle adoopts a higher energy state when energy is supplied

e.g. thermal excitation

VE: vortex excitation, refers to the occurrence of strong vibrations

where the natural vortex shedding frequency, f_v, conincides with the natural frequency, fn, of the fluid-cylinder system

1.2 khalak and Williamson,1997, JFS

https://doi.org/10.1006/jfls.1997.0110 1D viv of a elastically mounted rigid cylinder with very low mass and damping

title: DYNAMICS OF A HYDROELASTIC CYLINDER WITH VERY LOW MASS AND DAMPING

new results: ? setups:

NEW input variables:

Very low m*ξ

Q?

what is the dominant response frequency during excitation
lock-in region
A* vs. U_r

exp. U* = U/f_n D, where f_n is the natural frequency of the structure in water

Flow feature Re = 3900

cylinder-support system

low mass-damping ratio
flow induced vibration

The flow-induced vibration response is governed by the combined mass-damping ratio m ∗ ζ , not by the individual values m ∗ and ζ (Govardhan & Williamson 2006).

why is it interesting/important?

background: subsea pipelines, submarine tunnel, subsea cable

undersea pipe is subjected to vortex induced vibration

1.3 Konstantinidis 2013 – added mass in relative frame of reference

contribution:

derived a added mass for a circular cylinder in an inviscid potential flow at relative frame of reference.
Eq 4.4, new term, G(t;α)
difference compared to fixed frame of reference

debate: the added mass has significant effect on the VIV of cylindrical structures when density of the sturcture is comparable with the fluid density.

a virtual experiment reveals that the classical method to this problem leads to a paradox.

section 2 reals that some fundamental aspects of the added mass notation may have been ignored in the classical formulation

Results in other's research:

added mass can be properly defined in both ideal inviscid and real

viscous flows, but exact evalutions can be made only in the former case

inviscid flow added-mass effects are inherent in viscous flows,
the correct way to evaluate added masses is

in a relative frame of reference moving with the body in a fluid otherwise at rest far from the body.

increase quadratically for α < 0.5

http://dx.doi.org/10.1098/rspa.2013.0135

1.4 Sarpkaya, 2014 JSF review

Preliminary remarks
Nomenclature
Introduction
Added mass and virtual mass
Governing and influencing parameters
Linearized equations of the self-excited motion and their limitations
Unsteady force decomposition
Limitations of forced and free vibrations
Experiments with forced oscillations
The wake and VIV
Self-excited vibrations
VIV at high Re: facts, extrapolations, and conjectures
Numerical simulations
Conclusions and recommendations

1.5 Williamson, 2004, JFM

New in setup:

2DOF for same mass ratio in x, and y direction

Q: How does the inline vibration influence the dynamics of the VIV?

Results: observed new Supper-upper branch at low mass-damping ratio(m*<6) for 2 DOF, same damping ratio cylinder

for m* >6, slight difference between 2DOF and 1DOF case
2T mode (Fig 21)

1.6 Williamson, 2004, annu. Rev. Fluid Mechanics

1.7 khalak and Williamson,1997, JFS

https://doi.org/10.1006/jfls.1997.0110 1D viv of a elastically mounted rigid cylinder with very low mass and damping

title: DYNAMICS OF A HYDROELASTIC CYLINDER WITH VERY LOW MASS AND DAMPING

new in setups:

low m*ξ ( one order lower than wiliamson 1996)

conclusion:

m*ξ ↓ , then, A*, C_D, C_L ↑
new upper branch only for low m*
higher max A* than that of Feng
f* is higher than 1 in the lock-in region
C_d_fluctuation is 100 of C_d_fixed
- C_d_fixed: drag coefficient of fixed cylinder
C_l_fluctuation is 6 times of C_l_fixed

fig/low_mass_damping_effects_williamson_1997.pdf Q?

what is the dominant response frequency during excitation
lock-in region
A* vs. U_r

exp. U* = U/f_n D, where f_n is the natural frequency of the structure in water

1.8 zhao, 2014, JFS, 3D numerical simulation of viv of an elastically mounted rigid circular cylinder in steady current

new: effects of Re on A* and 3D effects

3D vs 2D comparison –>> Fig.7 fv/fn from 2D is higher than 3D results in the lock-in region (6<Ur<11)

setups:

1DOF,M*=2, Re=(150, 1e3), Ur=(2,12)

1.9 y. zhou, 2001, JFM, free vibrations of two side-by-side cylinders in a cross-flow

free vibration of two side-by-side cylinders with fixed support at both ends placed in a cross-flow were exerimentally investigated.

input variables: T/D ratios, 3.0, 1.7, 1.13 where T is the centre-to-centre cylinder spacing, and D is the diameter.

