Theory of pressure acoustics with viscous boundary layers and streaming in curved elastic cavities

Jacob Søberg Bach, Henrik Bruus*

*Corresponding author for this work

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Abstract

The acoustic fields and streaming in a confined fluid depend strongly on the acoustic boundary layer forming near the wall. The width of this layer is typically much smaller than the bulk length scale set by the geometry or the acoustic wavelength, which makes direct numerical simulations challenging. Based on this separation in length scales, we extend the classical theory of pressure acoustics by deriving a boundary condition for the acoustic pressure that takes boundary-layer effects fully into account. Using the same length-scale separation for the steady second-order streaming, and combining it with time-averaged short-range products of first-order fields, we replace the usual limiting-velocity theory with an analytical slip-velocity condition on the long-range streaming field at the wall. The derived boundary conditions are valid for oscillating cavities of arbitrary shape and wall motion as long as the wall curvature and displacement amplitude are both sufficiently small. Finally, we validate our theory by comparison with direct numerical simulation in two examples of two-dimensional water-filled cavities: The well-studied rectangular cavity with prescribed wall actuation, and the more generic elliptical cavity embedded in an externally actuated rectangular elastic glass block.
Original languageEnglish
JournalJournal of the Acoustical Society of America
Volume144
Issue number2
Pages (from-to)766-784
Number of pages19
ISSN0001-4966
DOIs
Publication statusPublished - 2018

Cite this

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title = "Theory of pressure acoustics with viscous boundary layers and streaming in curved elastic cavities",
abstract = "The acoustic fields and streaming in a confined fluid depend strongly on the acoustic boundary layer forming near the wall. The width of this layer is typically much smaller than the bulk length scale set by the geometry or the acoustic wavelength, which makes direct numerical simulations challenging. Based on this separation in length scales, we extend the classical theory of pressure acoustics by deriving a boundary condition for the acoustic pressure that takes boundary-layer effects fully into account. Using the same length-scale separation for the steady second-order streaming, and combining it with time-averaged short-range products of first-order fields, we replace the usual limiting-velocity theory with an analytical slip-velocity condition on the long-range streaming field at the wall. The derived boundary conditions are valid for oscillating cavities of arbitrary shape and wall motion as long as the wall curvature and displacement amplitude are both sufficiently small. Finally, we validate our theory by comparison with direct numerical simulation in two examples of two-dimensional water-filled cavities: The well-studied rectangular cavity with prescribed wall actuation, and the more generic elliptical cavity embedded in an externally actuated rectangular elastic glass block.",
author = "Bach, {Jacob S{\o}berg} and Henrik Bruus",
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language = "English",
volume = "144",
pages = "766--784",
journal = "Acoustical Society of America. Journal",
issn = "0001-4966",
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Theory of pressure acoustics with viscous boundary layers and streaming in curved elastic cavities. / Bach, Jacob Søberg; Bruus, Henrik.

In: Journal of the Acoustical Society of America, Vol. 144, No. 2, 2018, p. 766-784.

Research output: Contribution to journalJournal articleResearchpeer-review

TY - JOUR

T1 - Theory of pressure acoustics with viscous boundary layers and streaming in curved elastic cavities

AU - Bach, Jacob Søberg

AU - Bruus, Henrik

PY - 2018

Y1 - 2018

N2 - The acoustic fields and streaming in a confined fluid depend strongly on the acoustic boundary layer forming near the wall. The width of this layer is typically much smaller than the bulk length scale set by the geometry or the acoustic wavelength, which makes direct numerical simulations challenging. Based on this separation in length scales, we extend the classical theory of pressure acoustics by deriving a boundary condition for the acoustic pressure that takes boundary-layer effects fully into account. Using the same length-scale separation for the steady second-order streaming, and combining it with time-averaged short-range products of first-order fields, we replace the usual limiting-velocity theory with an analytical slip-velocity condition on the long-range streaming field at the wall. The derived boundary conditions are valid for oscillating cavities of arbitrary shape and wall motion as long as the wall curvature and displacement amplitude are both sufficiently small. Finally, we validate our theory by comparison with direct numerical simulation in two examples of two-dimensional water-filled cavities: The well-studied rectangular cavity with prescribed wall actuation, and the more generic elliptical cavity embedded in an externally actuated rectangular elastic glass block.

AB - The acoustic fields and streaming in a confined fluid depend strongly on the acoustic boundary layer forming near the wall. The width of this layer is typically much smaller than the bulk length scale set by the geometry or the acoustic wavelength, which makes direct numerical simulations challenging. Based on this separation in length scales, we extend the classical theory of pressure acoustics by deriving a boundary condition for the acoustic pressure that takes boundary-layer effects fully into account. Using the same length-scale separation for the steady second-order streaming, and combining it with time-averaged short-range products of first-order fields, we replace the usual limiting-velocity theory with an analytical slip-velocity condition on the long-range streaming field at the wall. The derived boundary conditions are valid for oscillating cavities of arbitrary shape and wall motion as long as the wall curvature and displacement amplitude are both sufficiently small. Finally, we validate our theory by comparison with direct numerical simulation in two examples of two-dimensional water-filled cavities: The well-studied rectangular cavity with prescribed wall actuation, and the more generic elliptical cavity embedded in an externally actuated rectangular elastic glass block.

U2 - 10.1121/1.5049579

DO - 10.1121/1.5049579

M3 - Journal article

VL - 144

SP - 766

EP - 784

JO - Acoustical Society of America. Journal

JF - Acoustical Society of America. Journal

SN - 0001-4966

IS - 2

ER -