Numerical simulations of transition and long-term response of a wind turbine airfoil

This paper presents numerical simulations using Nek5000 and EllipSys to analyze the transition and long-term flow response of an FFA-W3 airfoil at low Reynolds numbers, validating the EllipSys code's ability to capture Kelvin-Helmholtz instabilities and identifying a slow, periodic modulation of the normal-force coefficient linked to low-frequency oscillations and potential bubble bursting.

The Gist

Imagine a wind turbine blade as a giant, spinning wing. Just like an airplane wing, it needs smooth airflow to work efficiently. But when the wind hits it at certain angles, the air can get "stuck" and separate from the surface, creating a chaotic, swirling mess. This paper is like a high-tech wind tunnel experiment, but instead of using a physical model, the researchers built a virtual one inside a supercomputer to watch exactly how this air behaves.

Here is the story of their discovery, broken down into simple concepts:

1. The Virtual Wind Tunnel

The researchers wanted to study a specific slice of a massive wind turbine blade (from a 10-MW turbine). They used two different computer programs, NEK5000 and ELLIPSYS, to simulate the air flowing over this blade.

Think of NEK5000 as a high-end, ultra-precise camera that captures every tiny detail but is very slow and expensive to run. ELLIPSYS is like a slightly faster, more efficient camera. The team first had to prove that the "faster" camera (ELLIPSYS) could see the same things as the "high-end" one. They found that while ELLIPSYS missed a few tiny, faint ripples in the smooth air (because it smoothed things out a bit too much), it was excellent at capturing the big, chaotic swirls that actually matter for the blade's performance.

2. How Wide Does the Tunnel Need to Be?

Before running the long simulations, they had to figure out how wide their virtual "wind tunnel" needed to be. If the tunnel is too narrow, it might squeeze the air and create fake results. If it's too wide, it wastes computer power.

They tested a "narrow" tunnel (10% of the wing's width) against a "wide" tunnel (20% of the width).

• The Analogy: Imagine watching a river flow. If you only look at a narrow strip of the river, do you miss the big waves?
• The Result: They found that the narrow tunnel was actually enough. The big waves and swirls formed perfectly well in the narrow space. This meant they could save a lot of computer time by using the smaller, narrower simulation box.

3. The "Bubble" and the "Flap"

The most interesting part of the study happened on the top of the wing (the suction side).

• The Separation Bubble: As the air flows over the wing, it peels away for a moment, creating a small, recirculating pocket of air called a "Laminar Separation Bubble" (LSB). Think of this like a tiny, temporary whirlpool on the surface of the wing.
• The Instability: Inside this bubble, the air doesn't just sit still; it vibrates and rolls up into waves (like ripples on a pond). The researchers watched these waves grow. They found that the main "roller" in this bubble was a type of instability called the Kelvin-Helmholtz mode.
• The Discovery: They confirmed that the "faster" computer program (ELLIPSYS) could accurately predict how these waves grew and how the bubble behaved, matching the results of the ultra-precise program.

4. The Slow, Rhythmic Pulse (The Big Surprise)

After validating their tools, they let the simulation run for a very long time (equivalent to 50 times the air flowing past the wing). This is where they found something special.

While the air was churning with fast, chaotic movements, they noticed a very slow, rhythmic pulse in the force pushing on the wing.

• The Analogy: Imagine a drumbeat. The fast churning of the air is like a rapid, high-pitched drumroll. The slow pulse they found is like a deep, slow heartbeat that happens once every 48 seconds (in simulation time).
• The Effect: This slow heartbeat caused the force on the wing to wobble up and down by about 10.5%.
• The Connection to Real Turbines: When they translated this back to a real, spinning wind turbine, they realized this slow pulse happens once every 7.7 full rotations of the blade.

5. Why Does This Happen?

The researchers believe this slow pulse is caused by a cycle of the air "stalling" (getting stuck) and "unstalling" (letting go) on the wing.

• The Cycle: The air gets stuck, creating a big bubble. Then, something triggers the bubble to burst, and the air reattaches smoothly. Then, the pressure builds up again, the bubble forms, and the cycle repeats.
• The Trigger: They suspect this happens because the air is swirling backward so strongly on the wing that it creates a state of "absolute instability"—a fancy way of saying the air is so turbulent it can't help but oscillate on its own.

6. The Bottom Line

This study is a success story for computer modeling. They proved that a faster, more efficient computer program (ELLIPSYS) can be trusted to study complex wind turbine physics, provided you check it against the "gold standard" first.

They discovered that even on a thick wind turbine blade, there is a very slow, rhythmic "breathing" of the airflow that happens roughly every 8 rotations of the blade. This breathing causes the lift (the force that spins the turbine) to rise and fall significantly. Understanding this slow rhythm is crucial because, while it might not break the turbine immediately, these slow, large swings in force could eventually fatigue the materials over many years of operation.

