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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
4 Generalized Amiet model for isolated serrated edges
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)
4 / 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)
4 / 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)
4 / 24
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
4 Generalized Amiet model for isolated serrated edges
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)
7 / 24
TEN modelling for isolated airfoilsSerration profiles
x1
x3
U
2hs
ls
ls
2hs
ls
2hs
h′
slit thickness d
8 / 24
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
9 / 24
Edge spectra for serrated edges
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
9 / 24
Edge spectra for serrated edges
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
10 / 24
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
11 / 24
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
11 / 24
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)
12 / 24
Outline
1 Introduction
2 Theory
3 Results
4 Generalized Amiet model for isolated serrated edges
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
14 / 24
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
15 / 24
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
4h/ls= 1
15 / 24
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
4h/ls= 1
4h/ls= 2
15 / 24
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
4h/ls= 1
4h/ls= 2
4h/ls= 4
15 / 24
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
4h/ls= 1
4h/ls= 2
4h/ls= 4
4h/ls= 8
15 / 24
Sawtooth serration designEffect of serration height
Narrow sawtooth ls = δ/2
δ=2.0ls
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
16 / 24
Sawtooth serration designEffect of serration height
Narrow sawtooth ls = δ/2
δ=2.0ls
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
4h/ls= 1
16 / 24
Sawtooth serration designEffect of serration height
Narrow sawtooth ls = δ/2
δ=2.0ls
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
4h/ls= 1
4h/ls= 2
16 / 24
Sawtooth serration designEffect of serration height
Narrow sawtooth ls = δ/2
δ=2.0ls
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
4h/ls= 1
4h/ls= 2
4h/ls= 4
16 / 24
Sawtooth serration designEffect of serration height
Narrow sawtooth ls = δ/2
δ=2.0ls
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
4h/ls= 1
4h/ls= 2
4h/ls= 4
4h/ls= 8
16 / 24
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
17 / 24
Outline
1 Introduction
2 Theory
3 Results
4 Generalized Amiet model for isolated serrated edges
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
.
19 / 24
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.
20 / 24
Generalized Amiet model for serrated edgesResults
100 101
Non-dimensional frequency kC
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.
21 / 24
Outline
1 Introduction
2 Theory
3 Results
4 Generalized Amiet model for isolated serrated edges
5 Conclusions
22 / 24
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
23 / 24
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
Acknowledgements
Further information
http://www.sinayoko.comhttp://bitbucket.org/[email protected]@sinayoko
Thank you!24 / 24