viv ii notes
TRANSCRIPT
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13.42 Lecture
VIV II
Alex Techet
March 18, 2003
Vortex Induced Forces
Due to unsteady flow, forces, X(t) and Y(t), vary with time.
Force coefficients:
Cx = Cy =X(t)
1/2 U2 dY(t)
1/2 U2 d
Force Time Trace
Cx
Cy
DRAG
LIFT
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Amplitude Estimation
=b
2 k(m+ma*)
ma* = V Cma; where Cma = 1.0
Blevins (1990)
a/d
= 1.29/[1+0.43 SG]3.35~
SG=2 fn2
2m (2)
d2; fn = fn/fs; m = m + ma
*^^
__
Three Dimensional Effects
Shear layer instabilities as well as longitudinal (braid)
vortices lead to transition from laminar to turbulent flow in
cylinder wakes.
Longitudinal vortices
appear atRd= 230.
Longitudinal Vortices
C.H.K. Williamson (1992)
The presence of
longitudinal vortices leads
to rapid breakdown of the
wake behind a cylinder.
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Longitudinal Vortices
Strouhal Number for the taperedcylinder:
St= fd / U
where d is the average
cylinder diameter.
Oscillating Tapered Cylinder
x
d(x)U(x)=Uo
Spanwise Vortex Shedding from
40:1 Tapered Cylinder
Techet,etal(JFM1
998)
dmax
Rd= 400;St = 0.198; A/d = 0.5
Rd= 1500;St = 0.198; A/d = 0.5
Rd= 1500;St = 0.198; A/d = 1.0
dminNo Split: 2P
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Flow Visualization Reveals:AHybridShedding Mode
2P pattern results at
the smaller end
2S pattern at the
larger end
This mode is seen to
be repeatable over
multiple cycles
Techet, et al (JFM 1998)
DPIV of Tapered Cylinder Wake
2S
2P
Digital particle image
velocimetry (DPIV)
in the horizontal plane
leads to a clear
picture oftwo distinct
sheddingmodes along
the cylinder.
Rd = 1500; St = 0.198; A/d = 0.5
z/d=22.9
z/d=7.9
Evolution of the
Hybrid Shedding Mode
2P 2S
Rd = 1500; St = 0.198; A/d = 0.5
z/d = 22.9z/d = 7.9
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Evolution of the
Hybrid Shedding Mode
2S2P
Rd = 1500; St = 0.198; A/d = 0.5
z/d = 22.9z/d = 7.9
Evolution of the
Hybrid Shedding Mode
2S2P
Rd = 1500; St = 0.198; A/d = 0.5
z/d = 22.9z/d = 7.9
Evolution of the
Hybrid Shedding Mode
2S2P
Rd = 1500; St = 0.198; A/d = 0.5
z/d = 22.9z/d = 7.9
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NEKTAR-ALE Simulations
Objectives:
Confirm numerically the existence of a stable,
periodic hybrid shedding mode 2S~2P in the
wake of a straight, rigid, oscillating cylinder
Principal Investigator:
Prof. George Em Karniadakis, Division of Applied
Mathematics, Brown University
Approach:
DNS -Similar conditions as the MIT experiment
(Triantafyllou et al.) Harmonically forced oscillating straight rigid
cylinder in linear shear inflow
Average Reynolds number is 400
Vortex Dislocations, Vortex Splits & Force
Distribution in Flows past Bluff BodiesD. Lucor & G. E. Karniadakis
Results:
Existence and periodicity of hybrid mode
confirmed by near wake visualizations and spectral
analysis of flow velocity in the cylinder wake and
of hydrodynamic forces
Methodology:
Parallel simulations using spectral/hp methods
implemented in the incompressible Navier- Stokes
solverNEKTAR
VORTEX SPLIT
Techet, Hover and Triantafyllou (JFM 1998)
VIV Suppression
Helical strake
Shroud
Axial slats
Streamlined fairing
Splitter plate
Ribboned cable
Pivoted guiding vane
Spoiler plates
VIV Suppression by Helical Strakes
Helical strakes are a
common VIV suppresion
device.
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Trip Wire Experiments
Trip wires cause the shear layer totransition early and thus retards separation.The wires can reduce amplitude of vibration
but this reduction is very dependant onangle on incoming flow.
Lift Characteristics of Rigid Cylinder
a) mean lift coefficientb) phase angle between oscillating lift force and cylinder motion.
Tandem Rigid Cylinders-Amplitude
Leading cylinder
Trailing cylinder
10D
Trailing cylinder
5D
-single cylinder
-no offset
-1D lateral offset
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-single cylinder
-no offset
-1D lateral offset
Leading cylinder
Trailing cylinder
10D
Trailing cylinder
5D
Tandem Rigid Cylinders-Frequency
Leading cylinder
Trailing cylinder
10D
Trailing cylinder
5D
-single cylinder
-no offset
-1D lateral offset
Tandem Rigid Cylinders-Drag
Tandem Flexible Cylinders-Amplitude
A - Leading Cylinder B-Trailing Cylinder
-single inline -tandem inline-single transverse -tandem transverse
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Forced Oscillation in a Current
U
y(t) = a cos t
= 2 f = 2 / T
Parameters: a/d, , ,
Reduced velocity: Ur= U/fd
Max. Velocity: Vm = U + a cos
Reynolds #: Re = Vm d /
Roughness and ambient turbulence
Wall Proximity
e + d/2
At e/d > 1 the wall effects are reduced.
Cd, Cm increase as e/d < 0.5
Vortex shedding is significantly effected by the wall presence.In the absence of viscosity these effects are effectively non-existent.
GallopingGalloping is a result of a wake instability.
m
y(t), y(t).Y(t)
U
-y(t).
V
Resultant velocity is a combination of the
heave velocity and horizontal inflow.
Ifn
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Lift Force, Y()
Y(t)
V
Cy =Y(t)
1/2 U2 Ap
Cy Stable
Unstable
Galloping motion
m
y(t), y(t).Y(t)
U
-y(t).
V
b k
a my + by + ky = Y(t).. .
Y(t) = 1/2 U2 a Cy - ma y(t)
..
Cy() = Cy(0) + Cy (0)
+ ...
Assuming small angles, :
~ tan = - yU
.
= Cy (0)
V ~ U
Instability Criterion
(m+ma)y + (b +1/2 U
2 a )y + ky = 0.. .
U~
b + 1/2 U2 a
U
< 0If
Then the motion is unstable!
This is the criterion for galloping.
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is shape dependent
U
1
1
12
1
2
1
4
Shape Cy (0) -2.7
0
-3.0
-10
-0.66
b
1/2 a ( )
Instability:
= Cy (0)
Cy (0)
Torsional Galloping
Both torsional and lateral galloping are possible.
FLUTTER occurs when the frequency of the torsional
and lateral vibrations are very close.
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Galloping vs. VIV
Galloping is low frequency
Galloping is NOT self-limiting
Once U > Ucritical then the instability occurs
irregardless of frequencies.
References
Blevins, (1990) Flow Induced Vibrations,
Krieger Publishing Co., Florida.