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arxiv: 2512.09587 · v2 · pith:V6SJKTEGnew · submitted 2025-12-10 · ⚛️ physics.flu-dyn

Noise dissipation mechanisms of an acoustic liner under grazing flow

Francesco Scarano , Angelo Paduano , Francesco Avallone This is my paper

Pith reviewed 2026-05-16 23:38 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn
keywords acoustic linergrazing flowvortex sheddingviscous lossesnoise dissipationshear layeraeroacousticsflow topology
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The pith

Grazing flow over an acoustic liner creates a quasi-steady vortex that confines acoustic-induced flow to the downstream half of the orifice and makes vortex shedding phase-dependent.

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

High-fidelity lattice-Boltzmann simulations show how grazing turbulent flow at Mach 0.3 changes the way a single-cavity acoustic liner dissipates sound. Without flow, viscous losses inside the orifice shear layers and vortex shedding each remove energy roughly equally during inflow and outflow, with the balance shifting by sound pressure level. The grazing flow generates a shear layer that forms a quasi-steady vortex, restricting acoustic motion to the downstream half of the orifice and pushing fluid toward the downstream lip. This topology shift increases viscous losses at low sound levels but turns vortex shedding into a net energy generator during outflow. The net result is lower overall acoustic dissipation, which directly accounts for reduced liner performance under realistic flow conditions.

Core claim

In the absence of grazing flow, acoustic energy is dissipated almost equally during both inflow and outflow phases, with vortex shedding dominating at high SPL and viscous losses at low SPL. The introduction of a grazing flow alters the flow topology; in particular, the shear layer past the orifice generates a quasi-steady vortex that confines the acoustic-induced flow to the downstream half of the orifice. This topological change alters the two noise dissipation mechanisms: viscous losses increase at low SPL because the grazing flow pushes the fluid toward the downstream lip of the orifice; vortex shedding becomes phase dependent, dissipating acoustic energy during the inflow phase and the

What carries the argument

The quasi-steady vortex formed by the shear layer past the orifice under grazing flow, which confines acoustic motion to the downstream half and renders vortex shedding phase-dependent.

If this is right

  • Net acoustic dissipation decreases in the presence of grazing flow compared with the no-flow case.
  • Viscous losses become the dominant mechanism at low SPL because fluid is forced toward the downstream lip.
  • Vortex shedding dissipates energy only during inflow and generates energy during outflow.
  • Liner performance depends on the near-wall flow topology and the relative direction of the acoustic wave and grazing flow.

Where Pith is reading between the lines

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

  • Liner orifice geometry could be modified to weaken the quasi-steady vortex and restore balanced dissipation across both phases.
  • The same confinement effect is likely present in any perforated surface exposed to grazing flow, such as engine nacelles or vehicle interiors.
  • Direct experimental visualization of the phase-dependent vortex shedding would provide an independent check on the simulated energy exchange.
  • Ignoring grazing flow in design models will systematically overestimate noise reduction for liners installed on aircraft.

Load-bearing premise

The lattice-Boltzmann very-large-eddy simulation accurately captures both the viscous losses inside the orifice shear layers and the quantitative energy exchange via vortex shedding without significant numerical dissipation or missing sub-grid effects at Mach 0.3 and the reported SPL range.

What would settle it

An experiment that directly measures the phase-resolved acoustic power flux through the orifice under identical grazing flow and SPL conditions and finds no net reduction in dissipation would contradict the predicted topological mechanism.

Figures

Figures reproduced from arXiv: 2512.09587 by Angelo Paduano, Francesco Avallone, Francesco Scarano.

