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!