# Acoustic analogy

**Acoustic analogies**are applied mostly in numerical aeroacoustics to reduce aeroacoustic sound sources to simple emitter types. They are therefore often also referred to as**aeroacoustic analogies**.In general, aeroacoustic analogies are derived from the compressible

Navier-Stokes equations (NSE). The compressible NSE are rearranged into various forms of the inhomogeneous acousticwave equation . Within these equations, source terms describe the acoustic sources. They consist of pressure and speed fluctuation as well as stresstensor and force terms.Approximations are introduced to make the source terms independent of the acousticvariable s. In this way, linearized equations are derive which describe the propagation of the acoustic waves in a homogeneous, resting medium. The latter is excited by the acoustic source terms, which are determined from the turbulent fluctuations. Since the aeroacoustics are described by the equations of classical acoustics, the methods are called aeroacoustic analogies.The

**Lighthill-Analogy**considers a free flow, as for example with an engine jet. The nonstationary fluctuations of the stream are represented by a distribution ofquadrupole sources in the same volume.The

**Curle-Analogy**is a formal solution of the Lighthill Analogy, which takes hard surfaces into consideration.The

**Ffowcs Williams-Hawkings-Analogy**is valid for aeroacoustic sources in relative motion with respect to a hard surface, as is the case in many technical applications for example in the automotive industry or in air travel. The calculation involvesquadrupole ,dipole andmonopole terms.**Literature*** Blumrich, R.: "Berechnungsmethoden für die Aeroakustik von Fahrzeugen". Tagungsband der ATZ/MTZ-Konferenz Akustik 2006, Stuttgart, 17-18.5.2006..

* Lighthill, M. J.: "On sound generated aerodynamically. I. General theory". Proc. Roy. Soc. 211(A) S. 564-587, London, 1952.

* Lighthill, M. J.: "On sound generated aerodynamically. I. General theory". Proc. Roy. Soc. 222(A) S. 1-34, London, 1954.

* Ffowcs Williams, J. E. and Hawkings, D. L.: "Sound Generation by Turbulence and Surfaces in Arbitrary Motion". Philosophical Transactions of the Royal Society, Vol. A264, Nr. 1151, 1969, S. 321-342

* Curle, N.: "The Influence of solid boundaries upon aerodynamic sound". Proc. Roy. Soc. Lond., A23, 505-514. 1955

**External links*** [

*http://www.ias.et.tu-dresden.de/akustik/Publikationen/Stroemungsakustik/koe2004_3.pdf Contribution of the Technical University of Dresden to the modeling of flow sound sources with elementary emitters.*]* [

*http://www.ias.et.tu-dresden.de/akustik/Publikationen/Stroemungsakustik/koe2000-1.pdf Contribution of the Technical University of Dresden to the history of aeroacoustics.*]

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