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Flowinduced Vibrations
Prasanth TK Department of Aerospace Engineering
IIT Kanpur
Introduction
Encountered in many engineering situations Civil / marine structures in wind/water flow may
undergo large oscillations Also referred as Vortexinduced vibration (VIV)
Electrical Transmission Lines
• Natural frequency of the cable – 10 to 30 HzDiameter – 20 to 30 mmWind speed 3 to 15 m/s
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
VIV catastrophe: Tacoma Narrows Bridge in 1940
Wind Speed: 42mph (68 kmph) Frequency: 0.62 Hz (Vertical mode), 0.23 Hz (Torsional mode)
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
Offshore Applications
Nonuniform currents
Understanding the
forces acting along the
cable very challenging
Flow Past a Circular Cylinder
Reynolds Number Ratio of inertial to
viscous force Re = ρU D/µ Flow is turbulent at
large Re
UD
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
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
Vortex Shedding: Strouhal Number
Nondimensionalized Shedding frequency
St = fv.s D/U
St ~ 0.2 for a wide range of Re
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
• VIV is associated with
–Large amplitude oscillations
–Resonance like behaviour over a range of Re
(lockin)
–Hysteresis
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))
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
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?
• A Simple VIV Model: * Linear springs * Fluid has nonlinearity * Expect linear resonance when fv.s. ~ fN
Results2D Mesh
Effect of Blockage on VIV m* = 10
m* = 5Effect of Blockage on VIV
The Concept of Critical Blockage
Brika and Laneville(1993): m* =2054, B=2% (Hysteretic)
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