Rotating Cylinder: Magnus Effect

Flow past a spinning cylinder at Re=100. The Magnus effect creates a transverse force proportional to angular velocity. Ladd (1994) moving boundary applies tangential velocity on the cylinder surface. Variable spin ratio (S = 0.5, 1.0, 2.0) demonstrates lift enhancement.

Setup

Parameter Value
Grid 1200 × 800
Cylinder diameter D 60 cells
Reynolds number 100
Spin ratio S 0.5, 1.0, 2.0
Inlet velocity uinflow = 0.1 lu/ts
Tau (relaxation parameter) 0.68
Number of steps 15,000
Reference length D = 60 cells
Collision MRT (d'Humieres 2002)
Boundary condition Ladd (1994) moving boundary + Bouzidi
Lattice spacing / time step Δx = 1, Δt = 1

Flow Field

Use the tabs below to select a parameter variant. Top left: steady-state velocity contour with streamlines. Top right: flow evolution from rest to steady state. Bottom: pressure and vorticity fields at steady state.

Velocity (Contour | Streamlines)

Contour Streamlines
Contour
Streamlines

Drag the handle to wipe between the velocity-magnitude contour and the streamline plot.

Flow Evolution

Frame 0 / 50

Pressure Coefficient Cp

Cp

Pressure Coefficient Cp

Vorticity

Vorticity

Vorticity

Validation

Spin Ratio S Regime Computed Cd Computed Cl Cl (Kutta-Joukowski)
0.5 Moderate rotation 1.32 +0.60 3.14
1.0 Strong rotation 1.35 +1.13 6.28
2.0 Very strong rotation 1.45 +3.94 12.57
Computed Cl is ~19% of the Kutta-Joukowski inviscid prediction (Cl = 2πS) at S=0.5, rising to ~31% at S=2.0. The viscous effects at Re=100 and the Ladd (1994) moving boundary condition produce lower lift than the inviscid theory predicts. Reference: Mittal & Kumar 2003, Rao et al. 2015.

Discussion

The rotating cylinder exercises the Ladd (1994) moving boundary method, which modifies the standard bounce-back to include wall velocity: f_bb = f_opp - 2*w_i*rho*(e_i . u_wall)/c_s^2. The Magnus effect produces a transverse lift force perpendicular to the freestream, proportional to the spin ratio S. As S increases, the lift coefficient grows while the drag may decrease due to wake suppression on the spinning side.

At sufficiently high spin ratios, vortex shedding can be completely suppressed and the flow becomes steady with a deflected wake. The ratio of surface velocity to freestream velocity (S = u_surface / u_inflow) governs the transition between these regimes. For S > 1, the Flettner rotor regime produces net thrust in certain configurations, which is the basis for Flettner rotor ship propulsion concepts. The computed Cl is 50-60% of the Kutta-Joukowski prediction (Cl = 2πS), consistent with viscous effects at Re=100.