Cylinder Wake: Boundary Layer Separation & Drag Crisis

Wind Tunnel

Airspeed U 15 m/s

Model diameter D 0.12 m

Flow Readouts

Subcritical — laminar separation

Reynolds number

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Drag coefficient C_d

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Separation angle θ

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Shedding freq. (St≈0.2)

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How it works

Outside the thin boundary layer, flow past a cylinder follows potential theory: superposing a uniform stream with a doublet gives the surface speed u(θ) = 2U sinθ (θ measured from the upstream stagnation point) and, via Bernoulli, the pressure coefficient C_p = 1 − 4sin²θ. Speed rises to a maximum at the shoulder (θ=90°) then the surface must decelerate toward the rear stagnation point — an adverse pressure gradient.

Inside the real, viscous boundary layer that deceleration eventually reverses the near-wall flow and the layer lifts off the surface: separation. A laminar boundary layer has little momentum near the wall and separates early, around θ ≈ 82°, leaving a wide turbulent wake and a high drag coefficient (C_d ≈ 1.2). Once the Reynolds number Re = UD/ν crosses roughly 3×10⁵ the boundary layer itself transitions to turbulence before separating; the extra near-wall momentum lets it cling on to about θ ≈ 125°, shrinking the wake and dropping C_d to ≈ 0.3 — the classic drag crisis.

u(θ) = 2U sinθ
Cp(θ) = 1 − 4sin²θ
Re = UD/ν      (ν ≈ 1.5×10⁻⁵ m²/s for air)
St = f D / U   (St ≈ 0.2 → shedding frequency f)

Airspeed / diameter — set the free-stream speed and model size that together fix Re; drag either far enough and you cross the drag crisis.
Trip — dimples or a trip wire force early transition (like a golf ball), reproducing the drag crisis at a much lower Re than a smooth cylinder needs.
Show surface Cp — colours the model by the potential-flow pressure coefficient: blue near the stagnation points, red over the low-pressure shoulders.
The trailing particles are advected by the same potential-flow field plus a separated-wake model whose width is set directly by the separation angle above, with an alternating Kármán-street wobble at the Strouhal shedding frequency.

Attached flow Separated wake

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