# Aerodynamic Noise

- Sound generated by turbulent flow is just as if the field were generated by a distribution of quadrupole sources (Lighthill, "On sound generated aerodynamically, I. General theory.", 1952, Proc. Roy. Soc. London A 211, 564). Lighthill rearranged the basic equations of fluid dynamics to show this exact analogy.
- The frequency content is roughly determined by the length scale and velocity of hydrodynamic disturbances, e.g. consider a cylinder in an airstream.

- This vortex shedding can result in the production of whistles such as around car aerials or even structural damage as in the case of tall chimneys. This problem can be reduced dramatically by wrapping a helical strake around the cylinder.

- Assuming that the sound field is generated by a distribution of quadrupole sources, and assuming the typical frequency of the sound is proportional to the velocity divided by the fundamental dimension shows that the sound power:
- where
= Sound power, W*W*- ρ
_{0}= density of air, kgm^{-3} = flow velocity, ms*U*^{-1}= length scale (dimension of body), m*D**c*_{0}= speed of sound, ms^{-1}- i.e. the total sound power radiated by a compact, unheated jet at low Mach number increases by 24 dB for every doubling of jet velocity.

**Pure jet mixing scaling law**

- It was shown ("The influence of solid boundaries on aerodynamic sound", Curle, 1955, Proc. Roy. Soc. London A 231, 505.) that the sound generated by turbulent flow in the region of a solid body is exactly analogous to the sound radiated by a 'free space' distribution of quadrupole sources plus a surface distribution of dipoles.
- The scaling law for the sound power can be shown to be:
- where
= Sound power*W*- ρ
_{0}= density of air, kgm^{-3} = flow velocity, ms*U*^{-1}= length scale (dimension of body), m*D**c*_{0}= speed of sound, ms^{-1}- i.e. the total sound power radiated by turbulent flow in the region of a solid body increases by 18 dB for every doubling of flow velocity.

**Scaling laws for noise produced by flow over a solid surface**

- Tonal noise can be emitted by cavity flows. This is caused by feedback of sound from vortices impinging on the downstream edge back to the upstream edge, causing the formation of another vortex.

- This sequence shows the air flow generating a turbulent stream from the first edge that impinges on the next edge hence generating an acoustic wave that propagates away. When the acoustic wave approaches the first edge it triggers another turbulent stream and hence the cycle continues.

- The flow and the sound field become locked together and intense single frequency sound is often produced. A similar effect is produced by flow excited Helmholtz resonator. A rough guide suggests that 'singing' will occur in a Helmholtz resonator when the strouhal number is 0.25 or a multiple thereof:

- The flow acoustic coupling can be reduced by adding castellations to the leading edge as shown in the following diagram:
- The effect of using castellations is to produce turbulence with different length scales and hence a less constructive sound field will result. This is the same basic idea as wrapping a helical coil around a pole or chimney.

**Noise from cavity flows**

### Reference

M. J. Lighthill, "On Sound Generated Aerodynamically. I. General Theory," Proc. R. Soc. Lond. A 211 (1952) pp. 564-587.

M. J. Lighthill, "On Sound Generated Aerodynamically. II. Turbulence as a Source of Sound," Proc. R. Soc. Lond. A 222 (1954) pp. 1-32.

**See also: **Airflow, Flow Noise, Wind Noise.

**Subjects: ** Aerodynamics Automotive Noise & Vibration