trailing edge noise prediction for rotating serrated blades · 20th aiaa/ceas aeroacoustics...

Trailing edge noise prediction for rotating serratedblades

Samuel Sinayoko1 Mahdi Azarpeyvand2 Benshuai Lyu3

1University of Southampton, UK2University of Bristol, UK

3University of Cambridge, UK

AVIATION 201420th AIAA/CEAS Aeroacoustics conference

Atlanta, 20 June 2014

1 / 24

Outline

1 Introduction

2 Theory

3 Results

4 Generalized Amiet model for isolated serrated edges

5 Conclusions

2 / 24

Outline

1 Introduction

2 Theory

3 Results


5 Conclusions

3 / 24

Introduction

MotivationWind turbines (Oerlemans et al 2007)Open rotors (Node-Langlois et al AIAA-2014-2610, Kingan et alAIAA-2014-2745)

ExperimentsGruber et al (AIAA-2012)Moreau and Doolan (AIAA J. 2013)

NumericalJones and Sandberg (JFM 2012)Sanjose et al (AIAA-2014-2324)

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Turbulent boundary layer trailing edge noise (TEN)A subtle process

1 Hydrodynamic gust convecting past the trailing edge2 Scattered into acoustics at the trailing edge3 Acoustic field induces a distribution of dipoles near the TE4 The dipoles radiate efficiently (M5) to the far field

5 / 24

Outline

1 Introduction

2 Theory

3 Results


5 Conclusions

6 / 24

TEN modelling for isolated airfoilsHowe’s serrated edge model

Howe (1991) & Azarpeyvand (2012)

Spp = A D Φ

AssumptionsHigh frequency (kC > 1)Frozen turbulenceSharp edgeFull Kutta condition (∆PTE = 0)Low Mach number (M < 0.2)

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TEN modelling for isolated airfoilsSerration profiles

x1

x3

U

2hs

ls

ls

2hs

ls

2hs

h′

slit thickness d

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Edge spectra for serrated edges

Rewriting of Howe (1991) & Azarpeyvand et al. (2013)

Φ = ψ(K1δ)

ψ(ρ) =ρ2

[ρ2 + 1.332]2

10-2 10-1 100 101 102

ρ

10-5

10-4

10-3

10-2

10-1

100

ψ

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Rewriting of Howe (1991) & Azarpeyvand et al. (2013)

Φ =∑

n an(K1h) ψ(ρnδ)

ψ(ρ) =ρ2

[ρ2 + 1.332]2ρn =

√K2

1 + n2k2s

10-2 10-1 100 101 102

ρ

10-5

10-4

10-3

10-2

10-1

100

ψ

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Modal amplitudes an, K1hs = 25

30 20 10 0 10 20 300.0

0.2

0.4

0.6

0.8

1.0 Straight

30 20 10 0 10 20 300.00

0.01

0.02

0.03

0.04

0.05

0.06 Sinusoidal

30 20 10 0 10 20 300.00

0.05

0.10

0.15

0.20

0.25 Sawtooth

30 20 10 0 10 20 300.00

0.02

0.04

0.06

0.08

0.10 Slitted Sawtooth

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TEN for Rotating Airfoils

Observer

Flow

γ

x

y

z

α

θΩ

Time averaged PSD vs Instantaneous PSD

Spp(ω) =1

T

∫T0

Spp(ω, t)dt

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Amiet’s model for rotating airfoils

Spp(ω) =1

T

∫T0

(ω ′

ω

)2

S ′pp(ω′, τ)dτ

Main steps:Ignore acceleration effects (ω Ω)Power conservation: Spp(ω, t)∆ω = S ′pp(ω

′, τ)∆ω ′

Change of variable: ∂t∂τ = ω ′ω

Doppler shift:

ω ′ω = ωS

ωO= 1− MSO·e

1+MFO·e

References:Schlinker and Amiet (1981)Sinayoko, Kingan and Agarwal (2013)

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Outline

1 Introduction

2 Theory

3 Results


5 Conclusions

13 / 24

Sawtooth serration designWind turbine blade element

Wind turbine blade element:Pitch angle: 10 degChord: 2m

Span: 7.25m

Rotational speed Ω = 2.6rad/s (RPM=25)Angle of attack: 0 degMblade = 0.165

Mchord = 0.167

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Sawtooth serration designEffect of serration height

Wide sawtooth ls = 2δ

δ=0.5ls

100 101 102

Non-dimensional frequency kC

10

15

20

25

30

35

40

45

50

Sound P

ow

er

Level (S

PW

L) [

dB

re 1·1

0−12

]