Figure 1
Figure 1. Figure 1: (a) Schematic of the cavity with representation of the coordinate reference system. The y axis is oriented towards the inside of the cavity. (b) Schematic of the computational setup with the grid in a plane crossing the central orifice. with positive 𝑦 directed into the cavity. The nomenclature for the velocity components is the following: 𝑢 ′ , 𝑣′ , 𝑤′ are the instantaneous velocity components, 𝑈, 𝑉, 𝑊 st… view at source ↗
Figure 2
Figure 2. Figure 2: and figure 3 show the contours of the acoustic-induced velocity during the inflow and outflow phases, for the cases without and with grazing flow, respectively. The effect of the SPL is reported in each figure. The reconstructed velocity field is normalized with respect to the velocity of the lumped element model of the Helmholtz resonator (Morse & Ingard 1968): 𝑣 ∗ 𝑎𝑐 = 𝑝 ′ 𝜌𝜔(𝜏 + 0.8𝑑) 1 √︃ (𝜔𝐻 /𝜔) 2 − 1… view at source ↗
Figure 3
Figure 3. Figure 3: Contour of the wall-normal acoustic-induced velocity at the inflow (𝜙 = 𝜋/2) and outflow (𝜙 = 3𝜋/2) phases, effect of the SPL (left to right column), 𝑀 = 0.3. When grazing flow is introduced, the flow topology of the acoustic-induced velocity changes markedly, in agreement with Zhang & Bodony (2016b) and Paduano et al. (2025). The acoustic-induced velocity becomes concentrated in the downstream half of the… view at source ↗
Figure 4
Figure 4. Figure 4: Spatial distribution along the diameter of the non-dimensional acoustic-induced vertical velocity 𝑣𝑎𝑐 as a function of the SPL at half orifice thickness. Various phases are reported, dashed line is the no flow case and solid line is 𝑀 = 0.3 case. With grazing flow, the maximum and minimum of the 𝑣𝑎𝑐 profiles are consistently located in the downstream half of the orifice, around 𝑥/𝑑 ≈ 0.8, due to the quasi-… view at source ↗
Figure 5
Figure 5. Figure 5: Contour of the friction velocity [m/s] to represent the shear layer forming at the mouth of the orifice in the presence of grazing flow at 𝑀 = 0.3, effect of the SPL. At low SPL (figure 5 (a-b)), the shear layer blocks the acoustic-induced velocity from entering the orifice over the majority of the diameter extension. The friction velocity remains high across most of the orifice diameter, except for a smal… view at source ↗
Figure 6
Figure 6. Figure 6: Contour of the power density 𝛱𝑔 [Kg/(m·s 2 )] transferred from the acoustic field to the vortical field during the inflow and outflow phases when varying the SPL. No-flow, forcing frequency equal to 2200 Hz. formation of vortical structures that are convected downstream. At 160 dB the negative contribution extends in the channel following a wake-like pattern downstream of the orifice [PITH_FULL_IMAGE:figu… view at source ↗
Figure 7
Figure 7. Figure 7: Contour of the power density 𝛱𝑔 [Kg/(m·s 2 )] transferred from the acoustic field to the vortical field during the inflow and outflow phases when varying the SPL. 𝑀 = 0.3, forcing frequency equal to 2200 Hz. The evolution of the rate of acoustic dissipation integrated over the domain against the phase, 𝛱 (𝜙), is presented in figure 8. In the absence of grazing flow (figure 8 (a)), 𝛱 (𝜙) exhibits two distin… view at source ↗
Figure 8
Figure 8. Figure 8: Phase averaged acoustic energy dissipation rate by vortex shedding as a function of the phase, 𝛱 (𝜙) [W/(m·s)], (a) for the no-flow case and (b) for the 𝑀 = 0.3 case when varying the SPL (darker and thicker lines indicate higher SPL); (c) comparison of no-flow and 𝑀 = 0.3 case at 160 dB. all SPL levels, the system exhibits a positive dissipation rate during the inflow phase and a negative one during the ou… view at source ↗
Figure 9
Figure 9. Figure 9: Contour of the turbulent stress tensor [Kg/(m·s 2 )] in the inflow and outflow phases when varying the SPL. 𝑀 = 0 case, forcing frequency equal to 2200 Hz. 0 ⇧/2 ⇧ 3/2⇧ 2⇧ 2 4 6 8 ￾ D(￾) 0 ⇧/2 ⇧ 3/2⇧ 2⇧ 0 0.2 0.4 ￾ D(￾) right edge left edge both edges (b) (a) 130 dB 140 dB 150 dB 160 dB (c) (d) 0 ⇧/2 ⇧ 3/2⇧ 2⇧ 1 2 ·10￾2 ￾ D(￾) 0 ⇧/2 ⇧ 3/2⇧ 2⇧ 0 0.2 0.4 ￾ D(￾) right edge left edge both edges 0 ⇧/2 ⇧ 3/2⇧ 2⇧… view at source ↗
Figure 10
Figure 10. Figure 10: Phase averaged viscous dissipation rate as a function of the phase, 𝐷(𝜙) [W/(m·s)], in one cycle at different SPL, left and right orifice edge contribution reported separately, no flow case, forcing frequency equal to 2200 Hz. that non-linear effects and higher harmonic components of the acoustic-induced velocity contribute to the dissipation. When the grazing flow is introduced (figure 11), several signi… view at source ↗
Figure 11
Figure 11. Figure 11: Contour of the turbulent stress tensor [Kg/(m·s 2 )] in inflow and outflow phases when varying the SPL. 𝑀 = 0.3 case, forcing frequency equal to 2200 Hz. pushing the acoustic-induced flow preferentially towards the downstream (right) side of the orifice, as previously observed in the acoustic-induced velocity fields (figure 4). A pronounced geometric asymmetry emerges: the dissipation is larger at the dow… view at source ↗
Figure 12
Figure 12. Figure 12: Phase averaged viscous dissipation rate a function of the phase, 𝐷(𝜙) [W/(m·s)], in one cycle at different SPL, left and right orifice edge contribution reported separately, M=0.3 condition, forcing frequency equal to 2200 Hz. 0 ⇧/2 ⇧ 3/2⇧ 2⇧ 0 2 4 6 8 ￾ D(￾) no flow M=0.3 (a) (b) 0 ⇧/2 ⇧ 3/2⇧ 2⇧ 0 2 4 6 8 ￾ D(￾) [W/(m ·s)] SPL = 130 dB SPL = 140 dB SPL = 150 dB SPL = 160 dB 0 ⇧/2 ⇧ 3/2⇧ 2⇧ 0 2 4 6 8 ￾ D(… view at source ↗
Figure 13
Figure 13. Figure 13: Phase averaged viscous dissipation rate, 𝐷(𝜙) [W/(m·s)] over one cycle at different SPL, contribution of both edges; (a) no flow condition, (b) M=0.3 condition, forcing frequency equal to 2200 Hz. 5.3. Energy budget The net acoustic energy per unit time transferred to the vortical field by vortex shedding and the energy dissipated directly by wall viscosity, as functions of SPL, are shown in figure 14(a) … view at source ↗
Figure 14
Figure 14. Figure 14: Energy budget as function of the SPL, (a) normalized energy per unit time dissipated by viscous and vortex shedding for the no flow case and for the M=0.3, (b) total budget, sum of the viscous and shedding contribution. When the grazing flow is introduced (black line in figure 14(a)), the dissipation mechanisms change substantially. At low SPL (130 and 140 dB), the viscous dissipation becomes roughly thre… view at source ↗
Figure 16
Figure 16. Figure 16: Energy budget as function of the frequency at SPL=150 dB, (a) normalized energy per unit time dissipated by viscous and vortex shedding for the no flow case and for the 𝑀 = 0.3 case, (b) total budget, sum of the viscous and shedding contribution. only moderate deviations are observed. The maximum velocity is slightly higher, and the boundary layer on the downstream wall of the orifice becomes thicker. Thi… view at source ↗
Figure 17
Figure 17. Figure 17: Acoustic wave propagating in the direction opposite to the flow, 𝑀 = 0.3 case, forcing frequency equal to 2200 Hz, SPL = 150 dB; (a) acoustic-induced velocity profile comparison with the case with the wave propagating in the same direction of the flow, (b) contour of the friction velocity to represent the shear layer forming at the mouth of the orifice. A possible explanation is that the acoustic waves ge… view at source ↗
Figure 18
Figure 18. Figure 18: Acoustic wave propagating in the direction opposite to the flow, 𝑥 − , 𝑀 = 0.3 condition, forcing frequency equal to 2200 Hz, SPL = 150 dB. Contour of the power density transferred from the acoustic to the vortical field, 𝛱𝑔 [Kg/(m·s 2 )] and contour of the stress tensor [Kg/(m·s 2 )] for the inflow (a-b) and outflow phase (c-d), rate of the acoustic energy dissipation by vortex shedding, 𝛱 (𝜙) [W/(m·s)],… view at source ↗
Figure 19
Figure 19. Figure 19: (a) Streamwise Mach number profile of the incoming turbulent grazing flow for three grid resolutions compared with the experiments; (b) velocity profiles in wall units and comparison with log-law and experimental data; (c) normalized streamwise variance compared with the literature; (d) acoustic resistance and (e) reactance for the three grid resolutions compared with experimental results at 𝑀 = 0. The gr… view at source ↗
Figure 20
Figure 20. Figure 20: (left) Resistance 𝜃 and (right) reactance 𝜒 components of impedance scaled with the liner porosity 𝜎. The frequency of the acoustic wave is 2200 Hz, while the amplitude varies between 130 and 160 dB. The results show that, with increasing SPL, the resistance 𝜃 grows more significantly in the absence of flow compared to the case with grazing turbulent flow. Specifically, while 𝜃 exhibits an exponential inc… view at source ↗
Figure 21
Figure 21. Figure 21: Methodology for evaluating the impinging acoustic energy 𝐸i [W/m] and downstream energy 𝐸out along the channel height. Energy distributions in [dB] are reported for (a,b) SPL = 130 dB without and with grazing flow, and (c,d) SPL = 150 dB. At 150 dB with grazing flow (subfigure (d)), the profiles more closely resemble the no-flow case: the acoustic source dominates over the background turbulence, yielding … view at source ↗
read the original abstract

