Visualize streamlines from potential flow theory around a cylinder. Calculate Kármán vortex frequency, Magnus effect lift, and empirical drag in real time. Explore how Reynolds number affects flow separation.
Parameters
Presets
Cylinder diameter D
1 mm to 1 m (log scale)
Flow velocity U
m/s
Fluid
Circulation Γ (Magnus effect)
m²/s
Karman vortexAnimation
Playback Controls
Hint: Drag the cylinder on the canvas to change position. During playback, vortex animation progresses and elapsed time is displayed. Use "Save Streamlines" to overlay up to 5 streamline patterns for comparison.
Results
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Reynolds number Re
0.20
Strouhal Number St
—
Vortex shedding frequency f [Hz]
—
Drag forceCoefficient CD
—
Drag force FD [N/m]
—
Lift L [N/m]
Visualization
CAE Applications
Karman vortex-induced vibration analysis of chimneys and marine risers / Preliminary lift-drag estimation for wind turbine blade cross-sections / CFD (OpenFOAM/Fluent) validation cases. The Strouhal number is essential for VIV (vortex-induced vibration) natural frequency avoidance design.
Theory & Key Formulas
Potential flow (with circulation) streamfunction:
$$\psi = U r\!\left(1-\frac{R^2}{r^2}\right)\!\sin\theta - \frac{\Gamma}{2\pi}\ln r$$
Kutta-Joukowski theorem (lift per unit length):
$$L = \rho\, U\, \Gamma$$
Karman vortex shedding frequency:
$$f_{vs}= St \cdot \frac{U}{D}, \quad St \approx 0.2 \;(Re = 10^3 \text{ to }10^5)$$
What exactly is "potential flow" that this simulator shows? It looks like smooth lines wrapping around the cylinder.
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Basically, it's an idealized model where fluid has no viscosity and doesn't swirl internally. The flow is smooth and mathematically elegant. In this simulator, when you set the fluid to "Ideal" and the circulation (Γ) to zero, you're seeing pure potential flow. Try moving the "Flow velocity U" slider—the streamlines get closer together as speed increases, but the pattern stays symmetrical.
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Wait, really? But real air has viscosity. What happens then? I see an option for "Karman vortex Animation".
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Great question! That's where reality kicks in. With viscosity, like when you select "Water" or "Air" in the fluid dropdown, the flow can separate and create alternating vortices behind the cylinder—the famous Kármán vortex street. Turn on the animation and watch the swirling patterns shed. The frequency of this shedding is a big deal in engineering for predicting vibrations.
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And the "Circulation Γ" slider? That's for the Magnus effect, right? Like a curving soccer ball?
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Exactly! By adding circulation (Γ), you're simulating spin. The flow becomes asymmetric, creating a pressure difference and thus lift. This is the Magnus effect. Slide Γ from zero to a positive value and watch the streamlines deflect upward. The lift force card on the right updates instantly—that's the Kutta-Joukowski theorem in action. Try it with different cylinder diameters to see how size and spin interact.
Physical Model & Key Equations
The core of the potential flow model is the streamfunction, ψ. It describes the path a fluid particle would take. For flow around a spinning cylinder, it combines uniform flow, a doublet (to represent the cylinder), and a vortex (to represent spin).
$$\psi = U r\!\left(1-\frac{R^2}{r^2}\right)\!\sin\theta - \frac{\Gamma}{2\pi}\ln r$$
Here, U is the free-stream velocity, R is the cylinder radius (D/2), Γ is the circulation strength, and (r, θ) are polar coordinates. Lines of constant ψ are the streamlines you see on the canvas.
The most powerful result from this model is the Kutta-Joukowski theorem. It states that for a body in a potential flow with circulation, the lift force per unit length is directly proportional to the circulation and the flow speed.
$$L = \rho\, U\, \Gamma$$
L is the lift force (per unit length), ρ is the fluid density (set by your "Fluid" choice), U is velocity, and Γ is circulation. Notice drag is zero in this ideal model—a famous paradox! Real drag appears when you account for viscosity and vortex shedding.
Frequently Asked Questions
Increasing the flow velocity U increases lift and drag, and narrows the spacing of streamlines. Increasing the circulation Γ strengthens the lift due to the Magnus effect and increases the asymmetry of the streamlines. Changes can be observed in real time.
Using the empirical formula for the Strouhal number (St ≈ 0.2), the frequency is calculated as f = St · U / d from the flow velocity U and the cylinder diameter d. However, since potential flow theory does not directly reproduce vortex shedding, this value is displayed as a reference.
No. This tool is based on potential flow theory, which assumes an inviscid, incompressible ideal flow. It does not include the effects of actual viscosity or turbulence, so it is recommended for qualitative understanding and educational purposes.
Typical examples include a curveball in baseball and a knuckleball in soccer. By adjusting the circulation Γ in this tool, you can visually understand the changes in lift acting on a rotating sphere. It is also useful for engineering applications such as rotor sails on ships.
Real-World Applications
Bridge & Skyscraper Design: Wind flowing around bridge cables or building columns can shed vortices at a regular frequency. If this matches the structure's natural frequency, it causes dangerous resonance and oscillations. Engineers use simulations like this to predict the shedding frequency (Strouhal number) and design accordingly.
Sports Ball Aerodynamics: The Magnus effect is why a soccer ball curves, a baseball has a "curveball," or a tennis ball dips with topspin. By adjusting the spin (circulation Γ) and speed (U), players control the lift force to outmaneuver opponents.
Heat Exchanger & Pipeline Design: Arrays of cylinders (tube bundles) are common in heat exchangers. Understanding the flow patterns and vortex shedding is crucial for maximizing heat transfer efficiency and minimizing flow-induced vibration that can lead to fatigue failure.
Wind Turbine & Propeller Blades: The cross-section of a blade can be approximated as an airfoil, but the principles of circulation generating lift are directly derived from this cylinder model. It's the foundational concept for predicting the performance and loads on rotating machinery.
Common Misconceptions and Points to Note
Let's go over a few points that are easy for CAE beginners to misunderstand when using this simulator. First is the point that "potential flow is not a universal solution". The beautiful streamlines drawn by this calculation are an ideal model that ignores viscous effects. For example, right at the surface of a cylinder, a real fluid has zero velocity due to viscosity (the no-slip condition), but this simulation does not reproduce that. Think of this as just the first step to understanding the "fundamental mechanism of lift generation" or the "effect of circulation".
Next is the realism of parameter settings. For instance, if you set the circulation Γ to an extremely large value, the streamlines become unrealistically tightly wound. In an actual Magnus effect, only a finite circulation determined by the balance between rotation speed and flow velocity is generated. For example, for a ball with a diameter of 0.1m rotating at 30 revolutions per second (1800 rpm) in a flow of 20 m/s, the circulation Γ can be roughly calculated by $2\pi R^2 \omega$, and its order of magnitude is around a few m²/s. When you move the sliders, you'll get a better feel for it if you keep values of this scale in mind.
Finally, regarding the limitations of drag calculation. The drag coefficient $C_D$ used here is an "empirical rule" based on Reynolds number. Therefore, its value naturally differs from the drag obtained by integrating detailed pressure distributions and viscous stresses from actual CAE analysis (e.g., solving the Navier-Stokes equations with CFD). The drag from this tool is an "estimate", and you should treat it as a reference value, especially in high Reynolds number regions where flow separation becomes complex.