In short: They built a virtual wind tunnel, proved a fast computer could do the job, and discovered that wind turbine blades have a slow, rhythmic "heartbeat" caused by air bubbles forming and bursting on their surface.

Technical Summary

Technical Summary: Numerical Simulations of Transition and Long-Term Response of a Wind Turbine Airfoil

Problem Statement
Flow separation on wind turbine blades, driven by elevated flow incidence angles and thick airfoil geometries, significantly impacts performance and structural loading. Previous studies have identified multiple natural frequencies in separated flows, including wake shedding, Kelvin-Helmholtz (KH) modes, and low-frequency oscillations (LFOs). LFOs are characterized by strong lift variations and are often attributed to the periodic stalling and unstalling of the flow, potentially linked to absolute instability within laminar separation bubbles (LSBs). While LFOs have been observed in various airfoil studies, their occurrence at low angles of attack (AoA) on thick wind turbine airfoils, and the specific mechanisms driving them at these conditions, require further investigation. This study focuses on the transition and long-term response of a section of the DTU 10-MW Reference Wind Turbine airfoil (FFA-W3 series) at a chord Reynolds number ($Re_c$) of $1 \times 10^5$.

Methodology
The research employs wall-resolved large eddy simulations (LES) without subgrid-scale models to solve the incompressible Navier-Stokes equations. Two solvers are utilized:

1. NEK5000: A spectral element method (SEM) code known for minimal numerical dissipation and high accuracy.
2. ELLIPSYS: A finite volume code developed at DTU/Risø, traditionally used for RANS but here applied to implicit LES.

The study involves a systematic validation of ELLIPSYS against NEK5000. Key methodological steps include:

• Domain Sensitivity: Assessing the spanwise domain width ($L_z$) by comparing simulations with $L_z = 0.1c$ and $L_z = 0.2c$ to ensure the resolution of relevant flow structures.
• Solver Validation: Comparing mean flow fields, perturbation evolution, and spectral characteristics between the two solvers.
• Stability Analysis: Utilizing Parabolized Stability Equations (PSE) and Spectral Proper Orthogonal Decomposition (SPOD) to analyze the growth of instabilities (Tollmien-Schlichting and KH modes) and the spatial structure of coherent modes.
• Long-Term Integration: Using the computationally more efficient ELLIPSYS solver to simulate flow evolution over 50 flowthroughs ($T = 50c/U_\infty$) to capture low-frequency phenomena.

Key Results

• Domain Width: A spanwise width of 10% of the chord ($L_z = 0.1c$) was found sufficient to capture the evolution of main disturbances and reproduce time-averaged flow statistics, matching results from a wider domain ($L_z = 0.2c$).
• Solver Validation: ELLIPSYS demonstrated close agreement with NEK5000 for mean flow fields and the evolution of the most amplified perturbations. However, ELLIPSYS underpredicted the amplitude of Tollmien-Schlichting (TS) waves in the attached boundary layer due to higher numerical dissipation. Conversely, ELLIPSYS accurately predicted the evolution of the KH mode within the laminar separation bubble (LSB), aligning well with PSE predictions.
• Transition Mechanism: Transition on the suction side is driven by KH instability developing on the separated shear layer. The most amplified KH mode has a frequency of $f \approx 15$, and its downstream evolution is well-captured by both solvers and PSE.
• Low-Frequency Oscillations (LFOs): Long-term simulations revealed a slow modulation of the normal force coefficient ($C_N$) with an amplitude of 10.5% and a period of 48 flowthroughs. This corresponds to a frequency $f = 0.021$ and a Strouhal number $St = 0.0012$.
  • This frequency is approximately 720 times lower than the primary KH instability frequency.
  • In the context of the DTU 10-MW turbine, this period equates to roughly 7.7 blade rotations.
  • The observed $St$ is lower than values typically reported in literature for other airfoils, occurring at a relatively small effective angle of attack ($3.1^\circ - 3.3^\circ$).

Significance and Claims
The paper establishes that ELLIPSYS is a viable tool for wall-resolved LES of transitional flows, offering a computationally efficient alternative to spectral element codes for long-time integrations. The study confirms that the periodic stalling and unstalling of the flow, potentially triggered by absolute instability due to high reverse flow (up to -17% on the suction side), is responsible for the observed LFOs.

A significant finding is the identification of LFOs on a thick airfoil (24% thickness) at a low angle of attack, a condition distinct from the thin-airfoil stalls typically associated with such phenomena in literature. The authors note that the reverse flow on both sides of the airfoil is sufficient to allow absolute instability, which may drive the periodic bursting of the LSB into fully stalled flow. The study contributes to the understanding of how thick airfoil geometry influences the onset and characteristics of low-frequency oscillations, highlighting that these phenomena can occur at lower incidence angles and Strouhal numbers than previously documented for standard airfoils.