Noise Sources in Turbulent Shear Flows: Fundamentals and by Avraham Hirschberg (auth.), Roberto Camussi (eds.)

By Avraham Hirschberg (auth.), Roberto Camussi (eds.)

The articles during this quantity current the state of the art in noise prediction, modeling and dimension. The articles are in part in line with classification notes supplied in the course of the direction `Noise assets in turbulent shear flows', given at CISM on April 2011. the 1st half comprises common ideas of aero acoustics, together with vortex sound concept and acoustic analogies, within the moment half specific emphasis is placed into arguments of curiosity for engineers and suitable for plane layout: jet noise, airfoil broadband noise, boundary layer noise (including inside noise and its regulate) and the concept that of noise assets, their theoretical modeling and identity in turbulent lows. these kinds of arguments are handled commonly with the inclusion of many sensible examples and references to engineering applications.

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Now we will consider the influence of a uniform, steady outgoing flow Up in the pipe on the acoustic response of the pipe termination. For plane waves the convected d’Alembert solution is: p = p+ exp iω t − x c 0 + Up + p− exp iω t + x c 0 − Up . (168) Through substitution in the linearized momentum equation: ρ0 ∂u ∂u + Up ∂t ∂x =− ∂p ∂x (169) Aeroacoustics and Self-Sustained Oscillations of Internal Flows 45 we get: u = p+ x exp iω t − ρ0 c0 c 0 + Up − p− x exp iω t + ρ0 c 0 c 0 − Up (170) Looking at a pipe of a uniform cross section Sp , terminated by an orifice plate with opening S0 .

The amplitude of the transmitted and reflected waves is calculated from the continuity of pressure at the interface I + R = T complemented by the continuity of particle displacement at the interface. 1 31 Turbulence noise at low Mach numbers Isothermal free jet Considering the sound production of a turbulent free jet. This is the flow with a velocity U0 at the outlet of a pipe of diameter D. Turbulence is an unsteady chaotic fluid motion which appears when viscous forces are small compared to non-linear convective forces.

In figure 5 we provide an intuitive interpretation of the Doppler shift in frequency. Furthermore we note that for a moving object of volume V the sound 2 source is q(x, t) = ρ0 ddtV2 δ(x − xs (t)). Hence we have: p (x, t) = ρ0 ∂2 ∂t2 V (te ) 4π|1 − Mr ||x − xs (te )| . (114) It shows that due to the time dependency of the retarded time ∂te /∂t an object of constant volume will radiate sound if its velocity varies. This is the so called thickness noise pth , which is very important in aircraft fans.

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