Trailing Edge Noise Generation of Porous Airfoils

192 Pages·2011·29.06 MB·English

Trailing Edge Noise Generation
of Porous Airfoils
Von der Fakult¨at fu¨r Maschinenbau, Elektrotechnik und
Wirtschaftsingenieurwesen der Brandenburgischen Technischen
Universit¨at Cottbus zur Erlangung des akademischen Grades
eines Doktor-Ingenieurs genehmigte Dissertation
vorgelegt von
Diplom-Ingenieur
Thomas F. Geyer
geboren am 07.01.1981 in Radebeul
Vorsitzender: Prof. Dr.-Ing. Christoph Egbers
Gutachter: Prof. Dr.-Ing. Ennes Sarradj
Gutachter: Prof. Dr.-Ing. Thomas Carolus
Tag der mu¨ndlichen Pru¨fung: 18.08.2011

Contents
Nomenclature v
Danksagung ix
1 Introduction 1
2 Review on literature 5
2.1 Porous airfoils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.1.1 Aerodynamics of porous airfoils . . . . . . . . . . . . . . . . . . . . 5
2.1.2 Application of flow-permeable trailing edges for noise control . . . . 6
2.2 Airfoil trailing edge noise . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.1 Dependence on flow speed . . . . . . . . . . . . . . . . . . . . . . . 9
2.2.2 Dependence on angle of attack . . . . . . . . . . . . . . . . . . . . . 15
2.2.3 Trailing edge noise spectral shape . . . . . . . . . . . . . . . . . . . 15
2.3 Effects of surface roughness . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3 Measurement setup 21
3.1 Porous airfoils . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.1.1 Characterization of the porous materials . . . . . . . . . . . . . . . 21
3.1.2 Airfoil data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.2 Wind tunnel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
3.3 Aerodynamic force measurements . . . . . . . . . . . . . . . . . . . . . . . 34
3.4 Acoustic measurements and data processing . . . . . . . . . . . . . . . . . 37
3.4.1 Beamforming theory . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.4.2 Microphone array characteristics . . . . . . . . . . . . . . . . . . . 42
3.4.3 Two–dimensional beamforming . . . . . . . . . . . . . . . . . . . . 44
3.4.4 Three–dimensional beamforming . . . . . . . . . . . . . . . . . . . . 52
3.5 Constant temperature anemometry measurements . . . . . . . . . . . . . . 63
ii CONTENTS
4 Measurement results and discussion 69
4.1 Aerodynamic measurements . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.2 Acoustic measurements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.2.1 Two–dimensional beamforming results . . . . . . . . . . . . . . . . 74
4.2.2 Three–dimensional beamforming results . . . . . . . . . . . . . . . 75
4.3 Constant temperature anemometry measurements . . . . . . . . . . . . . . 91
4.3.1 Velocity profiles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.3.2 Boundary layer integral parameters . . . . . . . . . . . . . . . . . . 97
4.3.3 Turbulence parameters in the wake . . . . . . . . . . . . . . . . . . 105
4.3.4 Turbulence spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
5 Development of a basic trailing edge noise prediction model 119
5.1 Development of the model . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
5.1.1 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
5.1.2 Trailing edge noise prediction based on measured turbulence spectra
and measured mean velocity . . . . . . . . . . . . . . . . . . . . . . 122
5.1.3 Trailing edge noise prediction based on modeled turbulence spectra
and mean velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
5.2 Prediction of the trailing edge noise of porous airfoils . . . . . . . . . . . . 140
5.2.1 Comparison of predicted and measured trailing edge noise . . . . . 141
5.2.2 Discussion of the results and possible improvements to the model . 143
6 Conclusion 145
7 Zusammenfassung 149
Literature 153
List of Figures and Tables 161
A Additional wind tunnel data 169
B Microphone positions 171
C Photographs of the experimental setup 173
D Comparison of three–dimensional beamforming algorithms for a single
point source 175
CONTENTS iii
E Additional turbulence spectra 177
E.1 Influence of the spanwise position . . . . . . . . . . . . . . . . . . . . . . . 177
E.2 Normalization approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
E.3 Turbulence spectra at different chord positions . . . . . . . . . . . . . . . . 178
iv CONTENTS
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also das Recht, im Rahmen der gesetzlichen Aufgaben der Hochschulbibliotheken wei-
tere Kopien dieser Dissertation herzustellen und zu verbreiten bzw. in Datennetzen zur
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Nomenclature
Functions and scalars
a transfer function
A (acoustic) transfer matrix
A [m2] cross–sectional area of the porous sample
s
A [m2] cross–sectional area of the socket outlet for the measurement
socket
of the in situ air flow resistance