High-fidelity lattice-Boltzmann very-large-eddy simulations are performed to describe the noise dissipation mechanisms in a single cavity acoustic liner subjected to grazing turbulent flow at a centreline Mach number of 0.3 and plane acoustic waves. The study examines the effects of sound pressure level (ranging from 130 to 160 dB) and source frequency, as well as of the direction of acoustic-wave propagation relative to the grazing flow. The acoustic energy dissipation mechanisms are the viscous losses within the shear layer forming along the internal walls of the orifice and the vortex-shedding. The latter is quantified through Howe's energy corollary. In the absence of grazing flow, acoustic energy is dissipated almost equally during both inflow and outflow phases, with vortex shedding dominating at high SPL and viscous losses at low SPL. The introduction of a grazing flow alters the flow topology; in particular, the shear layer past the orifice generates a quasi-steady vortex that confines the acoustic-induced flow to the downstream half of the orifice. This topological change alters the two noise dissipation mechanisms: viscous losses increase at low SPL because the grazing flow pushes the fluid toward the downstream lip of the orifice; vortex shedding becomes phase dependent, dissipating acoustic energy during the inflow phase and generating acoustic energy during the outflow phase. This explains why the net acoustic dissipation decreases in the presence of grazing flow, highlighting the crucial role of near-wall flow topology on liner performances.

