On the impact of the turbulent grazing flow development on the acoustic response of an acoustic liner

This study utilizes Lattice-Boltzmann Very-Large-Eddy simulations to demonstrate that the spatial development of turbulent grazing flow over an acoustic liner significantly alters boundary layer dynamics and orifice flow behavior, leading to position-dependent acoustic energy dissipation and discrepancies in impedance measurements that current methods fail to fully capture.

The Gist

The Big Picture: Quieting the Jet Engine

Imagine a jet engine as a giant, noisy vacuum cleaner. To stop it from screaming, engineers line the inside of the engine's air ducts with special "acoustic sponges" called liners. These liners are like a honeycomb of tiny holes leading into small pockets (cavities). When sound waves hit them, the air rushes in and out of these holes, creating friction and tiny whirlpools that turn the sound energy into heat, effectively silencing the engine.

However, inside a real engine, air isn't just sitting still; it's rushing past these liners at high speeds (like a strong wind blowing over a flute). This paper investigates what happens when you combine sound waves, turbulent wind, and these acoustic sponges.

The Experiment: A Digital Wind Tunnel

The researchers didn't build a physical engine. Instead, they used a super-advanced computer simulation (a "digital wind tunnel") to recreate the conditions found in a university lab. They modeled a section of a duct with 11 rows of these honeycomb cavities and blasted them with sound waves while wind blew past them.

They tested different scenarios:

• Wind speed: How fast the air was moving.
• Sound volume: How loud the noise was (from a whisper to a jet roar).
• Sound direction: Did the sound travel with the wind or against it?

Key Findings: The "Moving Carpet" Effect

1. The Wind Pushes the Air Away

Think of the air right next to the liner surface as a thin, sticky carpet. When the wind blows over the liner, it doesn't just slide smoothly; the holes in the liner act like little fans. They push the air slightly away from the surface.

• The Analogy: Imagine a row of people (the holes) standing on a sidewalk. If a strong wind blows, they might lean back. If they start jumping up and down (due to sound), they push the wind even further away.
• The Result: This creates a "thicker" layer of air that the wind has to flow over. As the wind travels down the line of holes, this "air carpet" gets thicker and thicker.

2. The Wind Gets "Lazy" Downstream

Because the air carpet gets thicker as it moves down the line of holes, the wind speed right next to the holes slows down.

• The Analogy: Imagine a river flowing over a series of rocks. At the start, the water is fast and turbulent. As it moves past more rocks, the water gets sluggish and less energetic near the bottom.
• The Result: The "shear" (the friction between the fast wind above and the slow air near the holes) becomes weaker at the end of the liner compared to the beginning.

3. Sound Waves Behave Differently Depending on Direction

This is the most surprising part. The researchers found that it matters which way the sound is traveling relative to the wind.

• Going Against the Wind: If the sound travels against the wind, it hits the "lazy" end of the liner first (where the air carpet is thick and the wind is slow). It then moves toward the "fast" end.
• Going With the Wind: If the sound travels with the wind, it hits the "fast" end first and moves toward the "lazy" end.
• The Consequence: Because the wind conditions change along the liner, the sound wave experiences a different "landscape" depending on its direction. The paper found that the liner absorbs sound differently in these two scenarios. It's like walking up a hill versus walking down a hill; even if the hill is the same, your effort and experience are different.

4. The "Two Different Rulers" Problem

Engineers usually measure how well a liner works by calculating a single number called "impedance" (a measure of resistance to sound).

• The Problem: The paper shows that if you measure this number at the start of the liner, you get a different result than if you measure it at the end.
• The Analogy: Imagine trying to measure the "average temperature" of a room, but one side is freezing and the other is boiling. If you use a ruler that assumes the room is uniform, you get the wrong answer.
• The Finding: The computer simulations showed that the "impedance" isn't a single, fixed number for the whole liner. It changes as you move along the surface because the wind and the air layer change.

Why This Matters (According to the Paper)

The paper concludes that current methods for testing and designing these liners often assume the wind is uniform and the air layer is thin and unchanging. This study proves that assumption is wrong.

• The Wind Matters: The way the wind develops (gets thicker and slower) along the liner changes how the sound is absorbed.
• Direction Matters: The direction the sound travels changes how it interacts with the wind.
• The Takeaway: To design better, quieter engines, engineers need to stop treating the liner as a static object and start accounting for the fact that the wind and the air layer are constantly changing as they move across the surface.

In short: Acoustic liners aren't just static sponges; they are dynamic systems where the wind, the sound, and the air layer all dance together, and the direction of the dance changes the music.

Technical Summary

Technical Summary: On the impact of the turbulent grazing flow development on the acoustic response of an acoustic liner

Problem Statement
Acoustic liners, typically Single Degree of Freedom (SDOF) configurations, are critical for noise attenuation in aircraft engines. While the physics of liners under pure acoustic excitation or in the presence of grazing flow is partially understood, a quantitative gap remains regarding the interaction between acoustic waves and developing turbulent grazing flow over multi-cavity liners. Conventional impedance eduction techniques often assume spatially homogeneous impedance and simplified boundary layer profiles (e.g., infinitely thin vortex sheets). However, recent literature suggests that impedance is sensitive to the flow profile and the direction of acoustic wave propagation. This study addresses the lack of quantitative analysis on how the streamwise development of a turbulent boundary layer, modified by the liner itself and acoustic forcing, influences the local and global acoustic response.

