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arxiv: 2507.22714 · v3 · pith:XEZYUHHAnew · submitted 2025-07-30 · ⚛️ physics.flu-dyn

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

Angelo Paduano , Francesco Scarano , Julio Cordioli , Damiano Casalino , Francesco Avallone This is my paper

Pith reviewed 2026-05-21 23:47 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn
keywords acoustic linergrazing flowturbulent boundary layerdisplacement thicknessshear layerimpedanceLattice-Boltzmann simulation
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The pith

Turbulent boundary layer growth alters acoustic dissipation along an acoustic liner by weakening downstream orifice shear layers.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper uses Lattice-Boltzmann Very-Large-Eddy simulations to study how a developing turbulent grazing flow interacts with a single-degree-of-freedom acoustic liner containing 11 streamwise cavities. It shows that the boundary layer displacement thickness increases along the liner compared with a smooth wall, forming localized humps after each orifice. This growth displaces the mean flow and weakens the shear layer inside downstream orifices, changing the acoustic-induced mass flow rate and therefore the local dissipation of sound energy. The in-situ impedance method captures strong spatial variations while averages hide differences between upstream- and downstream-propagating waves, indicating that eduction techniques must incorporate the spatially evolving flow.

Core claim

The boundary layer displacement thickness δ* grows along the streamwise direction over the liner, producing localized humps immediately downstream of each orifice. Orifices displace the grazing flow away from the face sheet, an effect strengthened by acoustic waves and dependent on propagation direction. The resulting increase in δ* weakens the shear layer at downstream positions, thereby modifying the acoustic-induced mass flow rate through the orifices and causing acoustic energy to be dissipated differently along the liner length.

What carries the argument

The streamwise growth of boundary-layer displacement thickness δ*, which progressively weakens orifice shear layers and modulates acoustic mass flow.

If this is right

  • In-situ impedance shows strong spatial variations while averaged values remain similar for opposite wave directions.
  • Mode-matching reveals clearer differences between upstream- and downstream-propagating waves.
  • Acoustic energy dissipation varies along the liner because of changing near-wall flow features.
  • Current impedance eduction methods omit the effect of spatially developing turbulent flow.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Liner performance in long ducts may vary with position because of cumulative boundary-layer growth.
  • Accounting for flow development could improve accuracy when extrapolating short-sample impedance data to full-scale applications.
  • Similar position-dependent effects may appear in other perforated surfaces exposed to grazing flow.

Load-bearing premise

The simulations faithfully reproduce the experimental boundary-layer development and orifice flows without significant numerical or modeling errors that would mask the reported spatial variations.

What would settle it

Experiments that measure constant δ* along the liner or uniform acoustic mass-flow rates through every orifice regardless of streamwise position would falsify the claim.

Figures

Figures reproduced from arXiv: 2507.22714 by Angelo Paduano, Damiano Casalino, Francesco Avallone, Francesco Scarano, Julio Cordioli.

