vortex-induced vibrations at low reynolds numbersinduced vibrations ... also referred as...
TRANSCRIPT
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Flowinduced Vibrations
Prasanth TK Department of Aerospace Engineering
IIT Kanpur
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Introduction
Encountered in many engineering situations Civil / marine structures in wind/water flow may
undergo large oscillations Also referred as Vortexinduced vibration (VIV)
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Electrical Transmission Lines
• Natural frequency of the cable – 10 to 30 HzDiameter – 20 to 30 mmWind speed 3 to 15 m/s
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BridgesGolden Gate Bridge, San Francisco (1951)
Wind Speed: 70mph (110 kmph)Peak to peak amplitude of vibration: 12 ft (3.5m), 0.13 HzTorsional peak to peak amplitudes of 22 degrees, 0.1 Hz
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VIV catastrophe: Tacoma Narrows Bridge in 1940
Wind Speed: 42mph (68 kmph) Frequency: 0.62 Hz (Vertical mode), 0.23 Hz (Torsional mode)
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Ferrybridge Power Station, UK (1960)
3 of 8 cooling tower collapsed in a wind storm
Tower height – 375 ft Reason: Serious
underestimation of wind loads in design
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Offshore Applications
Nonuniform currents
Understanding the
forces acting along the
cable very challenging
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Flow Past a Circular Cylinder
Reynolds Number Ratio of inertial to
viscous force Re = ρU D/µ Flow is turbulent at
large Re
UD
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Vortex Shedding: Laminar behaviourRe<5:* Fluid flow follows the cylinder surface
5≤Re≤45:* Flow separates * A pair of vortices is formed
45≤Re≤150:* Vortices break away * Periodic wake of staggered vortices formed
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Vortex shedding: Turbulent behaviour150≤Re≤300* Transition range to turbulence in vortex300≤Re 3x10≲ 5
* Vortex street fully turbulent
3x105≲Re 3.5x10≲ 6
* Turbulent boundary layer* Narrower wake
3x106≲Re* Reestablishment of turbulent vortex street
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Vortex Shedding: Strouhal Number
Nondimensionalized Shedding frequency
St = fv.s D/U
St ~ 0.2 for a wide range of Re
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vonKarman Vortex shedding beyond Re=50 Its asymmetric nature induces unsteady force Unsteady forces cause body to oscillate The motion of the body may change the flow
drastically For eg: Shedding frequency may change
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• VIV is associated with
–Large amplitude oscillations
–Resonance like behaviour over a range of Re
(lockin)
–Hysteresis
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Hysteresis Different solution
possible depending upon the initial condition
Hysteresis originates from the fluid system, NOT from the model elastic system (Parkinson(1989), Brika and Laneville(1993))
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Blockage, B = D/H (inherent to the experimental set up) m* = mass of structure/mass of displaced fluid
What are blockage and m* ?
DH
Tunnel wall
Tunnel wall
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Earlier Works
Feng (1968) Bishop & Hassan (1964) Stansby (1976) Stansby (1976) Brika and Laneville (1993) Khalak and Williamson (1999) Triantafyllou et al. (2003)
8.2 Air 1.8 2 248 √ 8.3 Water 0.4 – 11 √ 3.6 Air 0.3 – 0.9 X 7.2 Air 0.3 – 0.9 √ 2.0 Air 0.341.18 2054 √ 10 Water 0.2 – 1.3 10 √ 6.3 Water 3 3 X
Study B% Fluid Re /10 4 m* Hysteresis
Most of the experiments are done at higher ReWhat about low Re?What is the role of blockage and m* in hysteresis?
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• A Simple VIV Model: * Linear springs * Fluid has nonlinearity * Expect linear resonance when fv.s. ~ fN
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Results2D Mesh
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Effect of Blockage on VIV m* = 10
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m* = 5Effect of Blockage on VIV
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The Concept of Critical Blockage
Brika and Laneville(1993): m* =2054, B=2% (Hysteretic)
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Conclusion Hysteresis is observed in the laminar regime Hysteresis is found to depend on blockage and m* At any mass ratio, there is a critical blockage above
which the behaviour will be hysteretic
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