1.10 邓小龙 2015 zju, 基于PC Newmark-β法的流固耦合涡激振动数值模拟

ch3, 2d rigid cylinder

flexiable

1.11 zhao, 2011, Numerical simulation of two degree-of-freedom vortex-induced vibration of a circular cylinder close to a plane boundary.

new: effects of the bounce back coefficient and the reduced velocity on the vibration of the cylinder

input variables:

bouonce back coeff
reduced velocity

e/D = 0.002, 0.3

M* = 2.6

Re (1e3, 1.5e4)

1.12 2017, Qin, JFM, Two tandem cylinders of different diameters in cross-flow: flow-induced vibration

New in setup: effect of d/D on vibration, especially for d/D < 1

initiation of vibration

the role of the added amss, added damping and energy transfer play in generating the vibration?

? would the wake strucuture mutate when the A grows?

variables: cylider distance,L, fixed/vibrating cylinder

setups:

front cylinder, fixed, back, viv

Y motion only

L/D 1.2-6 Ur: 3.8-47.8 M*: 275 ξ: 0.0021 M*ξ =0.58

conclusions:

four regions based on L/D

1.12.1 outline in results

3.1 Dependence of downstream cylinder vibration on L/d and d/D 3.2. Dependence of vortex shedding frequencies on L/d and d/D 3.3. Classification of structural vibration and flow structure 3.3.1 bistable flow regime 3.3.2 violent vibration regime 3.4 pressure and force on the vibrating cylinder 3.4.1 work done 3.4.2 added mass, added damping, and energy transfer model 3.4.3 energy transfer during stable vibrations 3.5 vibration generation mechanism 3.5.1 Force and vibration characteristics in the initiation stage 3.5.2 Energy transfer and added mass

1.13 williamson 2004 Vortex-induced vibrations – ANNUAL REVIEW OF FLUID MECHANICS

review

VIV: vortex-induced vibration
norminally: (adverb) in name only, and not in reality

e.g. he was nominally in charge of the company

at a cost that is very small and much less than the normal cost

e.g. tickets are nominally priced questions

(a) What is the maximum possible amplitude attainable for a cylinder undergoing VIV, for conditions of extremely small mass and damping? (b) Under what conditions does the classically employed mass-damping parameter collapse peak-amplitude data? What is the functional shape for a plot of peak amplitude versus mass-damping? (c) What modes of structural response exist, and how does the system jump between the different modes? (d) What vortex dynamics give rise to the different body response modes? (e) What generic features can be discovered that are applicable to all VIV systems? To what extent are the enormous number of studies for bodies restricted to motion transverse to the flow, relevant to other, more complex VIV systems? ( f ) Because almost all of the studies of VIVs are at low and moderate Reynolds numbers, how do these results carry across to high Reynolds numbers?

1.14 刘爽 (T)- 低雷诺数下并列圆柱涡激振动的数值模拟及其机理研究

tianjing Uni. supervisor: :及春宁

solver: Cgles

methods: lES, immersed boundary method

goal: vortex induced vibration aquatic clean energy

1.15 ref

annual Review

Willamson, cornel,

Bearman, Imperial colleage

Trantafyllou MIT

Mittal (numerical modeling)

A critical review of the intrinsic nature of vortex-induced vibrations T. Sarpkaya*

papers http://web.mit.edu/shear7/papers.html

1.16 slides

viv by prof. A. H. Techet http://web.mit.edu/13.42/www/handouts/reading-VIV.pdf

1.17 textbook

Blevins 1990

M.M.Zdravkovich, flow around circular cylinder vol1 fundamental

ch8, Sumer BM, FredsÃ¸e J. 1997. Hydrodynamics around Cylindrical Structures. Singapore: World Sci.

Hamidzadeh, Hamid R., and Reza N. Jazar. Vibrations of thick cylindrical structures. New York: Springer, 2010.

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