Making a flow-generated period dimensionless
The Strouhal number scales the frequency f of a repeating flow event with a length L and a speed U. Written as a ratio of times, its meaning is clear.
L/U is the time the fluid takes to travel one body size; 1/f is one oscillation period. St = 0.2 means the shedding cycle advances one fifth of a period while the fluid moves one cylinder diameter, so the fluid travels five diameters per cycle. The CFD Direct notes introduce the Strouhal number as the coefficient of the unsteady term in the nondimensional momentum equation, the ratio of transient to steady inertia. Two flows with similar St have equally fast time variation relative to their transit time, whatever their size and speed.
Where to read f, L and U
The calculator returns fL/v from f (Hz), L (m) and v (m/s). For vortex shedding from a cylinder, L is the diameter and U the undisturbed free-stream speed upstream. The input most often wrong is f, because the measured signal can show up to twice the shedding frequency.
| Signal | Frequency | Basis |
|---|---|---|
| Lift coefficient; wake velocity or pressure off the centreline | Shedding frequency f | NASA NPARC cylinder case |
| Drag coefficient | 2f | Same: feels both vortices |
| Velocity on the wake centreline | 2f | Same: vortices from both sides pass |
Divide rpm by 60 to get Hz and angular frequency ω (rad/s) by 2π; entering ω makes St about 6.28 times too large. Divide km/h by 3.6 for m/s.
Open this calculatorCylinder St values and the Re range behind them
| Value | Condition | Source |
|---|---|---|
| St nearly constant at 0.2 | Peak Aeolian-tone frequency, 60 < Re < 10⁶, including the drag crisis | NASA TM 107730 |
| St 0.179–0.182 | Re = 150, experiment (Roshko) | NASA NPARC case |
| St 0.150–0.183 | Re = 150, CFD (depends on time-integration order and frequency method) | NASA NPARC case |
NASA TM 107730 notes that above Re ≈ 60 the cylinder flow becomes unstable and forms a von Kármán vortex street. Over that range the drag coefficient changes more than fivefold, with the drag crisis near Re = 5 × 10⁵, yet St from the peak noise frequency stays near 0.2. The Re = 150 experiment gives about 0.18, 10 % lower. Use less than 0.2 below a few hundred, and do not judge Re above 10⁶ from these data.
Re needs ν: 1.0020 × 10⁻⁶ m²/s for water at 20 °C (IAEA Table 3.3), and for air at 20 °C, μ = 1.819 × 10⁻⁵ Pa·s (IAEA Table 3.1) over the 1 atm density 1.2043 kg/m³, ν = 1.5104 × 10⁻⁵ m²/s.
Singing cable, pipe thermowell and a CFD check
Example 1. Shedding frequency of a 30 mm cable in wind
Given. Wind at 36 km/h blows across a 30 mm cable (assumed values). Air at 20 °C, 1 atm: ν = 1.5104 × 10⁻⁵ m²/s.
Unit conversion. D = 30 mm = 0.03 m; U = 36 km/h ÷ 3.6 = 10 m/s.
Calculation. Re = UD/ν = 10 × 0.03 ÷ (1.5104 × 10⁻⁵) ≈ 19,862, inside the 60 < Re < 10⁶ range where NASA TM 107730 reports St near 0.2. So f = St·U/D = 0.2 × 10 ÷ 0.03 ≈ 66.7 Hz, a period of 0.015 s.
Interpretation. 66.7 Hz is a low audible tone; at 15 m/s it rises in proportion to 100 Hz. A 2 m chimney in 20 m/s wind gives Re ≈ 2.65 × 10⁶, outside that range. St = 0.2 would give f = 2 Hz, but that is an extrapolation; comparing it with a structural natural frequency needs data for that Re range.
Example 2. Vibration frequency of a thermowell in a water pipe
Given. A 10 mm cylindrical thermowell stands across a pipe carrying 20 °C water at 2 m/s at the well (assumed values); ν = 1.0020 × 10⁻⁶ m²/s.
Unit conversion. D = 10 mm = 0.01 m.
Calculation. Re = 2 × 0.01 ÷ (1.0020 × 10⁻⁶) ≈ 19,960, so St ≈ 0.2 applies: f = 0.2 × 2 ÷ 0.01 = 40 Hz. The drag (in-line) force varies at 2f, exciting in-line vibration at 80 Hz. At 8 m/s, Re ≈ 79,840 and f = 160 Hz.
Interpretation. Check whether any operating speed puts f or 2f near the thermowell natural frequency. Near it, shedding can lock in to the structural frequency and amplitudes grow. Because f scales with speed, include speeds passed during start-up and shutdown, not just the maximum.
