Foundations of acoustic analogies

Seppo Uosukainen

Research output: Book/ReportReport

Abstract

This report presents the best-known acoustic analogies, and their equations are derived mathematically in detail to allow their applicability to be extended when necessary. In the acoustic analogies, the equations governing the flow-generated acoustic fields are rearranged in such a way that the field variable connections (wave operator part) are on the left-hand side and that which is supposed to form the source quantities for the acoustic field (source part) is on the right-hand side. Lighthill's analogy was originally developed for unbounded flows. The analogy assumes that, outside the source region, there is no static flow and the fluid is ideal. The refraction effects are not included in the wave operator. Powell's analogy is an approximate version of Lighthill's analogy. The Ffowcs Williams-Hawkings analogy is such an extension of Lighthill's analogy that, being based on the same starting point, it takes into account the effects of moving boundaries by equivalent Huygens sources. Curle's analogy is obtained from the Ffowcs Williams-Hawkings analogy by assuming that the boundaries are not moving. In Phillips' analogy, the effects of a moving medium are partially taken into account, and the refraction effects are included in the wave operator. The fluid outside the source region is assumed to be ideal. Lilley's analogy is based on the same starting point as Phillips' analogy, but all the 'propagation effects' occurring in a transversely sheared mean flow are inside the wave operator part of the equation. In Howe's analogy, the vorticity vector (in the form of Coriolis acceleration) and the entropy gradients are put in the source part of the equation, forming the main part of the sources; the compressibility of the medium is assumed to be constant and the viscous losses are assumed to vanish. In Doak's analogy, the compressibility of the medium does not need to be constant, the vorticity and the entropy gradients do not need to disappear outside the source region, and the viscous and thermal losses can be taken into account, somehow, inside and outside the source region. The four last-presented analogies assume that the medium is an ideal gas, so without modifications they cannot be applied to acoustic fields in liquids.
Original languageEnglish
Place of PublicationEspoo
PublisherVTT Technical Research Centre of Finland
Number of pages121
ISBN (Electronic)978-951-38-7725-5
ISBN (Print)978-951-38-7724-8
Publication statusPublished - 2011
MoE publication typeD4 Published development or research report or study

Publication series

SeriesVTT Publications
Number757
ISSN1235-0621

Fingerprint

acoustics
operators
vorticity
compressibility
refraction
entropy
ideal fluids
gradients
ideal gas
propagation
fluids
liquids

Keywords

  • noise
  • acoustic fields
  • source
  • flow
  • vorticity
  • jet
  • moving boundaries
  • applicability

Cite this

Uosukainen, S. (2011). Foundations of acoustic analogies. Espoo: VTT Technical Research Centre of Finland. VTT Publications, No. 757
Uosukainen, Seppo. / Foundations of acoustic analogies. Espoo : VTT Technical Research Centre of Finland, 2011. 121 p. (VTT Publications; No. 757).
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Uosukainen, S 2011, Foundations of acoustic analogies. VTT Publications, no. 757, VTT Technical Research Centre of Finland, Espoo.

Foundations of acoustic analogies. / Uosukainen, Seppo.

Espoo : VTT Technical Research Centre of Finland, 2011. 121 p. (VTT Publications; No. 757).

Research output: Book/ReportReport

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T1 - Foundations of acoustic analogies

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N2 - This report presents the best-known acoustic analogies, and their equations are derived mathematically in detail to allow their applicability to be extended when necessary. In the acoustic analogies, the equations governing the flow-generated acoustic fields are rearranged in such a way that the field variable connections (wave operator part) are on the left-hand side and that which is supposed to form the source quantities for the acoustic field (source part) is on the right-hand side. Lighthill's analogy was originally developed for unbounded flows. The analogy assumes that, outside the source region, there is no static flow and the fluid is ideal. The refraction effects are not included in the wave operator. Powell's analogy is an approximate version of Lighthill's analogy. The Ffowcs Williams-Hawkings analogy is such an extension of Lighthill's analogy that, being based on the same starting point, it takes into account the effects of moving boundaries by equivalent Huygens sources. Curle's analogy is obtained from the Ffowcs Williams-Hawkings analogy by assuming that the boundaries are not moving. In Phillips' analogy, the effects of a moving medium are partially taken into account, and the refraction effects are included in the wave operator. The fluid outside the source region is assumed to be ideal. Lilley's analogy is based on the same starting point as Phillips' analogy, but all the 'propagation effects' occurring in a transversely sheared mean flow are inside the wave operator part of the equation. In Howe's analogy, the vorticity vector (in the form of Coriolis acceleration) and the entropy gradients are put in the source part of the equation, forming the main part of the sources; the compressibility of the medium is assumed to be constant and the viscous losses are assumed to vanish. In Doak's analogy, the compressibility of the medium does not need to be constant, the vorticity and the entropy gradients do not need to disappear outside the source region, and the viscous and thermal losses can be taken into account, somehow, inside and outside the source region. The four last-presented analogies assume that the medium is an ideal gas, so without modifications they cannot be applied to acoustic fields in liquids.

AB - This report presents the best-known acoustic analogies, and their equations are derived mathematically in detail to allow their applicability to be extended when necessary. In the acoustic analogies, the equations governing the flow-generated acoustic fields are rearranged in such a way that the field variable connections (wave operator part) are on the left-hand side and that which is supposed to form the source quantities for the acoustic field (source part) is on the right-hand side. Lighthill's analogy was originally developed for unbounded flows. The analogy assumes that, outside the source region, there is no static flow and the fluid is ideal. The refraction effects are not included in the wave operator. Powell's analogy is an approximate version of Lighthill's analogy. The Ffowcs Williams-Hawkings analogy is such an extension of Lighthill's analogy that, being based on the same starting point, it takes into account the effects of moving boundaries by equivalent Huygens sources. Curle's analogy is obtained from the Ffowcs Williams-Hawkings analogy by assuming that the boundaries are not moving. In Phillips' analogy, the effects of a moving medium are partially taken into account, and the refraction effects are included in the wave operator. The fluid outside the source region is assumed to be ideal. Lilley's analogy is based on the same starting point as Phillips' analogy, but all the 'propagation effects' occurring in a transversely sheared mean flow are inside the wave operator part of the equation. In Howe's analogy, the vorticity vector (in the form of Coriolis acceleration) and the entropy gradients are put in the source part of the equation, forming the main part of the sources; the compressibility of the medium is assumed to be constant and the viscous losses are assumed to vanish. In Doak's analogy, the compressibility of the medium does not need to be constant, the vorticity and the entropy gradients do not need to disappear outside the source region, and the viscous and thermal losses can be taken into account, somehow, inside and outside the source region. The four last-presented analogies assume that the medium is an ideal gas, so without modifications they cannot be applied to acoustic fields in liquids.

KW - noise

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KW - source

KW - flow

KW - vorticity

KW - jet

KW - moving boundaries

KW - applicability

M3 - Report

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T3 - VTT Publications

BT - Foundations of acoustic analogies

PB - VTT Technical Research Centre of Finland

CY - Espoo

ER -

Uosukainen S. Foundations of acoustic analogies. Espoo: VTT Technical Research Centre of Finland, 2011. 121 p. (VTT Publications; No. 757).