Methodology
The authors employed high-fidelity Lattice-Boltzmann Very-Large-Eddy Simulations (LB-VLES) using the commercial solver PowerFLOW. The computational domain replicated a Grazing Flow Impedance Tube (GFIT) experiment conducted at the Federal University of Santa Catarina (UFSC), featuring a liner with 11 streamwise-aligned cavities, each containing eight orifices.

• Flow Solver: The simulations utilized the D3Q19 lattice scheme with a VLES approach, resolving large turbulence scales while modeling sub-grid scales via a Renormalisation Group (RNG) $k-\epsilon$ model. An extended turbulent wall model (PGE-WM) accounted for pressure gradients.
• Test Cases: Twenty simulations were performed, covering:
  • Smooth wall vs. lined wall configurations.
  • Centerline Mach numbers of 0.0 (no flow) and 0.32 (grazing flow).
  • Acoustic frequencies of 800, 1400, and 2000 Hz.
  • Sound Pressure Levels (SPL) of 130 dB and 145 dB.
  • Acoustic sources located both upstream (co-flow) and downstream (counter-flow) of the liner.
• Impedance Extraction: Two methods were compared:
  1. Mode Matching (MM): An inverse method fitting the global acoustic field to determine average impedance.
  2. In-situ (Dean's method): A point-wise calculation based on pressure measurements at the face sheet and cavity backplate.
• Flow Analysis: A triple decomposition technique was used to separate mean, coherent (acoustic-induced), and stochastic (turbulent) velocity components to analyze flow dynamics within and around the orifices.

Key Results

1. Impedance Variability and Directionality:

   • Spatial Heterogeneity: The in-situ method revealed strong spatial variations in impedance across the liner surface. Resistance values varied by up to a factor of three depending on the sampling location relative to the orifices.
   • Eduction Method Discrepancy: Averaged resistance values obtained via the in-situ method showed minimal difference between upstream and downstream wave propagation. In contrast, the Mode Matching method indicated significant differences, with resistance being lower for upstream-propagating waves. This highlights that the choice of eduction technique significantly impacts the perceived directionality of the liner.
   • Flow Influence: Grazing flow increased the resistance component of impedance. The reactance showed smaller variations, primarily influenced by cavity depth and end corrections.

2. Boundary Layer Development and Displacement Thickness ($\delta^*$):

   • The presence of the liner and its orifices caused the flow to displace away from the face sheet, leading to a significant increase in the boundary layer displacement thickness ($\delta^*$) along the streamwise direction (up to 30% increase compared to a smooth wall).
   • $\delta^*$ exhibited localized "humps" downstream of each orifice.
   • The growth of $\delta^*$ was sensitive to acoustic parameters: it increased with higher SPL, frequencies near resonance, and was dependent on the propagation direction of the acoustic wave.

3. Shear Layer Weakening and Flow Dynamics:

   • The streamwise growth of $\delta^*$ resulted in a weakening of the shear layer over downstream orifices compared to upstream ones.
   • This weakening altered the flow dynamics within the orifices. Specifically, the reduced shear strength in downstream cavities allowed for greater penetration of the acoustic-induced velocity field into the cavity.
   • Consequently, the acoustic-induced mass flow rate through the orifices was higher in downstream cavities when the acoustic wave propagated against the mean flow (downstream source), as the wave encountered weaker shear layers and larger effective orifice areas.

4. Acoustic-Induced Flow Asymmetry:

   • The flow field experienced by an acoustic wave is asymmetric depending on its propagation direction relative to the mean flow. A wave traveling upstream encounters a boundary layer that has not yet fully developed over the liner (thinner $\delta^*$, stronger shear), whereas a wave traveling downstream encounters a fully developed, thicker boundary layer with weaker shear.
   • This asymmetry suggests that acoustic energy dissipation is not uniform along the liner but varies spatially due to the evolving flow topology.

Significance and Conclusions
The study concludes that the assumption of a spatially homogeneous impedance and a static boundary layer is insufficient for characterizing acoustic liners in grazing flow. The development of the turbulent boundary layer over the liner significantly alters the local shear layer strength, which in turn modulates the acoustic-induced mass flow rate and energy dissipation.

The authors assert that:

• The boundary layer displacement thickness ($\delta^*$) is a critical parameter that varies significantly along the liner and must be accounted for in impedance models.
• Current impedance eduction methods, which often assume uniform impedance or simplified boundary conditions, may fail to capture the spatial evolution of the flow-acoustic interaction.
• The direction of acoustic wave propagation relative to the mean flow creates distinct flow environments (different $\delta^*$ and shear profiles) that affect the measured impedance, particularly when using global fitting methods like Mode Matching.

The paper provides a comprehensive, open-access database of these high-fidelity simulations, serving as a benchmark for future studies on acoustic-flow coupling and the development of more robust semi-empirical models for impedance estimation. The findings suggest that future liner characterization and eduction techniques should consider spatially evolving turbulent flows rather than assuming a uniform state.