Vortex-Induced Vibration (VIV)
Theory: shedding frequency vs natural frequency
Overview
I've heard chimneys and subsea pipes can shake in wind or current.
Vortices are shed alternately from either side of a cylinder, applying a sideways force that reverses each time. If the shedding frequency is near a natural frequency, resonance causes large motion — vortex-induced vibration. Once motion starts, shedding is captured by the structure and stays synchronised even as flow speed shifts; this is lock-in. Design first finds the critical speed, then estimates amplitude, and adds damping or shape changes if needed.
Shedding frequency and reduced velocity
St is the Strouhal number, about 0.2 for cylinders over a wide range. Vibration grows for Ur of 4–8 and peaks near 5 (U = Ucr).
Amplitude estimate
m is mass per metre, ζ damping ratio and ρ fluid density. Larger S_G means smaller amplitude. m* is the mass ratio; it is small for structures in water, which also widens the lock-in speed range.
Tacoma Narrows was not VIV
The Tacoma Narrows Bridge, which collapsed in wind in 1940, is sometimes cited as VIV. It is now attributed to torsional flutter, an aerodynamic self-excited vibration. VIV amplitude saturates at a certain size, whereas flutter grows without limit once wind exceeds a critical speed. The two differ in mitigation and analysis, so distinguishing them matters. VIV itself remains a real problem for chimneys, power lines and offshore risers.
Worked examples
Example 1: steel chimney (D 2 m, fn 1 Hz)
| Case | S_G | A/D | Amplitude |
|---|---|---|---|
| 1,000 kg/m, 0.5% damping | 2.6 | 0.106 | 0.21 m |
| 2,000 kg/m, 0.5% damping | 5.2 | 0.026 | 51 mm |
| 1,000 kg/m, 2% damping | 10.3 | 0.004 | 9 mm |
Critical wind is 1×2/0.2 = 10 m/s (Reynolds number about 1.3×10⁶). At 5 m/s, Ur is 2.5 and there's no resonance; at 15 m/s, Ur is 7.5, at the edge of lock-in. The mass ratio is large, about 265.
Example 2: subsea riser (D 0.3 m, fn 0.5 Hz)
| Current | Shedding freq. | Ur |
|---|---|---|
| 0.5 m/s | 0.33 Hz | 3.3 |
| 1.0 m/s | 0.67 Hz | 6.7 |
| 1.5 m/s | 1.00 Hz | 10.0 |
With 150 kg/m and 2% damping, mass ratio is about 2.1, S_G 0.08, and A/D 1.15 (about 0.35 m). Critical current is 0.75 m/s.
With the same 2% damping, the chimney moves 9 mm but the riser moves about a diameter.
Fluid density. Air is about 1/850 as dense as water, so aerodynamic forces are tiny relative to chimney weight and modest damping suppresses motion. Underwater, pipe weight and displaced water are comparable, so damping alone struggles. A low mass ratio also widens the lock-in range, so motion can persist even at Ur 10 (1.5 m/s). Offshore, helical strakes or fairings disrupt shedding itself. Persistent motion causes fatigue, so evaluate cycle counts as well as amplitude.
Handling VIV in CFD
- Find critical speeds from St and Ur to narrow the speeds to simulate.
- Use a time step of about 1/100 of the shedding period (0.01 s chimney, 0.015 s riser).
- Use 2D only for trends; quantitative work needs 3D with at least 3–4D span.
- Model the structure as mass–spring–damper, coupled two-way with the flow.
- Step flow speed up and down to check lock-in range and hysteresis.
“It didn't vibrate in the simulation”
A factory exhaust stack vibrated strongly after completion, but only at winds around 10 m/s. Design CFD had covered only strong winds of 15 and 20 m/s, where vibration was small. VIV occurs not in strong wind but at the specific speed where shedding matches the natural frequency, and that speed had never been simulated. Helical strakes eventually fixed it. Hand-calculate the critical speed before choosing simulation conditions.
Common mistakes
Mistakes and fixes
| Mistake | Effect | Fix |
|---|---|---|
| Only strong winds simulated | Critical speed missed | Find Ucr first |
| Amplitude from 2D | Lift overpredicted | 3D with enough span |
| Coarse time step | Shedding misrepresented | 1/100 of period |
| Added mass ignored | Wrong natural frequency | Use in-water frequency |
| Confused with flutter | Wrong mitigation | Check amplitude saturation |
I'd like to learn related topics.
Related pages include two-way FSI, one-way FSI, aeroelasticity, ALE FSI and mooring analysis.
Related Topics
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