› Wake of Bluff Bodies Simulator Back
Fluid Dynamics Simulator

Wake of Bluff Bodies Simulator — C_D and Strouhal Number

Compare the wakes behind circular, square and teardrop cross sections. Compute the subcritical drag coefficient C_D, vortex shedding frequency f and wake width in real time, and watch the Karman vortex street.

Parameters
Free-stream velocity U
m/s
Characteristic size D
m
Cross section Cylinder
—

0 = Cylinder / 1 = Square / 2 = Teardrop

Fluid density ρ
kg/m³

Air kinematic viscosity ν = 1.5×10⁻⁵ m²/s is fixed. Subcritical Re ~ 10⁴–10⁵ representative values are used.

Results
—
Reynolds number Re
—
Drag coefficient C_D
—
Drag per unit span F_D
—
Shedding frequency f
Flow and wake (Karman vortex street)

Free stream U enters from the left and meets the body; alternating vortices form downstream. Dashed lines show the wake width W_wake.

C_D and St by section shape

Blue bars = drag coefficient C_D (left axis). Orange line = Strouhal number St (right axis). The current shape is highlighted.

Theory & Key Formulas

Wake width, drag and vortex shedding frequency are governed by the cross-section shape and the Reynolds number.

Reynolds number (ν = kinematic viscosity):

$$Re = \frac{U\,D}{\nu}$$

Drag per unit span (ρ = fluid density, C_D = shape-specific drag coefficient):

$$F_D = \tfrac{1}{2}\,\rho\,U^{2}\,D\,C_D$$

Vortex shedding frequency from the Strouhal number:

$$St = \frac{f\,D}{U}, \qquad f = St\,\frac{U}{D}$$

Subcritical (Re ~ 10⁴–10⁵) representative values: cylinder C_D ~ 1.2 / St ~ 0.20, square C_D ~ 2.05 / St ~ 0.13, teardrop C_D ~ 0.08 / St ~ 0.20. Wake width W_wake ~ C_w·D (cylinder 1.5, square 1.8, teardrop 0.3).

What is the wake of bluff bodies simulator?

🙋
Does the wake behind a chimney or a bridge pier really change that much with shape?
🎓
A surprising amount. Roughly, a circular cylinder has C_D about 1.2, a square section about 2.05, and a teardrop about 0.08. At the same speed and size, the drag changes by a factor of 25. Move the shape slider from 0 to 2 and watch the wake width and the bar chart change with it.
🙋
The vortices are shedding alternately. Is that the Karman vortex street?
🎓
Exactly. In the subcritical range (Re ~ 10^4 to 10^5), vortices peel off the top and bottom of the cylinder in turn. The frequency is f = St * U / D, where St ~ 0.20 for a cylinder, 0.13 for a square and 0.20 for a teardrop. With U = 5 m/s and D = 5 cm you get f = 20 Hz. It is below hearing, but the singing of a wire in the wind is the same effect.
🙋
Was the Tacoma Narrows collapse caused by this?
🎓
It was a mix of vortex-induced vibration and aerodynamic flutter, but vortex shedding approaching a natural frequency was one of the triggers. So for chimneys, power lines and bridges, engineers compute the resonant wind speed from St and add fairings or helical strakes to disturb the shedding. In the simulator you can see how the regularity of the shedding changes with the shape too.
🙋
Only the teardrop has a very narrow wake, around 0.3D.
🎓
That is the essence of streamlining. By pushing the separation point downstream, the wake stays narrow and the low-pressure region behind the body, the main source of pressure drag, shrinks. That is why airfoil sections, the nose of a Shinkansen and even competitive swimming caps all use the same idea. Compare F_D in the simulator and the orders of magnitude really stand out.