Figure 1
Figure 1. Figure 1: Sampling location for the in-situ technique for both experiments and [PITH_FULL_IMAGE:figures/full_fig_p008_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Schematic representation of the full computational domain. [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: However, both configurations maintain the same number of orifices per cavity, [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Schematic representation of the VR regions. [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: (a) Mean velocity profile comparison with experimental data by Bonomo [PITH_FULL_IMAGE:figures/full_fig_p012_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: SPL decay along the channel centerline ( [PITH_FULL_IMAGE:figures/full_fig_p013_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: SPL along the liner’s surface for the case with SPL = 145 dB and [PITH_FULL_IMAGE:figures/full_fig_p014_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: (a) Resistance and (b) reactance along the liner’s surface obtained with in-situ [PITH_FULL_IMAGE:figures/full_fig_p015_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Streamwise distribution of resistance and reactance compared with the semi [PITH_FULL_IMAGE:figures/full_fig_p015_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Comparison of (a, c) resistance and (b, d) reactance components of impedance [PITH_FULL_IMAGE:figures/full_fig_p016_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: (a, c, e) Resistance and (b, d, f) reactance obtained from the MM and in [PITH_FULL_IMAGE:figures/full_fig_p018_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: (a, b) Instantaneous streamwise u ′ (c, d) and wall-normal v ′ velocity components at y/h = 0.003. (e, f) Instantaneous vertical velocity v ′ component at z/l = 0.5. (a, c, e) Represent the smooth wall case while (b, d, f) represent the lined wall case [PITH_FULL_IMAGE:figures/full_fig_p019_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Time-average of streamwise velocity profile in outer coordinates sampled at [PITH_FULL_IMAGE:figures/full_fig_p020_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Time-averaged velocity profiles sampled at (a, d, g) [PITH_FULL_IMAGE:figures/full_fig_p021_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: Streamwise development of δ over the liner. (a) Effect of acoustic waves’ amplitudes at a fixed frequency of 1400 Hz; (b) effect of the acoustic waves’ frequency at a fixed amplitude of 145 dB; (c) effect of different propagation directions at a fixed frequency of 1400 Hz and amplitude of 145 dB [PITH_FULL_IMAGE:figures/full_fig_p023_15.png] view at source ↗
Figure 16
Figure 16. Figure 16: Streamwise development of δ ∗ over the liner. (a) Effect of different acoustic waves’ amplitude at a fixed frequency of 1400 Hz ; (b) effect of acoustic waves’ frequency at a fixed amplitude equal to 145 dB; (c) effect of different propagation directions at a fixed frequency of 1400 Hz [PITH_FULL_IMAGE:figures/full_fig_p024_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Contour of mean velocity component (a, c) and wall-normal velocity [PITH_FULL_IMAGE:figures/full_fig_p025_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Contour of ν(|dU/dy|) 1/2 for (a) the first and (b) the last cavity for the flow￾only case. even more pronounced in the last cavity: the shear over its first orifice is already weaker than that in the first cavity, and it diminishes sharply over the second orifice. The stronger shear layer at the first cavity obstructs the penetration of the acoustic wave into the orifice with respect to what happens at t… view at source ↗
Figure 21
Figure 21. Figure 21: Spatial distribution of σv/U0 into two adjacent orifices of the seventh cavity at (a) y/τ = 0, (b) y/τ = −0.5, (c) y/τ = −1. Lined flow only case, flow and acoustics with SPL = 145 dB f = 1400 Hz and upstream acoustic source, SPL = 145 dB f = 1400 Hz and downstream acoustic source. displacement thicknesses. As established earlier, a thicker δ ∗ results in a weaker shear layer over the orifices, which in t… view at source ↗
Figure 23
Figure 23. Figure 23: Contour plots of the acoustic-induced velocity at the peak of the inflow phase [PITH_FULL_IMAGE:figures/full_fig_p034_23.png] view at source ↗
Figure 18
Figure 18. Figure 18: Consequently, both during the inflow and outflow phases, the high-intensity [PITH_FULL_IMAGE:figures/full_fig_p034_18.png] view at source ↗
Figure 24
Figure 24. Figure 24: Contour plots of the acoustic-induced velocity inside the orifices for different [PITH_FULL_IMAGE:figures/full_fig_p035_24.png] view at source ↗
Figure 25
Figure 25. Figure 25: Comparison of the phase-locked mass flow rate over a cycle for a whole cavity. [PITH_FULL_IMAGE:figures/full_fig_p035_25.png] view at source ↗
Figure 26
Figure 26. Figure 26: Streamwise distribution of the mass flow rate. [PITH_FULL_IMAGE:figures/full_fig_p036_26.png] view at source ↗
Figure 27
Figure 27. Figure 27: Comparison of skin friction coefficient with friction law Eq. A 1 and [PITH_FULL_IMAGE:figures/full_fig_p038_27.png] view at source ↗
Figure 28
Figure 28. Figure 28: Boundary layer velocity profiles upstream of the liner and at three spanwise [PITH_FULL_IMAGE:figures/full_fig_p039_28.png] view at source ↗
read the original abstract

The interaction between acoustic waves and turbulent grazing flow over an acoustic liner is investigated using Lattice-Boltzmann Very-Large-Eddy simulations. A single-degree-of-freedom liner with 11 streamwise-aligned cavities is studied in a grazing flow impedance tube. The conditions replicate reference experiments from the Federal University of Santa Catarina. The influence of grazing flow (with a centerline Mach of 0.32), acoustic wave amplitude, frequency, and propagation direction relative to the mean flow is analysed. Impedance is computed using both the in-situ and the mode-matching methods. The in-situ method reveals strong spatial variations; however, averaged values throughout the sample show minimal differences between upstream and downstream propagating waves, in contrast to the mode-matching method. Flow analyses reveal that the orifices displace the flow away from the face sheet, with this effect amplified by acoustic waves and dependent on the wave propagation direction. Consequently, the boundary layer displacement thickness (${\delta}$*) increases along the streamwise direction compared to a smooth wall and exhibits localised humps downstream of each orifice. The growth of ${\delta}$* alters the flow dynamics within the orifices by weakening the shear layer at downstream positions. This influences the acoustic-induced mass flow rate through the orifices, suggesting that acoustic energy is dissipated differently along the liner. The role of near-wall flow features highlights the need to consider a spatially evolving turbulent flow when studying the acoustic-flow interaction and measuring impedance. The spatial development of the turbulent flow may also partly explain the upstream-downstream impedance differences, as current eduction methods do not account for it.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The paper investigates the interaction between acoustic waves and a developing turbulent grazing flow over a single-degree-of-freedom acoustic liner with 11 streamwise-aligned cavities using Lattice-Boltzmann Very-Large-Eddy Simulations (LBM-VLES). Replicating reference experiments at a centerline Mach number of 0.32, impedance is computed via both in-situ and mode-matching methods, revealing strong spatial variations in the former. Flow diagnostics show that orifices displace the flow, increasing boundary-layer displacement thickness δ* along the streamwise direction with localized humps, which in turn weakens downstream orifice shear layers, alters acoustic-induced mass flow rates, and produces spatially varying acoustic dissipation. The work concludes that spatially evolving turbulent flow must be accounted for in impedance measurements and may partly explain upstream-downstream differences.

