Empirical prediction of flap tip noise
Karl-Stéphane Rossignol
∗
German Aerospace Center (DLR), Lilienthalplatz 7, D-38108 Braunschweig
In this paper, DLR’s empirical prediction model for flap tip noise is presented and
discussed in details. The prediction scheme is based on a comprehensive acoustic and
aerodynamic database acquired in the Acoustic Wind Tunnel Braunschweig. It was
verified, through successful scaling of the measured noise spectra, that the cross-flow
velocity at the flap tip is an important parameter characterizing the flow mechanism(s)
responsible for the noise production. This finding led to the definition of a universal
flap tip noise spectral shape in terms of a linear least-squares fit of the corresponding
measurement data. Using a similar approach, a model for the flap tip noise direc-
tivity was formulated. The prediction model was compared against full-scale fly-over
measurement data (B747-400 and A319) and an acceptable agreement of the overall
predictions was found. A slight underprediction of the noise levels at high frequen -
cies suggests th at additional airframe noise sources might be needed in the complete
aircraft noise prediction scheme to get a better agreement between measured and pre-
dicted noise levels. It is also found that, for large flap deflection angles, flap tip noise
dominates the high frequency part of the predicted complete aircraft high-lift noise
spectra. Knowledge of the flap tip noise peak frequency and high-frequency decay are
therefore sufficient to account for this noise source in the total aircraft noise prediction.
Finally, the limitations of the prediction scheme are discussed and research needs are
identified.
Nomenclature
U
0
Free stream velocity [m/s]
U
c
Cross-flow velocity [m/s]
M Mach number (= U
0
/a)
Re Reynolds number (= U
0
c/ν)
St
0
Strouhal number based on flap chord and free-stream velocity (= f c/U
0
)
St
c
Strouhal number based on flap chord and cross-flow velocity (= fc/U
c
)
a Speed of sound [m/s]
c Flap chord length [m]
f 1/3-octave band central frequency [Hz]
p Acoustic pressure [Pa]
D Directivity function [dB]
δ
f
Flap geometrical deflection angle [
◦
]
ν Kinematic viscosity [m
2
/s]
φ Polar angle [
◦
]
ρ Density of air [kg/m
3
]
θ Azimuthal angle [
◦
]
SPL 1/3-octave band sound pressure level [dB]
SPL
n
1/3-octave band scaled sound pressure level [dB]
I. Introduction
I
t is commonly known that an important part of the airframe noise generated by an aircraft is due to the
deployment of the components of its high-lift system. The flap was, already in the eighties, identified
∗
Research Engineer, Department of Technical Acoustics, Institute of Aerodynamics and Flow Technology, German
Aerospace Center (DLR), karl-stephane.rossignol@dlr.de
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17th AIAA/CEAS Aeroacoustics Conference(32nd AIAA Aeroacoustics Conference)
05 - 08 June 2011, Portland, Oregon
AIAA 2011-2733
Copyright © 2011 by the author(s). Published by the American Institute of Aeronautics and Astronautics, Inc., with permission.
as a major noise contributor in the approach and landing phases. By theoretical considerations, Howe
1
evaluated that noise generated at a single flap tip could be as much as 3 dB higher than trailing-edge
(TE) noise integrated along the whole of the flap span.
Since then, many experimental
2–8
and theoretical
1, 9–12
work on flap tip noise was done, providing a
large amount of knowledge regarding its production mechanisms as well as noise reduction approaches.
In regard to the current need for accurate and efficient semi-em pirical airframe noise prediction tools,
only a few authors
3, 6
have proposed appropriate models for flap tip noise. This scarcity may be e xplained
by the non-triviality to assess it in wind tunnels. For open-section wind tunnels, the effect of the shear-
layers on noise propagation is a major problem to be overcome. The sole presence of the shear-layers
also limits greatly the spatial extent where measurements can effectively be performed. Moreover and
especially for multi-element high-lift system models, the occurence of many spurious noise sources as well
as the presence of other loud components renders the isolation of flap tip noise very difficult. In closed
section wind tunnels, low signal to noise ratio (SNR) due to dominant wall boundary layer hydrodynamic
pressure fluctuations are also major causes of concern.
In a previous work done by the author,
13
the aerodynamic and acoustic characteristics of a single flap
tip (see figure 1) were studied. The acoustic me asureme nts have revealed the most imp ortant s pectral
characteristics of the model tip noise source while providing a preliminary description of its directivity.
Based upon these findings an empirical prediction model for noise produced by an isolated flap tip was
formulated and implemented. In this paper a description of the prediction scheme is given along with
details regarding its limitations and the assumptions made in the process.
(a) Large aperture array (96 1/2” LinearX M51 micro-
phones).
(b) Small aperture array on its positioning system (48
1/4” LinearX M31 microphones).