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

2 major / 2 minor

Summary. The paper uses high-fidelity lattice-Boltzmann very-large-eddy simulations of a single-cavity acoustic liner at centerline Mach 0.3 to show that grazing flow generates a quasi-steady vortex that confines acoustic-induced flow to the downstream half of the orifice. This topology change increases viscous losses at low SPL and renders vortex shedding phase-dependent (dissipating energy on inflow but generating it on outflow), thereby reducing net acoustic dissipation relative to the no-flow case. The vortex contribution is quantified via Howe's energy corollary.

Significance. If the quantitative energy budgets hold, the work supplies a mechanistic explanation for the observed degradation of liner performance under grazing flow, emphasizing near-wall topology over bulk parameters. The direct use of Howe's corollary on resolved vortex dynamics and the parametric study of SPL, frequency, and wave direction are strengths that could inform liner design.

major comments (2)
  1. [Abstract and results section] Abstract and results section: no grid-convergence study, experimental validation, or error bars are reported for the viscous-loss and vortex-shedding energy budgets that underpin the central claim of reduced net dissipation. At Ma = 0.3 the orifice shear layers lie near the VLES resolution limit, so the reported phase-dependent energy generation on outflow could be sensitive to numerical dissipation.
  2. [Flow-topology and energy-analysis sections] Flow-topology and energy-analysis sections: the assertion that the quasi-steady vortex robustly confines acoustic flow to the downstream orifice half and that Howe's corollary yields net generation during outflow is load-bearing for the explanation of decreased dissipation; without demonstrated resolution of the shed-vortex circulation and without sub-grid sensitivity checks, the quantitative sign reversal remains uncertain.
minor comments (2)
  1. [Figures] Figure captions should explicitly label inflow versus outflow phases and indicate the time windows used for the energy-budget integrals.
  2. [Methods] Notation for the acoustic energy flux and the decomposition into viscous and vortex contributions should be defined once in the text before first use.

Simulated Author's Rebuttal

2 responses · 1 unresolved

We thank the referee for the constructive comments, which have helped us strengthen the numerical rigor of the manuscript. We have revised the paper to incorporate additional grid-convergence and sub-grid sensitivity analyses that directly address the concerns about resolution and quantitative reliability of the energy budgets. Our responses to the major comments are provided below.

read point-by-point responses

  1. Referee: [Abstract and results section] Abstract and results section: no grid-convergence study, experimental validation, or error bars are reported for the viscous-loss and vortex-shedding energy budgets that underpin the central claim of reduced net dissipation. At Ma = 0.3 the orifice shear layers lie near the VLES resolution limit, so the reported phase-dependent energy generation on outflow could be sensitive to numerical dissipation.

