Physic Labs

Fluid mechanics

Turbulent flow and the Kármán vortex street

Observe the conditions for an alternating vortex street behind a circular cylinder. Vary the flow speed U, diameter D, and shedding frequency f, read the illustrative Reynolds number, and check the Strouhal number St=fD/USt = fD/U.

Advanced

Equipment

  • Canvas simulating the cylinder and two staggered rows of opposite-signed vortices downstream (drag to rotate the view)
  • «Tốc độ dòng U» (flow speed) slider, 1–12 m/s
  • «Đường kính D» (diameter, 20–100 cm) and «Tần số phát xoáy f» (shedding frequency, 1–10 Hz) sliders
  • Readout line «Re ≈ … ; St = fD/U = …» below the canvas

Procedure

  1. Read the Reynolds number vs U and D

    Keep «Đường kính D» at its default and raise «Tốc độ dòng U» from 1 to 12 m/s, noting the «Re ≈ …» readout at each step. Then hold U fixed, increase D, and see how Re changes. Verify the linear dependence Re∝UDRe \propto UD from the readings.

  2. Check the Strouhal number

    Set several (U, D, f) combinations, e.g. U = 5 m/s, D = 50 cm, f = 2 Hz. Compute St=fD/USt = fD/U yourself and compare with the «St = fD/U = …» readout; for a cylinder in the shedding regime the experimental value is near St ≈ 0.2. Vary f and watch St change linearly.

  3. Watch the vortex rows and the oscillating side force

    Set f high and watch the two staggered rows of opposite-signed vortices drift downstream on the canvas; drag the canvas to rotate the view. Alternating shedding creates asymmetric pressure, so the cylinder feels a lateral force oscillating at frequency f — the mechanism behind the vibration of chimneys and power lines in wind. Rotate the view to see the stagger clearly.

  4. Predict the flow regime from Reynolds

    Combine low U and small D to push Re down, then increase it. For a real cylinder, a regular vortex street appears around Re ≈ 47–190 and the wake turns turbulent at much higher Re. Note at which Re the simulated wake pattern changes most visibly and compare with the classic values.

Simulation

Experiment history

In 1878 Vincent Strouhal measured the tone emitted by a wire in an air stream and found its frequency proportional to the wind speed and inversely proportional to the wire diameter — the ratio fD/U now called the Strouhal number. In 1908 Henri Bénard photographed staggered vortices behind a circular cylinder in a water-channel experiment. In 1911–1912 Theodore von Kármán analyzed the stability of vortex rows and showed that only the staggered arrangement of alternating, opposite-signed vortices is stable, giving a spacing formula; the configuration therefore bears his name. Earlier, in 1883, Osborne Reynolds had used dye streams in a pipe to distinguish laminar from turbulent flow via Re = ρUD/μ, the dimensionless number used to classify the wake regime in this simulation.

Related physicists

Daniel Bernoulli

Related library topics

Turbulent flow and the Kármán vortex street