Acoustic analogy

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Acoustic analogies are mostly used in numerical aeroacoustics to reduce aeroacoustic sound sources to simple radiator types. They are therefore often referred to as aeroacoustic analogies .

In general, the aeroacoustic analogies are derived from the compressible Navier-Stokes equations (NSG). The compressible NSG are brought into different forms of the inhomogeneous , acoustic wave equation . Within these equations, source terms describe the acoustic sources. They consist of pressure and velocity fluctuations as well as stress tensors and force terms.

In order to make the source terms independent of the acoustic variable , approximations are introduced. In this way, linearized equations are derived that describe the propagation of acoustic waves in a homogeneous , stationary medium. The latter is stimulated by the acoustic source terms, which are determined from the turbulent fluctuations. Since aeroacoustics is described here by equations of classical acoustics, these methods are called aeroacoustic analogies.

The Lighthill analogy first considers a free flow, such as B. in an engine jet. The unsteady fluctuations of the flow are represented by a distribution of quadrupole sources in the same volume.

The curle analogy is a formal solution to the Lighthill analogy that can take hard surfaces into account. However, the normal speed on the surface is set to zero here.

The Ffowcs-Williams- Hawkings analogy does not have this limitation. It is valid for aeroacoustic sources with relative movement to a hard surface, as is the case with many technical applications, e.g. B. is the case in vehicles or in aviation. The calculation includes quadrupole , dipole and monopole terms .

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