What 72 pitching cycles reveal about NACA 0012 dynamic stall

The airfoil pitches about the quarter-chord point with a mean angle $\alpha_0=10^\circ$ and amplitude $\alpha_a=15^\circ$. The resulting range $-5^\circ \leq \alpha \leq 25^\circ$ crosses the linear regime, stall onset, and deep-stall region during every cycle. A circular sliding region isolates the moving airfoil from the stationary outer domain.

Motion

$\alpha(t)=10^\circ+15^\circ\sin(\Omega t)$

Pivot

$x_p/c=0.25$

Freestream

$U_\infty=14\,\mathrm{m\,s^{-1}}$

Reynolds numbers

$Re=1.35\times10^5$ and $Re=5.0\times10^3$ comparison runs

Reported reduced frequency

$\kappa=\Omega c/(2U_\infty)=0.1$ under the source convention

Boundary layout

Velocity inlet, pressure outlet, upper/lower symmetry

The $28c$-long outer domain places the airfoil $8c$ from the inlet and uses a sliding interface around the pitching body.

The prescribed motion rotates about $x_p/c=0.25$ and sweeps from $-5^\circ$ to $25^\circ$.

The vorticity sequence shows the near-wall shear layer rolling into coherent structures, convecting through the near wake, and organizing into an alternating vortex street. A fixed color range is used throughout so changes in apparent intensity reflect the solution rather than frame-by-frame rescaling.

Spanwise vorticity, 852 frames at 15 fps. The web version is downsampled to 1920 px while preserving the full 56.8-second sequence.

The late-time window shows two closely repeating cycles. Lift follows a strong periodic response while drag contains secondary features associated with separated-flow events. Plotting the same data against angle of attack converts phase lag into a loop: upstroke and downstroke no longer collapse onto a single steady curve.

Late-time load history over $20 \leq t/T \leq 22$, used to inspect cycle-to-cycle repeatability.

Twenty overlaid cycles form persistent $C_L$–$\alpha$ and $C_D$–$\alpha$ envelopes rather than single-valued steady relationships.

A useful comparison must match the force normalization, reference length and phase convention before interpreting differences in load magnitude or startup duration. For restart checks, align the motion phase and compare the developed cycles rather than isolated early peaks. For different Reynolds numbers, compare the loop shape and separation timing alongside peak values; a visually similar response alone does not establish the same numerical accuracy.