Energy dissipation mechanisms in an acoustically-driven slit

TL;DR

This study investigates how acoustic energy is converted into vortical motion and dissipated as heat in a slit, revealing key mechanisms and parameters that influence acoustic damping.

Contribution

It provides a detailed numerical analysis of energy dissipation mechanisms in a slit driven by sound, highlighting the roles of vortex shedding and boundary layer dynamics.

Findings

Vortex shedding dominates damping at certain amplitudes and frequencies.

Viscous loss accounts for 20-60% of kinetic energy dissipation.

Higher Reynolds numbers can suppress broadband fluctuations.

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.