Energy dissipation mechanisms in an acoustically-driven slit

TL;DR

This work addresses nonlinear acoustic damping in narrow slit openings by quantifying how incident acoustic energy converts into vortical kinetic energy (KE) and viscous loss (VL) using 2D direct numerical simulations (DNS) and spectral proper orthogonal decomposition (SPOD). By spanning broad ranges of $ISPL$, $St$, and $Re$, the authors extract mode-by-mode KE and VL and relate them to coherent near-slit structures, showing that VL concentrates near the slit mouth and that vortex shedding dominates dissipation at high $ISPL$ when the Keulegan–Carpenter number $K_c$ is near unity. The key findings reveal that at $ISPL=150$ dB maximum energy transfer to vortices occurs when the acoustic displacement matches slit thickness, triggering boundary-layer separation and leading to pronounced shedding with VL contributing $20$–$60\%$ of KE; at higher frequencies, Stokes-layer confinement yields X-shaped near-slit modes and roughly 50% reduction in total energy input. Across conditions, over $99\%$ of VL is localized near the slit mouth, and the KE–VL spectra define parameter regimes that either enhance or suppress damping, offering physically interpretable guidelines for designing slit-based acoustic absorbers and metasurfaces with targeted impedance and nonlinear damping characteristics.

Abstract

We quantify how incident acoustic energy is converted into vortical motion and viscous dissipation for a two-dimensional plane-wave passing through a slit geometry. We perform direct numerical simulations over a broad parameter space in incident sound pressure level (ISPL), Strouhal number (St), and Reynolds number (Re). Spectral proper orthogonal decomposition (SPOD) yields energy-ranked coherent structures at each frequency, from which we construct mode-by-mode fields for spectral kinetic energy (KE) and viscous loss (VL) components to examine the mechanisms of acoustic absorption. At ISPL=150dB, the acoustic-hydrodynamic energy conversion is highest when the acoustic displacement amplitude is comparable to the slit thickness, corresponding to a Keulegan-Carpenter number of order unity. In this regime, the oscillatory boundary layer undergoes periodic separation, resulting in vortex shedding that dominates acoustic damping. VL accounts for 20-60% of the KE contribution. For higher acoustic frequencies, the confinement of the Stokes layer produces X-shaped near-slit modes, reducing the total energy input by approximately 50%. The influence of Re depends on amplitude. At ISPL=150dB, larger Re values correspond to suppressed broadband fluctuations and sharpened harmonic peaks. At ISPL = 120dB, the boundary layers remain attached, vortex shedding is weak, absorption monotonically scales with viscosity, and the Re- and St-dependencies become comparable. Across all conditions, more than 99% of the VL is confined to a compact region surrounding the slit mouth. The KE-VL spectra describe parameter regimes that enhance or suppress acoustic damping in slit geometries, providing a physically interpretable basis for acoustic-based design.

Figures (22)

• Figure 1: Schematics of (a) the parameter space explored in this study and (b) the global energy pathways, showing the conversion of incident acoustic energy into the kinetic energy of shed vortices and its subsequent viscous dissipation.
• Figure 2: Schematic of the flow configuration in the $x$--$y$ domain simulated in this work.
• Figure 3: A 2D slit resonator for verification showing (a) the computational domain with acoustic source (not to scale) and (b) comparison of power absorption coefficient spectra among direct numerical simulation (DNS) and experiment (Expt.) of tam2001numerical with discrete tones at $\mathrm{ISPL}= 150dB$.
• Figure 4: Instantaneous VL (integrated across the $y$ direction), $\vec{D}(\vec{x};t_i)$, and vorticity fields, $\vec{\omega}(\vec{\mathbf{x}};t_i)$, for different $\hbox{St}\xspace$--$\hbox{Re}\xspace$ combinations at $\mathrm{ISPL} = 150dB$. Temporal-averaged VL fields, ${\overline{\vec{D}}(\vec{x})}$, are shown for comparison. Cases in column (a)--(c) represent $\hbox{Re}\xspace=\hbox{Re}\xspace_0$, $\hbox{Re}\xspace_0/2$, and $\hbox{Re}\xspace_0/3$. Cases in row (i)--(iv) represent $\hbox{St}\xspace=\hbox{St}\xspace_0$, $4\hbox{St}\xspace_0$, $8\hbox{St}\xspace_0$,and $12\hbox{St}\xspace_0$.
• Figure 5: Instantaneous VL (integrated across the $y$ direction), $\vec{D}(\vec{x};t_i)$, and vorticity fields, $\vec{\omega}(\vec{\mathbf{x}};t_i)$, at $\mathrm{ISPL} = 120dB$ and $\hbox{St}\xspace=\hbox{St}\xspace_0$: (a) $\hbox{Re}\xspace=\hbox{Re}\xspace_0$; (b) $\hbox{Re}\xspace_0/2$; and (c) $\hbox{Re}\xspace_0/3$.