Download - Trailing edge noise for rotating blades
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Trailing edge noise for rotating blades
Analysis and comparison of two classical approaches
Samuel Sinayoko1 Mike Kingan2 Anurag Agarwal1
1University of Cambridge, UK2University of Southampton, Institute of Sound and Vibration Research, UK
18th AIAA/CEAS Aeroacoustics Conference, Colorado Springs, 6 June 2011
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Motivation
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Outline
Isolated airfoil theory
Amiet’s theory for rotating airfoils
Kim-George’s theory for rotating airfoils
Results
Conclusions
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Review
Trailing edge for isolated airfoils
I Amiet 1974, 1975, 1976I Roger and Moreau 2005, 2009
Trailing edge for rotating airfoils
I Amiet 1976I Schlinker and Amiet 1981I Kim and George 1982I Blandeau and Joseph 2011
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Review
Trailing edge for isolated airfoils
I Amiet 1974, 1975, 1976I Roger and Moreau 2005, 2009
Trailing edge for rotating airfoils
I Amiet 1976I Schlinker and Amiet 1981I Kim and George 1982I Blandeau and Joseph 2011
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Outline
Isolated airfoil theory
Amiet’s theory for rotating airfoils
Kim-George’s theory for rotating airfoils
Results
Conclusions
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Isolated airfoil theory
I Amplitude
Spp = a |Ψ|2 ly Sqq
I Acoustic liftI Spanwise correlation lengthI Surface spectrum
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Isolated airfoil theory
I Amplitude
Spp = a |Ψ|2 ly Sqq
I Acoustic liftI Spanwise correlation lengthI Surface spectrum
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Isolated airfoil theory
I Amplitude
Spp = a |Ψ|2 ly Sqq
I Acoustic lift
I Spanwise correlation lengthI Surface spectrum
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Isolated airfoil theory
I Amplitude
Spp = a |Ψ|2 ly Sqq
I Acoustic liftI Spanwise correlation length
I Surface spectrum
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Isolated airfoil theory
I Amplitude
Spp = a |Ψ|2 ly Sqq
I Acoustic liftI Spanwise correlation lengthI Surface spectrum
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Outline
Isolated airfoil theory
Amiet’s theory for rotating airfoils
Kim-George’s theory for rotating airfoils
Results
Conclusions
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Rotating airfoil
Observer
Flow
γ
x
y
z
α
θΩ
Spp(ω) =
∫Spp(ω,γ)dt
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Rotating airfoil
Observer
Flow
γ
x
y
z
α
θΩ
Spp(ω) =
∫Spp(ω,γ)dt
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Change of reference frame
rotor plane
E
P
MSO
MFO
Observerz
θ
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Change of reference frame
rotor plane
E
PMSOMFO
Observerz
θ
MFS z′θ′
MOS
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Change of reference frame
P
Observer
MFS z′θ′
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Moving observer in wind tunnel
I p(x, t) : no effectI p(x,ω) : Doppler shift ω ′ → ω
PSD for moving observer
Spp(ω,γ) =ω ′
ωS ′pp(ω
′,γ)
Time for moving observer
dt =ω ′
ωdt ′
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Moving observer in wind tunnel
I p(x, t) : no effectI p(x,ω) : Doppler shift ω ′ → ω
PSD for moving observer
Spp(ω,γ) =ω ′
ωS ′pp(ω
′,γ)
Time for moving observer
dt =ω ′
ωdt ′
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Moving observer in wind tunnel
I p(x, t) : no effectI p(x,ω) : Doppler shift ω ′ → ω
PSD for moving observer
Spp(ω,γ) =ω ′
ωS ′pp(ω
′,γ)
Time for moving observer
dt =ω ′
ωdt ′
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Amiet’s theory for rotating blade
Spp(ω) =1
2π
∫ 2π0
(ω ′
ω
)2
S ′pp(ω
′,γ)dγ
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But... not everyone agrees
Spp(ω) =1
2π
∫ 2π0
(ω ′
ω
)eS ′pp(ω
′,γ)dγ
Source Exponent eAmiet (1976) 1Rozenberg et al (2010) 1Schlinker and Amiet (1981) 2Blandeau and Joseph (2011) -2
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Outline
Isolated airfoil theory
Amiet’s theory for rotating airfoils
Kim-George’s theory for rotating airfoils
Results
Conclusions
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Kim-George approach
p(x, t)
p(x,ω)
Spp(x,ω)
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Kim-George approach
I Amplitude
Spp =∑m
B |Ψ|2 ly Sqq
I Acoustic liftI Spanwise correlation lengthI Surface spectrum
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Kim-George approach
I Amplitude
Spp =∑m
B |Ψ|2 ly Sqq
I Acoustic liftI Spanwise correlation lengthI Surface spectrum
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Kim-George approach
I Amplitude
Spp =∑m
B |Ψ|2 ly Sqq
I Acoustic lift
I Spanwise correlation lengthI Surface spectrum
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Kim-George approach
I Amplitude
Spp =∑m
B |Ψ|2 ly Sqq
I Acoustic liftI Spanwise correlation length
I Surface spectrum
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Kim-George approach
I Amplitude
Spp =∑m
B |Ψ|2 ly Sqq
I Acoustic liftI Spanwise correlation lengthI Surface spectrum
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Summary
Amiet:
Spp =
∫A |Ψ|2 ly Sqq dγ
Kim-George:
Spp =∑m
B |Ψ|2 ly Sqq
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Outline
Isolated airfoil theory
Amiet’s theory for rotating airfoils
Kim-George’s theory for rotating airfoils
Results
Conclusions
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Blade elements
Blade Mach number
Pit
chan
gle
Wind Turbine
Open propellorat cruise
Open propellorat take-off
Cooling fan
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Wind turbine kc = 5
0
30
60
90
120
150
1807272 6262
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Open propellor takeoff kc = 5
0
30
60
90
120
150
1807878 6464
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Wind turbine kc=0.5
0
30
60
90
120
150
1807070 6060
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Wind turbine kc=5
0
30
60
90
120
150
1807272 6262
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Wind turbine kc=50
0
30
60
90
120
150
1805959 4949
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Cooling fan kc=0.5
0
30
60
90
120
150
1801010 55
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Cooling fan kc=5
0
30
60
90
120
150
1802727 1717
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Cooling fan kc=50
0
30
60
90
120
150
1802626 2121
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Open propellor take-off kc=0.5
0
30
60
90
120
150
1807171 6161
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Open propellor take-off kc=5
0
30
60
90
120
150
1807070 6060
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Open propellor take-off kc=50
0
30
60
90
120
150
1806767 5757
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Open propeller cruise kc=0.5
0
30
60
90
120
150
1807373 6868
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Open propeller cruise kc=5
0
30
60
90
120
150
1807373 6868
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Open propeller cruise kc=50
0
30
60
90
120
150
1807171 6666
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Outline
Isolated airfoil theory
Amiet’s theory for rotating airfoils
Kim-George’s theory for rotating airfoils
Results
Conclusions
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Conclusions
1. Right exponent in Amiet’s theory is 2
2. Amiet’s approach exact if Mch 6 0.85 andkc > 0.5
3. Applicable to a wide range of applications
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Conclusions
1. Right exponent in Amiet’s theory is 2
2. Amiet’s approach exact if Mch 6 0.85 andkc > 0.5
3. Applicable to a wide range of applications
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Conclusions
1. Right exponent in Amiet’s theory is 2
2. Amiet’s approach exact if Mch 6 0.85 andkc > 0.5
3. Applicable to a wide range of applications
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