Stall cells over an airfoil. Part 1: Three-dimensional flow organisation and vorticity dynamics

Using a hybrid RANS/LES approach, this study characterizes the three-dimensional evolution of stall cells over an airfoil, revealing how spanwise separation variations and Crow-type instabilities between vortex tubes drive complex vorticity dynamics and a previously unreported linear rotation of spanwise velocity structures.

The Gist

The "Wobbly Wing" Mystery: Why Airfoils Don't Always Fly Smoothly

Imagine you are driving a car on a perfectly smooth highway. Everything feels stable, predictable, and steady. Now, imagine that same highway suddenly turns into a series of rolling hills, side-to-side dips, and unpredictable gusts of wind that push your car left and right.

In the world of aerodynamics, this "bumpy ride" happens to airplane wings and wind turbine blades when they go into a state called stall. When a wing "stalls," the smooth air flowing over it breaks apart, creating chaotic, swirling patterns. Scientists call these patterns "stall cells."

This paper is a deep dive into the "DNA" of these swirls to understand why they form and how they move.

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1. The "Dance of the Two Snakes" (The Mechanism)

To understand what’s happening, imagine two long, thin snakes made of smoke.

• Snake A is the air separating from the top of the wing.
• Snake B is a swirling vortex of air trailing from the back edge of the wing.

These two "smoke snakes" are rotating in opposite directions. As they pass each other, they don't just ignore one another; they start to influence each other. This creates a "Crow-type instability."

Think of it like two dancers spinning in opposite directions. If they get too close, they won't stay in straight lines; they will start to wobble and bend in a wave-like pattern. This "wobble" is what creates the stall cells. Instead of the air being a smooth sheet, it becomes a series of alternating "humps" and "hollows."

2. The "Spinning Carousel" (The Discovery)

The researchers found something brand new. They noticed that as these air swirls move further away from the wing (downstream), they don't just travel in a straight line. They actually rotate.

Imagine a carousel spinning as it moves down a track. The "peaks" of the air swirls (where the wind is strongest) seem to rotate around fixed points, like a spinning top moving along a path. The researchers even found a mathematical "rule" (a formula) that predicts exactly how much they will rotate based on how far they have traveled. It’s like being able to predict exactly how much a spinning top will tilt after it has rolled ten feet.

3. The "Unstable Seesaw" (Why it Matters)

The study also looked at what happens when you tilt the wing further (increasing the "Angle of Attack").

• At a moderate tilt (14°): The stall cells are like a steady, rhythmic heartbeat. They are predictable and stay in the same place.
• At a steeper tilt (16°): The system becomes "unstable." It’s like a seesaw that won't stay level. The patterns start to shift, change shape, and fight for dominance. One side becomes stronger than the other, making the airflow very "jittery."

Why should we care?

If you are designing a massive wind turbine or a new airplane, you want to know exactly how much "shake" the machine will feel.

If the air is hitting the wing in these "humps and hollows" rather than a smooth stream, it creates uneven pressure. This is like a person walking with one heavy boot and one light shoe—it makes the whole structure vibrate and puts stress on the materials.

In short: By understanding the "dance" of these air vortices, engineers can build better, stronger, and more efficient wings that can handle the "bumpy road" of high-speed flight and heavy winds.

Technical Summary

Technical Summary: Stall Cells over an Airfoil (Part 1)

1. Problem Statement

The study addresses the complex three-dimensional (3D) flow structures known as stall cells that emerge in the separated flow regions of airfoils. While traditional aerodynamic models often treat trailing-edge separation as a 2D phenomenon, experimental evidence shows that stall cells—organized spanwise patterns of alternating flow direction—significantly impact aerodynamic load distribution, stability, and performance.

The authors identify several critical knowledge gaps:

• The lack of characterization of stall cell behavior under moderate turbulence (typical of real-world wind turbine applications).
• The limited understanding of the streamwise evolution (downstream development) of these structures.
• The need for a clearer understanding of the vorticity dynamics (the interaction between spanwise, streamwise, and vertical vorticity) that drive these cells.
• The difficulty in capturing these phenomena using either low-fidelity RANS or computationally prohibitive LES models.

2. Methodology

The researchers employed a high-fidelity hybrid RANS/LES approach using Delayed Detached Eddy Simulation (DDES) with the Shear Stress Transport (SST) turbulence model.

• Computational Setup: The study used the ISIS-CFD solver. The mesh was adaptively refined, starting from 13 million cells and increasing to approximately 130 million cells to resolve high-gradient regions in the separated flow.
• Test Case: A scaled-down (1/10th) section of a 2MW wind turbine blade (resembling a NACA63-3-420 profile with 4% camber) was simulated at a chord-based Reynolds number of $Re_c = 2.0 \times 10^5$.
• Conditions: Simulations were conducted at various angles of attack (AoA), specifically focusing on $10^\circ, 14^\circ, 16^\circ,$ and $20^\circ$, under a moderate inflow turbulence intensity of $TI = 3\%$.

3. Key Contributions & Results

The paper provides a multi-faceted analysis of the stall cell mechanism:

• Vorticity Dynamics & Formation Mechanism: The study identifies a Crow-type instability as the primary driver. A separation vortex tube (carrying spanwise vorticity, $\Omega_z$) interacts with a counter-rotating trailing-edge vortex tube. This interaction causes the tubes to bend in a wave-like pattern. This bending induces vertical vorticity ($\Omega_y$), which in turn drives the alternating spanwise velocity ($w$) characteristic of stall cells.
• Local Load Non-uniformity: The 3D organization leads to significant spanwise variations in pressure. The mid-span experiences premature separation due to flow bifurcation (an unstable saddle point), while the regions at $z/c = \pm 1$ experience flow convergence (stable nodes), which sustains attached flow further downstream. This results in lower lift at the mid-span compared to the outer span.
• Discovery of a New Rotational Pattern: The authors report a previously undocumented phenomenon: the maxima of the spanwise velocity structures rotate around fixed spanwise axes ($z/c = \pm 1$) as they move downstream. This rotation angle ($\zeta$) follows a linear relationship with downstream distance:
  $$\zeta = 14.5(x/c) - 0.8$$
• Streamwise Evolution of Vorticity: The study tracks the evolution of streamwise vorticity ($\Omega_x$), identifying a Top Vorticity Area (TVA) and a Bottom Vorticity Area (BVA). As the flow moves downstream, the BVA becomes dominant due to its greater vortex strength.
• Effect of Angle of Attack (AoA): Increasing the AoA from $14^\circ$ to $16^\circ$ increases the number of stall cells (from 2 to 3) and triggers a transition from a stable, symmetric arrangement to an unstable, asymmetric, and irregular flow pattern.

4. Significance

This research is significant for both fundamental fluid mechanics and practical engineering:

• Aerodynamic Prediction: It demonstrates that single-spanwise measurements are insufficient for characterizing separated flows, highlighting the necessity of 3D analysis for accurate load prediction.
• Wind Energy: By proving that stall cells persist under $3\%$ turbulence, the study confirms that these structures are highly relevant to the structural loading and performance of real-world wind turbine blades.
• Theoretical Foundation: The findings provide the physical basis for a new vortex-based analytical model (presented in a companion paper), bridging the gap between linear stability theory and nonlinear observed dynamics.