Example 3. Checking St from the NASA NPARC cylinder CFD
Given. The NPARC case computes laminar flow over a cylinder at Re = 150 and Mach 0.2, with D = 1.0 m and U = 66.8163 m/s. For Run A, the mean nondimensional time between the last four wake-velocity peaks is 31.0, converted with Lr = 1.0 m and ar = 334.01 m/s.
Unit conversion. t = 31.0 × Lr/ar = 31.0 × 1.0 ÷ 334.01 ≈ 0.0928 s, so f = 1/t ≈ 10.77 Hz (the page prints 10.777). The Mach number 66.8163 ÷ 334.01 ≈ 0.200 matches the stated condition.
Calculation. St = fD/U = 10.77 × 1.0 ÷ 66.8163 ≈ 0.161. Matching the experimental 0.179–0.182 would need f = 11.96–12.16 Hz.
Interpretation. Run A, with first-order time integration, is about 11 % below the experimental midpoint (0.1805). Run D, second order with Global Newton iterations, gives 0.180 from peak spacing, inside the experimental range. If unsteady CFD under-predicts St, suspect the time-integration order and time step first. You can repeat the check by entering f = 10.77, L = 1 and v = 66.8163.
When St ≈ 0.2 is good enough for design
- Compute Re first. Below about 60 there is no periodic shedding; at a few hundred St is nearer 0.18; above 10⁶ these data do not apply.
- Check the shape. 0.2 is for a smooth single cylinder. Square sections, tapered chimneys, rough cables and tubes in bundles differ, and bundles often use the gap velocity. Follow the St and speed definition of data for that shape.
- Keep clear of natural frequencies. If f or 2f is near a structural natural frequency, lock-in can raise amplitude. St cannot predict amplitude, so use it to screen for risky speed bands.
- Use the free-stream speed upstream. For a probe in a pipe, the mean and local speed can differ; state which one you used.
Errors in measuring and reading the frequency
In the NPARC case, the frequency extraction method alone changes St. For Run A, peak spacing gives 0.161, an FFT over the last 2000 points 0.150, and over 3000 points 0.1667. A record of only a few cycles gives coarse FFT resolution. Record many cycles and compare peak spacing with the FFT.
Drop the initial transient and use the signal only once it is periodic. A signal from the wake centreline shows 2f and St near 0.4; check the probe location and signal type before calling that a new phenomenon.
Vortex shedding and Strouhal number FAQ
Over what Re range can I use St ≈ 0.2?
NASA TM 107730 reports St from the peak cylinder noise frequency near 0.2 across 60 < Re < 10⁶. The Re = 150 experiment gives 0.179–0.182, so use about 0.18 at low Re and check other data above 10⁶.
Why does my St come out near 0.4?
You probably read the frequency from drag or from velocity on the wake centreline. As the NPARC case explains, these feel both vortices and vary at twice the shedding frequency. Use lift or a point off the centreline.
My CFD St is 10 % below experiment. What should I change first?
In the NPARC case, first-order time integration gave 0.161 and second order with Global Newton gave 0.180. Check time-integration order and time step, then recompute f from a long periodic record.
Can I use St = 0.2 for shapes other than a cylinder?
Not directly; 0.2 comes from smooth cylinders. Other sections often take L as the width normal to the flow, but St and the reference speed should come from data for that shape.
Related dimensionless numbers
Re sets the shedding regime; interfaces and free surfaces add other time scales.
- Reynolds number (Re): Whether St ≈ 0.2 applies depends on Re, so report Re with any frequency.
- Weber number (We): (capillary time √(ρL³/σ) ÷ transit time L/v)² = We; use it with St for oscillating drops or jets.
- Froude number (Fr): For waves and sloshing driven by gravity, Fr checks gravity and St compares periods.
References
- NASA Langley: Reynolds Number Influences in Aeronautics (NASA TM 107730). Vortex street above Re ≈ 60; drag change over 60 < Re < 10⁶; noise-peak St near 0.2
- NASA Glenn / NPARC Alliance: Laminar Flow over a Circular Cylinder: Study #1. Re 150 case; Run A 0.161, FFT 0.150/0.1667; Run D 0.180; experiment 0.179–0.182; 2f in drag
- CFD Direct: Notes on CFD: Scale Similarity. St as transient over steady inertia
- IAEA: Thermophysical Properties of Materials for Nuclear Engineering (2008). Tables 3.1 (air) and 3.3 (water)