b [m] spanwise extent / wingspan
B transfer matrix of the six–component balance
c [m/s] speed of sound
c [m] chord length
l
C drag coefficient
D
C lift coefficient
L
d [m] fibre diameter
f
d [m] characteristic sensor size
min
d [m] pore diameter
p
d [m] thickness of the porous sample
s
D [m] nozzle diameter
D directivity function
e exponent
E{} expectation operator
f [s-1] frequency
f [s-1] third–octave band center frequency
c
f [s-1] sample frequency
S
F spectral shape function
F [N] drag force
D
F [N] lift force
L
F [N] side force
S
F matrix of aerodynamic forces and moment
g proportionality factor
G cross spectral matrices of microphone signals
ˆ
G estimate of the cross spectral matrices of microphone signals
h [m] trailing edge thickness
h steering vector
H shape factor
12
vi v
I [W/m2] sound intensity in the far field
I identity matrix
k [m-1] wave number
k(cid:48) [m2] thermal permeability
k [m2] viscous permeability
v
K constant
L [dB] third octave band sound pressure level
p
L [dB] overall sound pressure level
p,tot
m arbitrary integer
m slope of a linear function i
i
M number of sound sources
Ma Mach number
M [Nm] pitching moment
P
M [Nm] rolling moment
R
M [Nm] yawing moment
Y
n [Pa] amplitude of noise signals; arbitrary integer
n number of blocks
B
n matrix of noise signals
N number of microphones
p [Pa] sound pressure
p matrix of sound pressures p
p [Pa] reference sound pressure, 2·10−5 Pa
0
q [m3/s] sound energy flux
q [m3/s] volume flow velocity through a porous sample
s
r [Pa s/m2] air flow resistivity
R [m] distance between source and observer
R [Pa s/m] specific air flow resistance
s
Re Reynolds number based on chord length
s [m] distance between two adjacent pores
S [m2] wing area
S cross spectral matrices of source signals
S auto power spectral density
XX
Sr Strouhal number based on chord length
c
l
Sr Strouhal number based on boundary layer displacement thickness
δ1
SR [m-1] spatial resolution
T [s] (measurement) duration
TR [s-1] time resolution
Tu Turbulence intensity
u [m/s] turbulent velocity fluctuations
u¯ [m/s] mean velocity at the edge of the laminar sublayer
b
u [m/s] characteristic velocity scale of the turbulence
0
u [m/s] flow velocity through a porous sample
s
u [m/s] measure of the turbulent velocity fluctuations in the unsteady
v
vortical flow over an airfoil or wing according to [Lilley, 1998]
U [m/s] fluid velocity
U(cid:48) [m/s] (spline) fit of the fluid velocity
U [m/s] wind tunnel flow speed
0
U [m/s] turbulence convection velocity
c
Nomenclature vii
v [v] signals from the single load cells (i = 1, 2...,6)
i
V [m3] turbulent eddy volume
V [m3] pore volume of a porous material
p
V [m3] volume of the skeletal material of a porous material
s
V [m3] (total) volume of a porous material
t
V matrix of signals from load cells
w arbitrary scalar
W [kg] (aircraft) weight
x, y, z [m] cartesian coordinates
x position vector
∆x [m] streamwise extent of porous treatment
Greek symbols
α [◦] geometric angle of attack
β [◦] angular coordinate of a cylindrical eddy
according to [Ffowcs Williams and Hall, 1970]
γ normalized turbulence intensity
δ [m] boundary layer thickness
δ [m] thickness of the laminar sublayer
b
δ [m] boundary layer displacement thickness
1
δ [m] momentum thickness
2
δ [m] energy thickness
3
η [N s/m2] dynamic viscosity
θ [◦] inclination angle
Λ [m] characteristic viscous dimension
Λ(cid:48) [m] thermal characteristic dimension
λ [m] (sound) wave length
ν [m2/s] kinematic viscosity
Ξ [◦] angle between convection velocity and trailing edge
ρ [kg/m3] fluid density
ρ [kg/m3] density of the skeletal material of a porous material
s
ρ [kg/m3] (total) density of a porous material
t
σ surface porosity
s
σ volume porosity
v
τ tortuosity
Θ [◦] sideline angle
Φ [m2/s] power spectral density of streamwise velocity fluctuations
uu
Ψ [◦] elevation angle
ω [s-1] circular frequency
ω [s-1] characteristic source frequency of turbulent eddies
0
Ω [◦] trailing edge solid angle
(cid:96) [m] turbulence correlation length
viii v
Indices, superscripts and special characters
H conjugate transpose (Hermitian transpose)
+ Moore-Penrose pseudoinverse
D drag
i, j, k arbitrary indices
is in situ
L lift
n normalized
peak characterizing a spectral peak
por porous
ref reference (non–porous)
s (porous) sample; surface
v viscous; volume
W wing
¯ (overline) mean value
˜ (tilde) root–mean–square
Abbreviations
BPM noise prediction model by Brooks, Pope and
Marcolini [Brooks et al., 1989]
CFD Computational Fluid Dynamics
CTA Constant Temperature Anemometry
FFT Fast Fourier Transformation
LDA Laser Doppler Anemometry
PSD power spectral density
PSF point spread function
TNO noise prediction model developed at the Netherlands Organi-
sation for Applied Scientific Research [Moriarty et al., 2005]