A comparison of the silent base flow and vortex sound · 19th AIAA/CEAS Aeroacoustics Conference...
Transcript of A comparison of the silent base flow and vortex sound · 19th AIAA/CEAS Aeroacoustics Conference...
A comparison of the silent base flow and vortex soundanalogy sources in high speed subsonic jets
S. Sinayoko A. Agarwal
University of Cambridge, UK
19th AIAA/CEAS Aeroacoustics Conference Berlin, 27 May 2013
Outline
Introduction
Laminar jet
Turbulent jet
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Outline
Introduction
Laminar jet
Turbulent jet
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How can we define the sound sources?
Nq = 0
q = q + q ′
Lq ′ = s
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The silent base flow sources
M. E. GoldsteinOn identifying the true sources of aerodynamic sound.Journal of Fluid Mechanics, 526:333–347, 2005.
S. Sinayoko, A. Agarwal, and Hu Z.Flow decomposition and aerodynamic noise generation.Journal of Fluid Mechanics,668:335–350, 2011.
Radiation criterion: k = ω/c∞.
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The silent base flow sources
M. E. GoldsteinOn identifying the true sources of aerodynamic sound.Journal of Fluid Mechanics, 526:333–347, 2005.
S. Sinayoko, A. Agarwal, and Hu Z.Flow decomposition and aerodynamic noise generation.Journal of Fluid Mechanics,668:335–350, 2011.
Radiation criterion: k = ω/c∞.
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“Lighthill” silent base flow sources
Density formulation
Dependent variables
q = ρ, ρv,π
Sound sources
f ′1i = −∂
∂xj
(ρ vivj
) ′
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“Lighthill” silent base flow sources
Density formulation
Dependent variables
q = ρ, ρv,π
Sound sources
f ′1i = −∂
∂xj
(ρ vivj
) ′
vi = ρvi/ρ
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“Doak” silent base flow sources
Total enthalpy formulation
P. DoakFluctuating Total Enthalpy as the Basic Generalized AcousticField.Theoretical and Computational Fluid Dynamics, Vol. 10, No.1-4, Jan. 1998, pp. 115–133.
Dependent variables
q = h + v2/2, v, S
Sound sources
f ′2i = −(Ω× v
) ′i
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“Doak” silent base flow sources
Total enthalpy formulation
P. DoakFluctuating Total Enthalpy as the Basic Generalized AcousticField.Theoretical and Computational Fluid Dynamics, Vol. 10, No.1-4, Jan. 1998, pp. 115–133.
Dependent variables
q = h + v2/2, v, S
Sound sources
f ′2i = −(Ω× v
) ′i
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Dominant source in laminar jet: shear noise
S. Sinayoko and A. Agarwal.The silent base flow and the sound sources in a laminar jet.Journal of the Acoustical Society of America,131:1959–1968,2012.
Dominant source 1
f ′1zz ≈ ρ∞ ∂
∂z( v0vz )
′
Source 2 definition
Ω =∂vz
∂r−∂vr
∂zf ′2z = vrΩ
f ′2r = −vzΩ
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Dominant source in laminar jet: shear noise
S. Sinayoko and A. Agarwal.The silent base flow and the sound sources in a laminar jet.Journal of the Acoustical Society of America,131:1959–1968,2012.
Dominant source 1
f ′1zz ≈ ρ∞ ∂
∂z( v0vz )
′
Source 2 definition
Ω =∂vz
∂r−∂vr
∂zf ′2z = vrΩ
f ′2r = −vzΩ
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Outline
Introduction
Laminar jet
Turbulent jet
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Flow description
−5
0
5
y
0 10 20x
0
0.2
0.5
0.8
1
Mean flow excited at two frequencies:
ω1 = 2.2, ω2 = 3.4, ∆ω = 1.2.
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Laminar jet: unfiltered axial sources
(f1z)1.2
0
3
6
r/D
(f2z)1.2
0
3
6
r/D
0 5 10 15 20z/D
−0.06
−0.04
−0.02
0
0.02
0.04
0.06
Amplitude
0 5 10 15 20z/D
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Laminar jet: filtered axial sources
(f1z)′1.2
0
3
6
r/D
(f2z)′1.2
0
3
6
r/D
0 5 10 15 20z/D
−2
−1
0
1
2
Amplitude×
10−4
0 5 10 15 20z/D
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Laminar jet: filtered radial sources
(f1r)′1.2
0
3
6
r/D
(f2r)′1.2
0
3
6
r/D
0 5 10 15 20z/D
−0.9
−0.6
−0.3
0
0.3
0.6
0.9
1.2
Amplitude×
10−5
0 5 10 15 20z/D
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Outline
Introduction
Laminar jet
Turbulent jet
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Turbulent jet: density fluctuations
0246
r/R
−50 −40 −30 −20 −10 0 10 20 30 40 50 60 70 80z/R
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Turbulent jet: flow decomposition (n = 0, St = 0.3)
0246
r/R
−50 −40 −30 −20 −10 0 10 20 30 40 50 60 70 80
Fulln = 0St = 0.3
0246
r/R
−50 −40 −30 −20 −10 0 10 20 30 40 50 60 70 80
Acousticn = 0St = 0.3
0246
r/R
−50 −40 −30 −20 −10 0 10 20 30 40 50 60 70 80
Silentn = 0St = 0.3
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Turbulent jet: flow decomposition
0246
r/R
−50 −40 −30 −20 −10 0 10 20 30 40 50 60 70 80
Full
0246
r/R
−50 −40 −30 −20 −10 0 10 20 30 40 50 60 70 80
Acoustic|n| 6 2|St| 6 4
0246
r/R
−50 −40 −30 −20 −10 0 10 20 30 40 50 60 70 80
Silent
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Turbulent jet: axial source (f1zz)′0.3
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Turbulent jet: axial source (f1zz)′0.3 validation
15
30
45
6075
0 (deg)
90
0-60-120Density (dB)
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Turbulent jet: unfiltered axial sources
(f1z)0.3
012345
r/R
z/R
(f2z)0.3
012345
r/R
−50 −40 −30 −20 −10 0 10 20 30
z/R
0
0.1
Amplitude
−40 −20 0 20
z/R
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Turbulent jet: filtered axial sources
(f1z)′0.3
012345
r/R
z/R
(f2z)′0.3
012345
r/R
−50 −40 −30 −20 −10 0 10 20 30
z/R
−0.02
−0.01
0
0.01
0.02
Amplitude
−40 −20 0 20
z/R
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Turbulent jet: filtered radial sources
(f1z)′0.3
012345
r/R
z/R
(f2z)′0.3
012345
r/R
−50 −40 −30 −20 −10 0 10 20 30
z/R
−0.03
−0.02
−0.01
0
0.01
0.02
Amplitude
−40 −20 0 20
z/R
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Turbulent jet: source divergence ∇f = ∂zfz + ∂rfr
(f1z)′0.3
012345
r/R
z/R
(f2z)′0.3
012345
r/R
−50 −40 −30 −20 −10 0 10 20 30
z/R
−1
−0.5
0
0.5
Amplitude
−40 −20 0 20
z/R
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Conclusions
1. Vortex sound silent base flow sources2. Laminar jet: the formulations are equivalent3. Turbulent jet: the divergences are the same4. Validated axial NRBF source for n = 0 and St = 0.3 for a fully
turbulent jet
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Thank you!