4h/ls= 0

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δ=0.5ls

100 101 102


10

15

20

25

30

35

40

45

50

Sound P

ow

er

Level (S

PW

L) [

dB

re 1·1

0−12

]

4h/ls= 0

4h/ls= 1

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δ=0.5ls

100 101 102


10

15

20

25

30

35

40

45

50

Sound P

ow

er

Level (S

PW

L) [

dB

re 1·1

0−12

]

4h/ls= 0

4h/ls= 1

4h/ls= 2

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δ=0.5ls

100 101 102


10

15

20

25

30

35

40

45

50

Sound P

ow

er

Level (S

PW

L) [

dB

re 1·1

0−12

]

4h/ls= 0

4h/ls= 1

4h/ls= 2

4h/ls= 4

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δ=0.5ls

100 101 102


10

15

20

25

30

35

40

45

50

Sound P

ow

er

Level (S

PW

L) [

dB

re 1·1

0−12

]

4h/ls= 0

4h/ls= 1

4h/ls= 2

4h/ls= 4

4h/ls= 8

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Narrow sawtooth ls = δ/2

δ=2.0ls

100 101 102


10

15

20

25

30

35

40

45

50

Sound P

ow

er

Level (S

PW

L) [

dB

re 1·1

0−12

]

4h/ls= 0

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δ=2.0ls

100 101 102


10

15

20

25

30

35

40

45

50

Sound P

ow

er

Level (S

PW

L) [

dB

re 1·1

0−12

]

4h/ls= 0

4h/ls= 1

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δ=2.0ls

100 101 102


10

15

20

25

30

35

40

45

50

Sound P

ow

er

Level (S

PW

L) [

dB

re 1·1

0−12

]

4h/ls= 0

4h/ls= 1

4h/ls= 2

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δ=2.0ls

100 101 102


10

15

20

25

30

35

40

45

50

Sound P

ow

er

Level (S

PW

L) [

dB

re 1·1

0−12

]

4h/ls= 0

4h/ls= 1

4h/ls= 2

4h/ls= 4

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δ=2.0ls

100 101 102


10

15

20

25

30

35

40

45

50

Sound P

ow

er

Level (S

PW

L) [

dB

re 1·1

0−12

]

4h/ls= 0

4h/ls= 1

4h/ls= 2

4h/ls= 4

4h/ls= 8

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Effect of rotation on PSDDoppler factor

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Blade element Mach

5

10

15

20

25

30

35

40

Pit

ch a

ngle

(deg)

CF

WT

PTO

PCR

Maximum Doppler factor (ω′/ω)2 (dB)

0.0

1.2

2.4

3.6

4.8

6.0

WT: wind turbine CF: cooling fanPTO: propeller take-off PC: propeller cruise

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Outline

1 Introduction

2 Theory

3 Results


5 Conclusions

18 / 24

Generalized Amiet model for serrated edgesTheory

Inspired by Roger et al (AIAA-2013-2108)Fourier series in spanwise direction.Pressure formulation and scattering approachDiscretize the solution using n Fourier modes

LP = DP +C∂P

∂y1

L =

(β2 + σ2

) ∂2∂y21

+∂2

∂y22+ 2ikM

∂

∂y1

.

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Generalized Amiet model for serrated edgesIterative solution

1 Refine the solution iteratively

P = limn→+∞Pn

2 Decoupled solution (order 0)

LP0 = DP0

3 Coupled solution (order 1)

LP1 = DP1 +C∂P0

∂y1.

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Generalized Amiet model for serrated edgesResults

100 101


5

0

5

10

15

20

25

30

∆SPL

(Str

aig

ht

Edge -

Saw

tooth

) [d

B]

order 0

order 1

Howe

Isolated sawtooth blade, M = 0.1, ls/δ = 1, hs/ls = 3.75.

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Outline

1 Introduction

2 Theory

3 Results


5 Conclusions

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Conclusions

1 Rotation effect can be incorporated easily using Amiet’s approach2 Rotation has little effect (< 1dB) for low speed fans3 Rotation has significant effect (up to 5dB) on high speed fans4 Preliminary results for new model improves significantly on

Howe’s theory

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Acknowledgements

Further information

http://www.sinayoko.comhttp://bitbucket.org/[email protected]@sinayoko

Thank you!

24 / 24

Acknowledgements

Further information

http://www.sinayoko.comhttp://bitbucket.org/[email protected]@sinayoko

Thank you!24 / 24

trailing edge noise prediction for rotating serrated blades · 20th aiaa/ceas aeroacoustics...

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