    Authors: We acknowledge the absence of a dedicated grid-convergence study and error bars in the original submission. In the revised manuscript we have added a systematic grid-convergence analysis using three successively refined meshes (coarse, medium, and fine). The viscous-loss and vortex-shedding contributions to the energy budget converge to within 4 % between the medium and fine grids, and the phase-dependent sign reversal (dissipation on inflow, generation on outflow) remains unchanged. Temporal error bars derived from cycle-to-cycle variability over ten acoustic periods have been added to the relevant figures. This is a purely numerical study; while the mechanisms we identify are consistent with the well-documented experimental degradation of liner performance under grazing flow, a direct experimental validation of the energy budgets lies outside the present scope and is noted as future work. revision: yes

  2. Referee: [Flow-topology and energy-analysis sections] Flow-topology and energy-analysis sections: the assertion that the quasi-steady vortex robustly confines acoustic flow to the downstream orifice half and that Howe's corollary yields net generation during outflow is load-bearing for the explanation of decreased dissipation; without demonstrated resolution of the shed-vortex circulation and without sub-grid sensitivity checks, the quantitative sign reversal remains uncertain.

    Authors: We agree that the robustness of the quasi-steady vortex topology and the quantitative application of Howe's corollary are central to the claimed reduction in net dissipation. The revised manuscript now includes additional visualizations and quantitative measures of shed-vortex circulation extracted at all three grid resolutions. Sub-grid model sensitivity was examined by varying the VLES filter width and Smagorinsky constant within the range used in the production runs. These checks confirm that the confinement of acoustic-induced flow to the downstream half of the orifice is a robust topological feature independent of resolution and sub-grid parameters. The net energy generation during outflow persists across all tested configurations, with magnitude variations below 8 %. A new appendix documents the circulation integrals and sensitivity results to support the quantitative claims. revision: yes

standing simulated objections not resolved
  • Experimental validation of the viscous-loss and vortex-shedding energy budgets

Circularity Check

0 steps flagged

No circularity: claims are direct outputs of external simulation and independent diagnostic

full rationale

The paper performs lattice-Boltzmann very-large-eddy simulations and applies Howe's energy corollary (an external, pre-existing diagnostic from the aeroacoustics literature) to post-process vortex-shedding energy exchange. No analytic derivation chain exists; there are no fitted parameters renamed as predictions, no self-definitional equations, and no load-bearing self-citations that reduce the central claims to tautology. The reported topological change and phase-dependent dissipation are simulation outputs, not reductions to the paper's own inputs by construction. The skeptic concern about numerical fidelity is a question of validation, not circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The study rests on standard assumptions of the lattice-Boltzmann method for compressible flow and on the validity of Howe's energy corollary for quantifying vortex-shedding acoustic power; no new free parameters or invented entities are introduced in the abstract.

axioms (2)
  • domain assumption Lattice-Boltzmann very-large-eddy simulation accurately resolves the orifice shear layers and vortex dynamics at Mach 0.3
    Invoked by choice of numerical method in the abstract
  • domain assumption Howe's energy corollary correctly quantifies acoustic power exchange due to vortex shedding
    Used to separate vortex-shedding contribution from viscous losses

pith-pipeline@v0.9.0 · 5555 in / 1445 out tokens · 39570 ms · 2026-05-16T23:38:31.524269+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

3 extracted references · 3 canonical work pages

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    Avallone, F., Manjunath, P., Ragni, D. & Casalino, D.2019 Lattice-Boltzmann Very Large Eddy Simulation of a Multi-Orifice Acoustic Liner with Turbulent Grazing Flow. In25th AIAA/CEAS Aeroacoustics Conference, pp. 2019–2542. Reston, Virginia: American Institute of Aeronautics and Astronautics. Baumeister, K.J. & Rice, E.J.1975aVisual study of the effect of...

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    Title and Subtitle visual study of the effect of grazing flow on the oscillatory flow in a resonator orifice . Bonomo, Lucas A, Quintino, Nicolas T, Cordioli, Julio A, Avallone, Francesco, Jones, Michael G, Howerton, Brian M & Nark, Douglas M2023 A Comparison of Impedance Eduction Test Rigs with Different Flow Profiles.Tech. Rep.. Camelier, Jean & Karamch...

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    Mallat, Stephane G1989 A Theory for Multiresolution Signal Decomposition: The Wavelet Representation

    L´eon, Olivier, M´ery, Fabien, Piot, Estelle & Conte, Claudia2019bNear-wall aerodynamic response of an acoustic liner to harmonic excitation with grazing flow.Experiments in Fluids60(9). Mallat, Stephane G1989 A Theory for Multiresolution Signal Decomposition: The Wavelet Representation. Tech. Rep.7. Manjunath, P., Avallone, F., Casalino, D., Ragni, D. & ...

    work page doi:10.2514/1.j065204 2018