Energy dissipation mechanisms in an acoustically driven slit

Abstract

We quantify the conversion of incident acoustic energy into vortical motion and viscous dissipation for a plane wave passing through large-aspect-ratio slit geometries. We perform direct numerical simulations over a broad imposed parameter space in incident sound pressure level (ISPL), Strouhal number ( italic St <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:mrow> <mml:mtext mathvariant="italic" class="MJX-tex-mathit">St</mml:mtext> </mml:mrow> </mml:math> $\textit{St}$ ) and Reynolds number ( italic Re <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:mrow> <mml:mtext mathvariant="italic" class="MJX-tex-mathit">Re</mml:mtext> </mml:mrow> </mml:math> $\textit{Re}$ ). Spectral proper orthogonal decomposition 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) to examine the acoustic absorption mechanisms. At italic ISPL equals 150 dB <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:mrow> <mml:mtext mathvariant="italic" class="MJX-tex-mathit">ISPL</mml:mtext> </mml:mrow> <mml:mo>=</mml:mo> <mml:mrow> <mml:mn>150</mml:mn> </mml:mrow> <mml:mspace width="thinmathspace"/> <mml:mrow> <mml:mtext>dB</mml:mtext> </mml:mrow> </mml:math> $\textit{ISPL} = {150}\,\textrm{dB}$ , the acoustic–hydrodynamic energy conversion is highest when italic St less than or equals 4 italic St Subscript 0 Baseline <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:mrow> <mml:mtext mathvariant="italic" class="MJX-tex-mathit">St</mml:mtext> </mml:mrow> <mml:mo>≤</mml:mo> <mml:mn>4</mml:mn> <mml:msub> <mml:mrow> <mml:mtext mathvariant="italic" class="MJX-tex-mathit">St</mml:mtext> </mml:mrow> <mml:mn>0</mml:mn> </mml:msub> </mml:math> $\textit{St} \le 4\textit{St}_0$ , corresponding to an effective Keulegan–Carpenter number ( upper K Subscript c <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:mrow> <mml:msub> <mml:mi>K</mml:mi> <mml:mi>c</mml:mi> </mml:msub> </mml:mrow> </mml:math> ${K_c}$ ) larger than 40. In this regime, three-dimensional simulations show that the dominant flow response is two-dimensional, with the oscillatory shear layer near the slit corners rolling up into shedding vortices. The VL accounts for 20 %–60 % of the KE contribution. For larger italic St <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:mrow> <mml:mtext mathvariant="italic" class="MJX-tex-mathit">St</mml:mtext> </mml:mrow> </mml:math> $\textit{St}$ , the Stokes-layer confinement produces X-shaped near-slit modes, reducing the energy input by approximately 50 %. The influence of italic Re <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content"> <mml:mrow> <mml:mtext mathvariant="italic" class="MJX-tex-mathit">Re</mml:mtext> </mml:mrow> </mml:math> $\textit{Re}$