Significance. If the LBM-VLES faithfully reproduces the experimental boundary-layer growth and near-orifice structures, the results would establish a concrete physical link between streamwise δ* evolution and spatially nonuniform dissipation, providing a mechanistic explanation for impedance asymmetries that current uniform-flow eduction methods cannot capture. The direct coupling of flow-field diagnostics to both in-situ and mode-matching impedance calculations is a notable strength.

major comments (1)
  1. [Flow analyses (abstract and §4)] The central claim that δ* growth weakens downstream orifice shear layers and thereby changes acoustic mass flow (abstract and flow-analyses section) is load-bearing for the reported spatial dissipation variations. No quantitative validation of simulated mean velocity profiles, turbulence intensity, or δ* evolution at multiple streamwise stations against the Santa Catarina reference experiments is presented; without such metrics it remains possible that numerical dissipation or sub-grid modeling in the LBM-VLES artificially produces the observed trends.
minor comments (1)
  1. [Abstract] The abstract states that in-situ impedance shows strong spatial variations yet averaged values exhibit minimal upstream-downstream differences, but supplies no quantitative error bars, grid-convergence data, or explicit validation metrics against the reference experiments.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive review and for recognizing the potential significance of linking boundary-layer evolution to spatially varying dissipation. We address the single major comment below and outline the changes planned for the revised manuscript.

read point-by-point responses

  1. Referee: The central claim that δ* growth weakens downstream orifice shear layers and thereby changes acoustic mass flow (abstract and flow-analyses section) is load-bearing for the reported spatial dissipation variations. No quantitative validation of simulated mean velocity profiles, turbulence intensity, or δ* evolution at multiple streamwise stations against the Santa Catarina reference experiments is presented; without such metrics it remains possible that numerical dissipation or sub-grid modeling in the LBM-VLES artificially produces the observed trends.

    Authors: We agree that quantitative validation of the simulated mean flow and turbulence quantities would strengthen in the reported δ* growth mechanism. The present manuscript replicates the experimental geometry, Mach number (0.32), and acoustic conditions but does not include side-by-side comparisons of velocity profiles, turbulence intensity, or δ* at multiple streamwise stations. In the revised version we will add these comparisons, using both the available experimental reference data and the expected turbulent boundary-layer scaling, together with a brief discussion of grid resolution and sub-grid modeling sensitivity. We note that the observed spatial trends in orifice mass flow and in-situ impedance remain consistent with the physical picture of orifice-induced displacement thickening, independent of the precise numerical values of δ*. revision: yes

Circularity Check

0 steps flagged

No significant circularity in derivation chain

full rationale

The paper reports results from Lattice-Boltzmann Very-Large-Eddy simulations of acoustic-flow interaction over a liner, with claims about streamwise δ* growth, orifice shear-layer weakening, and spatially varying acoustic mass flow derived directly from the simulated velocity fields and mass-flow diagnostics. No equations are presented that reduce these observations to quantities defined by the same fitted data or target acoustic results. Impedance values are computed via standard in-situ and mode-matching post-processing of the simulation outputs rather than by construction from the reported trends. The work replicates external experimental conditions but does not invoke self-citations as load-bearing uniqueness theorems or smuggle ansatzes; the derivation remains independent of the specific spatial dissipation differences it reports.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available, so the ledger is necessarily incomplete. No explicit free parameters, ad-hoc axioms, or new entities are named in the provided text.

pith-pipeline@v0.9.0 · 5836 in / 1160 out tokens · 33368 ms · 2026-05-21T23:47:38.046917+00:00 · methodology

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Realistic sheared flow profile effects on acoustic impedance eduction in small 3D-ducts

    physics.flu-dyn 2025-11 conditional novelty 6.0

    Realistic sheared flow profiles in small 3D ducts can be approximated by uniform or 1D profiles for acoustic impedance eduction when the bulk Mach number is correctly accounted for.