Tools · Flow-induced vibration
Vortex shedding frequency
Flow past a cylinder (a thermowell, a pipe in wind or current, a tube in a bundle) sheds vortices at a predictable frequency. If that lands on a natural frequency, it can lock in and drive large vibration.
St ≈ 0.2 for a circular cylinder over a wide subcritical Reynolds range (roughly 300 to 2×10⁵).
| In-line (drag) shedding frequency, 2·fs | |
| Reynolds number | |
| Reduced velocity V / (fn·D) | |
| Velocity for cross-flow lock-in (fs = fn) |
The formulas
fs = St · V / D Re = ρVD / μ Vr = V / (fn·D)
Vortices shed alternately from each side, so the lift force (cross-flow) oscillates at fs while the drag force (in-line) oscillates at about 2·fs. In-line vibration can therefore start at roughly half the velocity needed for cross-flow lock-in, which matters for thermowells in liquid service.
This is a screening check. Lock-in depends on mass ratio, damping and the actual geometry, and thermowells have their own dedicated method (ASME PTC 19.3 TW). Use those for design.
Method & sources
What it calculates
- Strouhal relation fs = St·V/D for cross-flow (lift) shedding; in-line (drag) shedding at 2·fs.
- Reynolds number Re = ρVD/μ to check the flow regime for the chosen St; reduced velocity Vr = V/(fn·D).
Assumptions & limits
- St ≈ 0.2 holds for circular cylinders over the subcritical range; it changes near the drag crisis (Re around 2×10⁵ and above).
- Lock-in depends on mass ratio and damping (Scruton number), which are not included. Thermowells must be assessed to ASME PTC 19.3 TW.
Verified: 5 m/s past a 25 mm cylinder in water gives fs = 40 Hz and Re = 1.25×10⁵, matching Python.