Acoustic Analogy - NASA
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Acoustic Analogy Marvin Goldstein NASA Glenn Research Center NASA/CP—2001-211152 277
Transcript of Acoustic Analogy - NASA
Acoustic
Analogy
Marvin Goldstein
NASA Glenn Research Center
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Formal Solution for Pressure
u p L S sum on jj j4 41≡ ′ = − ( )
′ = ′ − ′( ) ′ ′( ) ′ ′→∞ −
∫∫p G t t t S t d dtT
kT
T
klim ; ; , ,4 x x x xσ
′ +( ) ′( ) =p t p pressure auto correlation functionτ τ, ,x x
= ′ ′′ ′( ) ′ ′ +( ) ′′( ) + ′ ′′ ′( ) ′ ′ +( ) ′′( )[ ] ′ ′ ′′+ −∫∫∫ Γ Γk k k kt t S t S t t S t S dt d dl l l lx x x x x x x x x x x x, , , , , , , , , ,τ τ τ τ
• ≡ • =→∞−
∫lim T T
Td time averageτ
f t g For tophat filter in Fourier space+( ) ′ = ( )τ τ( ) 0
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CD-00-80053
Dis
tanc
e fr
om
cen
terl
ine,
y/D
(a) M = 0.95 (b) M = 1.4
(c) M = 1.8
0.8
0.4
0.0
Dis
tanc
e fr
om
cen
terl
ine,
y/D
0.8
0.4
0.0
0.25
0.12
0.06
0.25
0.12
0.06
Distance from nozzle, x/D
0 5 10
0 5 10
5 10
Sr = 1.5
1.0
0.5
0.25
0.12
0.06
Sr = 1.5
1.0
0.5
0.25
0.12
0.06
Sr = 1.5
1.0
0.5
0.25
0.12
0.06
0.0244
0.0132
0.0020
rrms(rj-ra)
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CD-00-80054
10–4
10–1
10–3
10–2
10–4
10–3
10–1
10–2
Frequency, Hz
Co
here
nce
Co
rrel
atio
n, (k
g/m
3 P
a)
10–5
10–3
10–4
Den
sity
sp
ectr
um
100
101
103
102
So
und
sp
ectr
um
0 1 2 4 5x1043
(a)
(b)
(c)
(d)
10–4
10–1
10–3
10–2
Frequency, Hz
Co
here
nce
0 1 2 4 5x1043
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M. Goldstein References 1. Goldstein, M. E. Aeroacoustics, McGraw-Hill 1976.
2. Olsin (Only published in Aeroacoustics Pg. 105).
3. Goldstein, M. E. (1984) Aeroacoustics of Turbulent Shear Flows, Annual
Reviews of Fluid Mechanics Vol. 16, Pg. 263-286.
4. Goldstein, M. E. (1999) Program and Abstracts of the 6th International Congress on Sound and Vibration, Copenhagen "Some Recent Development in Jet Noise Modeling."
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