Tracking stall cell dynamics at high Reynolds numbers

The spanwise organization of the flow over a thick airfoil is investigated using surface pressure measurements for a range of angles of attack around maximum lift and high Reynolds numbers (1 Million). Locally strong pressure fluctuations, which are not detected in the global lift coefficient, are shown to be associated with the presence of a stall cell. The stall cell width is of the order of the chord length and increases linearly with the angle of attack, with a weak dependence on the Reynolds number. Its dynamics at Reynolds numbers larger than 1 Million is dominated by a coherent motion in the spanwise direction with a characteristic velocity of order tenth of the freestream velocity. The motion can be decomposed into a large-scale, low-frequency sweep with a Strouhal number equal to 0.001 combined with faster, smaller-scale oscillations. The coherence of the stall cell makes it possible to track global dynamics from local measurements.

💡 Research Summary

This paper presents a comprehensive experimental investigation of stall‑cell formation and dynamics on a thick two‑dimensional airfoil representative of a wind‑turbine blade section, performed at high Reynolds numbers (Re ≈ 0.5–3.4 × 10⁶) and a wide range of angles of attack (AoA) around the static‑stall region. The airfoil (NACA 0012‑type, 20 % thickness, 4 % camber) was instrumented with 476 pressure taps distributed along three chordwise stations (y = ±0.36 c, 0) and four spanwise lines (x = 0.2 c, 0.4 c, 0.55 c, 0.75 c). Pressure signals were sampled at 512 Hz, filtered to a cut‑off of ~200 Hz, and calibrated using an inverse transfer function. Global lift was measured with a balance, while local lift coefficients were obtained by integrating the pressure distribution.

Key Findings

1. Local vs. Global Lift Discrepancy
   For AoA between 9° and 12°, the locally computed lift coefficient exhibits a pronounced peak and a subsequent negative slope, whereas the global lift curve rises smoothly to its maximum near 18°. This indicates that strong, localized pressure fluctuations associated with a stall cell are largely invisible to global force measurements. The standard deviation of the local lift shows two distinct peaks (12°–15° and >24°), the former being twice as large as the global lift fluctuation level.

2. Steady Stall‑Cell Geometry
   By mapping time‑averaged pressure coefficients onto a colour scale that distinguishes attached, partially separated, and fully separated flow, a mushroom‑shaped three‑dimensional structure is revealed. The pressure standard‑deviation field shows two symmetric maxima on each spanwise line, located roughly at y/c ≈ ±0.5 for the 0.4 c line and at y/c ≈ ±1 for the 0.55 c line. Connecting these maxima defines a “stall‑cell separation line” (SCSL) that marks the front of the cell. The cell width, measured as the maximum spanwise distance between points on the SCSL, is of order one chord at the onset of stall (AoA ≈ 12°) and grows linearly with AoA, exceeding two chords by AoA ≈ 16°. Reynolds‑number dependence is weak: increasing Re from 1.7 × 10⁶ to 3.4 × 10⁶ reduces the width by only 10–20 %. At the lowest Reynolds numbers (0.5 × 10⁶ and 0.85 × 10⁶) the SCSL exhibits a kink, suggesting a split into two adjacent cells, which is confirmed by a third fluctuation peak at mid‑span.

3. Unsteady Dynamics and Spectral Content
   Spectrograms of pressure signals along all chords and spanwise lines show dominant low‑frequency content below 1 Hz. When non‑dimensionalised as Strouhal numbers St = f c sin(AoA)/U, the peaks lie in the range St ≈ 10⁻³–10⁻², with a clear global maximum at St ≈ 0.001 for AoA = 15°. Notably, the locations of these spectral maxima coincide with the SCSL, indicating that the cell front is the source of the coherent low‑frequency oscillation. The dynamics can be interpreted as a large‑scale, low‑frequency “sweep” of the cell front across the span at a characteristic velocity of order 0.1 U, superimposed with faster, smaller‑scale oscillations likely linked to shear‑layer vortices.

4. Coherence and Tracking Capability
   Cross‑correlation analysis between pressure sensors shows that the SCSL propagates spanwise with a nearly constant speed (~0.1 U). Consequently, the motion of the entire three‑dimensional stall cell can be inferred from a single local pressure measurement, providing a practical means for real‑time monitoring of stall‑cell activity on large‑scale aerodynamic surfaces.

Implications
The study demonstrates that at high Reynolds numbers typical of utility‑scale wind turbines, stall cells are robust, spanwise‑coherent structures whose size and dynamics are primarily governed by AoA, with only modest Reynolds‑number effects. The identification of a low‑frequency global mode (St ≈ 0.001) associated with the cell front offers a potential diagnostic signal for active stall control strategies. Moreover, the ability to reconstruct global stall‑cell behaviour from sparse pressure data opens avenues for low‑cost sensor networks on operational blades, where full‑field measurements are impractical.

In summary, the paper provides a detailed experimental characterization of stall‑cell geometry, scaling, and unsteady behaviour, bridging the gap between local pressure diagnostics and global aerodynamic performance at Reynolds numbers relevant to modern wind‑energy applications.