Frequently Asked Questions

On a square section the flow separates sharply at the upstream corners and the separation point is fixed by the geometry. On a smooth circular cylinder the separation point is determined by the pressure distribution and stays relatively rearward, so the wake is narrower. The square always sheds at its front corners, producing a wide wake and low base pressure, so its subcritical C_D is about 2.05 versus 1.2 for a circular cylinder.
It is a useful starting estimate. When the vortex shedding frequency f = St U/D approaches a natural frequency of the structure, vortex-induced vibration may occur. The Tacoma Narrows collapse is a famous example of wind-driven resonance. Designers estimate the resonant wind speed from St (about 0.20 for cylinders and 0.13 for square sections) and add fairings, helical strakes or dampers.
Streamlining narrows the wake and reduces the low pressure region behind the body, which is the main source of pressure drag. A teardrop section has C_D ~ 0.08, about 1/15 of a circular cylinder and 1/25 of a square. The wake also shrinks from about 1.5D for a cylinder to about 0.3D. Because aerodynamic drag scales with the square of speed, streamlining brings large gains in fuel economy and top speed.
Flow around a cylinder goes through laminar separation, transition and turbulent reattachment as Re increases; the range Re ~ 10^4 to 10^5 is called the subcritical regime. This tool uses representative subcritical values (C_D = 1.2 for a cylinder, 2.05 for a square, 0.08 for a teardrop). The defaults U = 5 m/s, D = 0.05 m in air give Re ~ 1.7 x 10^4, which sits inside the subcritical regime.

Real-world applications

Wind loading and vibration of bridges, chimneys and power lines: long-span bridge piers and decks, tall chimneys and overhead lines are classic slender structures susceptible to vortex-induced vibration. Engineers compute the shedding frequency from St and check that it is well separated from the natural frequencies. Helical strakes on chimneys, fairings on bridge decks and Stockbridge dampers on lines are added to disrupt the shedding coherence.

Aerodynamic design of cars, trains and aircraft: aerodynamic drag drives fuel economy, top speed and stability, so vehicle bodies are pushed toward teardrop shapes. The Shinkansen nose, F1 rear bodywork and truck cab deflectors all narrow the wake and cut the pressure drag. Aircraft wings are essentially teardrop sections, with cruise C_D values on the order of 0.01.

Wind environment around buildings: in clusters of high-rise buildings, the wake of each tower creates pedestrian-level wind problems downstream, including gusts and persistent vortices. Wind-tunnel tests and CFD evaluate wake widths and vortex shedding so that planting, podiums and corner treatment can be tuned for comfort.

Underwater structures and offshore platforms: deep-water risers, submerged piers and offshore platform legs experience vortex-induced vibration from currents. Because water is about 800 times denser than air, even at low speeds the drag and vibration energy are non-negligible. Strakes, fairings and shaped cross sections are used as VIV (vortex-induced vibration) suppression devices.

Common misconceptions and cautions

The most common misconception is that "sharper means lower drag". A square section, with sharp edges on the upstream face, has a larger C_D than a smooth cylinder (2.05 vs 1.2): the corners force separation and widen the wake. What really helps is streamlining the downstream side so that the separation point moves rearward. Switch the shape between 1 (square) and 2 (teardrop) in the simulator and compare the wake width and F_D.

The next pitfall is to assume that the C_D values used here hold at all Reynolds numbers. The C_D of a circular cylinder actually changes with Re; near Re ~ 3 x 10^5 there is a "critical transition" where C_D drops abruptly to about 0.3 because the boundary layer turns turbulent and separation moves rearward. This tool uses representative subcritical (Re ~ 10^4 to 10^5) values, so it deviates from real machines at very high or very low Re. The displayed Re is there as a sanity check.

Finally, note that F_D = 0.5 * rho * U^2 * D * C_D is the drag per unit span. To get the total drag on a real chimney or pier you must multiply by the span L. The tool also lumps form drag (pressure plus friction) into a single C_D and ignores 3D effects (end vortices, span-wise correlation), interference with support structures and the effect of inflow turbulence intensity I_u. Real designs add corrections from wind-engineering handbooks, CFD or wind-tunnel tests.

Related Tools

Drag Coefficient Calculate drag force, Reynolds number, terminal velocity & power for any shape. Input fluid... Strouhal Number & Vortex Shedding Simulator — Karman Vortices and Lock-on Strouhal number simulator: compute the Karman vortex shedding frequency behind a cylinder f... Drag Calculation Calculate drag & lift forces, terminal velocity, and vortex frequency in real time. Interac... Airfoil Simulate NACA 4-digit airfoils in real time. Generate profiles, calculate lift/drag coeffic... Buckingham Pi Theorem Simulator — Dimensional Analysis & Model Similitude Buckingham Pi simulator reduces five cylinder-drag variables to two dimensionless groups (R... Terminal Settling Velocity Simulator — Sphere Drag and Reynolds Regimes Iteratively compute the terminal settling velocity of a spherical particle across Stokes, i...