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Effects of Wind-Tunnel Noiseon Array Measurements in Closed Test Sections
K. Ehrenfried1, L. Koop1, A. Henning2 and K. Kaepernick2
1Institute of Aerodynamics and Flow TechnologyGerman Aerospace Center (DLR), Gottingen
2Institut fur Luft und RaumfahrtTechnical University of Berlin
1
Overview
• Motivation
• Experimental setup
• Source maps
• Effects of background noise
• Wavenumber spectrum
• Algorithm to remove noise effect in source maps
• Improved results
Background noise 2
Motivation
• Economic efficiency in aerodynamic and aeroacoustic testing
– Aerodynamic and aeroacoustic tests in parallel
• Acoustically optimized wind tunnels
– Open jet configuration in anechoic chamber
– Surfaces line with absorbing material
– Little background noise
• Aerodynamic measurements
– Closed test sections
– Well defined boundary conditions
– Ideal for comparison with numerical results
=⇒ Aeroacoustic experiments in closed test sections
Background noise 3
Experimental parameters
• Wind tunnel
– 2.0m × 1.4m test section, hard side walls
– 30 m/s flow velocity
• Array
– 144 microphones on 9 spiral arms, 1 m diameter of microphone field
– 25 mm thick array body
– Electret microphones (RTI)
– 120 kHz sampling frequency, 30 sec measurement time
• Wing model
– Swept-wing constant-chord half-model (SCCH model)
– 1.2m span, 0.4 m chord
– Slat deployed, flap retracted, 7 degree angle of attack
Background noise 5
Array processing
• Delay-and-sum beamforming in frequency domain
• 4096 samples window length (rectangle), ∆f = 29.3 Hz
• Diagonal removal
• 10 mm source map resolution
• Observation plane turned with SCCH model
• Array maps using local coordinates
• Assumption of homogeneous flow (U = 30 m/s)
• Model-frequency scaling ≈ 1:6
Background noise 7
Effect of absorbing layer
Untreated side wall With foam layer
f = 2900.4 Hz (narrow band)
Background noise 15
Wavenumber spectrum at side wall
• Wavenumber vector k = (kx, ky, kz) with |k| = 2πfM/c
fM: Frequency in moving reference frame
• Uniform flow → 2πf = 2πfM + kxU and |k| = (2πf − kxU)/c
• Acoustic domain limited by ellipse
kx
k0=
cos θ
1 + M cos θand
ky
k0=
sin θ
1 + M cos θ
with k0 = 2πf/c and 0 ≤ θ ≤ 2π
• Duct modes
kz =mπ
Wand ky =
nπ
HW,H: Width and height (2m, 1.4m)
Background noise 16
Estimation of the wavenumber spectrum
• Beamforming with an infinite focus distance
• Steering vector
sj = exp [−i(kxxj + kyyj)]
(xj, yj): Position of j-th microphone
• Map in wavenumber space
• Normalization with k0 = 2πf/c
• Summation over 1/3-octave of values for fix (kx/k0, ky/k0)
Background noise 18
Maps in wavenumber space
Untreated side wall With foam layer
f = 3000 Hz (1/3-octave)
Background noise 19
Method to remove background noise
• Split cross-spectral matrix in two parts: R = R1 + R2
R1 represents waves from the model
R2 represents background noise
• Iterative procedure: R(0) = R, R(0)1 = 0 and R(0)
2 = 0
1. Calculate source map in object plane and map in wavenumber space
using current R(j)
2. Search absolute maximum over both maps
3. Construct a synthetic cross-spectral matrix using steering vector sbelonging to this maximum
Rs = DR(s · sH)
DR(): Diagonal removal
Background noise 20
Method to remove background noise
4. Normalize synthetic cross-spectral matrix
Rs = Rs
(sH R(j) ssH Rs s
)
5. Set R(j+1) = R(j) − Rs
6. If absolute maximum belongs to source map in object plane then
{ R(j+1)1 = R(j)
1 + Rs } else { R(j+1)2 = R(j)
2 + Rs }
• Iteration can be stopped when maximum is below predetermined
threshold (here: 200 iterations)
• Remaining R(j) is added to R(j)1 and then R(j)
1 is taken as new
cross-spectral matrix to replace the initial R
Background noise 21
Method to remove background noise
Object plane
32 × 41 grid
Wavenumber space
21 × 11 grid
Grids used in iterative procedure
Background noise 22
Comparison
Raw cross-spectral matrix Reduced cross-spectral matrix
f = 2900.4 Hz (narrow band)
Background noise 24