VIV resonance margin

Measured

• extracted St in [0.1818, 0.1909], validated band [0.16, 0.21] for this grid
• min |f_struct − f_shed| / f_struct = 0.236 against a 0.15 placard minimum
• four sweeps returned a finite, oscillating wake

A cylindrical member sheds vortices at a frequency set by flow speed. When that frequency approaches a structural mode, the member is driven at resonance.

This example reports the margin between the two across an airspeed sweep. The flow solve is an intermediate step; the margin table is the output.

What runs per row

Each airspeed gets a full DEC incompressible Navier–Stokes march past a circular member. A probe in the wake records transverse velocity; the shedding frequency comes from that signal, and the Strouhal number follows as St = f·D/U.

Four marches run concurrently under the parallel feature. The concurrent result is bit-identical to the sequential run.

Output

airspeed [m/s]   Re      St      f_shed [Hz]   margin
      0.75       100  0.1818        68.2     0.545
      0.90       120  0.1818        81.8     0.455
      1.05       140  0.1909       100.2     0.332
      1.20       160  0.1909       114.5     0.236

Member D = 2.0 mm, structural mode f_struct = 150 Hz.

The margin column falls monotonically from 0.545 to 0.236. One further step at the same increment would cross the 0.15 placard.

Gates

[PASS] strouhal band: extracted St in [0.1818, 0.1909], validated band [0.16, 0.21] for this grid
[PASS] resonance margin: min |f_struct - f_shed| / f_struct = 0.236, placard minimum 0.15
[PASS] finite wake: 4 sweeps returned a finite, oscillating wake

The first gate checks St against a band validated for this grid rather than against the 0.164 to 0.21 range for a smooth cylinder. A coarse grid biases Strouhal high, and the extracted values sit at the upper end of the validated band. Gating against the literature value would fail a correct run at this resolution.

The third gate requires oscillation, not only finiteness. A wake march that decays to steady produces a finite signal, and the frequency extractor will report noise as a frequency. The cylinder verification records this case: a staircase boundary yields a steady wake and a reported Strouhal of 0.244 taken from seventh-decimal noise.

Applicability limits

The sweep covers Re 100 to 160, which is laminar shedding. A flight-Reynolds strut operates orders of magnitude above this range and depends on the staged turbulence work.

The structural frequency and the 0.15 placard are demonstration values, not measured properties of a member.

Stated limitation

Re 100 to 160. Nothing here claims turbulent shedding; a flight-Reynolds strut sits far above this range and waits on the staged turbulence work. The structural frequency and margin placard are stated demonstration values, not measured properties of a real member.