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Source Characterization By Correlation Techniques

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Aeroacoustic Measurements

Part of the book series: Experimental Fluid Mechanics ((FLUID))

Abstract

The use of correlation techniques provides a vital tool in understanding and characterizing mechanisms of flow induced sound and vibration. This chapter outlines the basic mathematical relations used in the derivation of such techniques, introducing fundamental quantities such as the cross-correlation function and coherence function. These techniques are then applied to specific aeroacoustic examples, establishing the causal relationship between measured sound and its source. These examples include the measurement of trailing edge noise by suppression of background acoustic contamination, correlation measurements between surface pressure and far field radiated acoustic pressure fields, and the characterization of a turbulent flow field using the integrated surface pressure response of a rotating propeller.

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Abbreviations

A c :

spatial correlation area

A s :

surface area

C(r):

local propeller blade chord at radial position, r

c :

pressure wave propagation speed

D :

propeller diameter

F :

RMS force on a surface

G(x,y,ω):

Dirichlet Green’s function

H(ω):

frequency response function

l i :

spatial correlation length in the i th direction

J :

propeller advance ratio

k o :

acoustic wave number

n s :

propeller rotational speed (revolutions per second)

p :

surface pressure

p rad :

radiated acoustic pressure

R :

distance between acoustic source and receiver

R 12 (Ï„):

cross-correlation between signals 1 and 2

r :

spatial separation variable or radial position

S e (r,ω) :

Sears function

St :

Strouhal number

T :

propeller thrust variable

t :

time variable

U :

freestream or reference velocity

v i (t):

signal time series i

x :

position variable

β :

polar angle between field point and propeller thrust axis

γ(r):

local pitch of propeller blade at radial position, r

γ 2 :

coherence function

Λ r (r, ω):

frequency-dependent radial correlation length

λ :

acoustic wavelength

Φ 12 (ω):

cross-spectral density between signals 1 and 2

ϱ :

density of given fluid

Ï„ :

time constant

ω :

frequency variable

ξ :

fractional chordwise distance downstream of leading edge of propeller blade

RMS:

Root Mean Square

SPL:

Sound Pressure Level

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Author information

Authors and Affiliations

  1. Carderock Division, Naval Surface Warfare Center, Bethesda, MD, 20084-5000, USA

    William K. Blake (Chief Research Scientist)

  2. Department of Aerospace and Mechanical Engineering, University of Notre Dame, Notre Dame, IN, 46556, USA

    Denis A. Lynch III (Research Associate)

Authors
  1. William K. Blake
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  2. Denis A. Lynch III
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Editor information

Editors and Affiliations

  1. Aerospace and Mechanical Engineering, University of Notre Dame, 112 Hessert Center, 46556-5684, Notre Dame, IN, USA

    Thomas J. Mueller

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© 2002 Springer-Verlag Berlin Heidelberg

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Blake, W.K., Lynch, D.A. (2002). Source Characterization By Correlation Techniques. In: Mueller, T.J. (eds) Aeroacoustic Measurements. Experimental Fluid Mechanics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-05058-3_4

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  • DOI: https://doi.org/10.1007/978-3-662-05058-3_4

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-07514-8

  • Online ISBN: 978-3-662-05058-3

  • eBook Packages: Springer Book Archive

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