Figure 1: Isolated flap model (modified A320 flap geometry). Experimental setups for the large and
small aperture microphone arrays.
II. Experimental measurements
Measurements performed in 2008 (see Rossignol
13
for more details regarding the experiment) and
2011 in DLR’s anechoic wind tunnel in Braunschweig, Germany (AWB) consitute the database used for
the subsequent development of DLR’s flap tip noise prediction model. The AWB is an anechoic open-jet
wind tunne l capable of running at speeds of up to U
0
= 65 m/s. It is optimized for noise measurements
at frequencies above 250 Hz.
The prediction model described in the following sections is based solely on acoustic and aerodynamic
measurements made at an isolated flap having a modified A320 geometry. This model is nearly in full
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scale dimensions with a flat square tip geometry which ensures the formation of a well developed side-
edge vortex system an d a correspondingly loud noise source which can be easily quantified using the
microphone array technique. The model was mounted as a cantilever wing in the open test section of
the wind tunnel using only one supporting side-plate (se e figure 1).
θ
0
◦
180
◦
90
◦
−90
◦
y
z
U
0
Microphone array
Model
Nozzle
(a) Looking upstream at the model.
φ
y
x
×
U
0
0
◦
−90
◦
90
◦
180
◦
40
◦
−20
◦
Microphone array
Model
(b) Looking down at the model.
Figure 2: Spatial extent of the directivity measurements (from Rossignol
13
).
Sound source localization as well as quantification was performed using both large and small aperture
microphone arrays (see Rossignol
13
). Measurements were done for Mach numbe rs ranging from M =
0.087 to 0.175, corresponding to Reynolds numbers (based on the flap chord) ranging from Re = 0.96×10
6
to 1.92 × 10
6
(see table 1).
Boundary layer tripping was used on the suction side of the isolated flap at x/c = 0.01 and on its
pressure side at x/c = 0.34 to reduce the ap pearance of TE tones as well as to ensure the development
of fully turbulent boundary layers and prevent p remature separation of the boundary layers. Boundary
layer separation was first observed for δ
f
= 30
◦
. For this configuration a small zone of detached flow
exists near the supporting plate at the TE and on the suction side of the model.
U
0
m/s M Re
40 0.117 1.28 × 10
6
50 0.146 1.60 × 10
6
60 0.175 1.92 × 10
6
Table 1: Non-d imens ional flow parameters. a = 343 m/s, ρ = 1.204 kg/m
3
, ν = 1.5 × 10
−5
m
2
/s.
During the 2008 measurement campaign
13
information regarding the mean flow field in the vicinity
of the model tip was gathered at numerous streamwise position using a 7-hole probe. Based on these
measurements the dependen dc y of the cross-flow velocity (U
c
) on the model flap angle was established. U
c
is the local spanwise mean flow velocity at the fl ap tip lower edge and a chordwise position of x/c = 0.7.
The maximum value of U
c
being reached at that chordwise position, nearly independent of δ
f
. This
parameter was shown to be representative of the flow mechanism leading to noise radiation at the flap
tip.
13
III. Data acquisition and processing
Two different microphone arrays were used for the acoustic me asureme nts: a small aperture array
consisting of 48 1/4” LinearX M31 microphones and a large aperture array having 96 1/2” LinearX M51
microphones. Both experimental setups are shown in figure 1. The first array is made of a metal plate
covered with a five centimeter thick foam sheet in order to reduce sound reflections. The transducers are
flush mounted through the foam. For the second array a wire grid is used to support the microphones. A
computer controlled traversing system enables a precise positioning of the small aperture array around
the model (see figure
1). The range of the measurements is summarized in table 2, whereas measurement
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coordinates are defined in figure 2. The given ranges correspond to the maximal displacements attainable
considering the physical constraints imposed by the wind tunnel nozzle. For the second array a wire grid
is used to support the microphones.
Data acquisition was done using two 48-channel GMB Viper measuring units at a sampling rate of
45.0 kHz. Measurement duration was set to 22 seconds, which gives a total of 245 blocks of 4096 samples,
for a frequency resolution of 10.99 Hz.
θ[
◦
] φ[
◦
]
min max ∆ min max ∆
48M −90 90 15 −20 40 10
96M −90 0 90 0 0 0
Table 2: Range of the directivity measurements for the isolated flap model.
Noise source identification was done using conventional beamforming
14
(CB). To quantify the noise
level a of particular source, power integration as described by Brooks et al.
15
was used. For the present
work, noise levels lower than 10 dB below the peak sound pressure level (SPL) value were excluded from
the integration. The scanning grid (and integration region) was chosen to be parallel to the x − z plane
or to the x − y plane depending on microphone array location. Also, extensive use of diagonal removal
(DR) is made to reduce the noise flo or level induced by the microphones auto-powers.
Background noise correction was performed down to 3 dB differences. The background noise is taken
here as the noise measured at δ
f
= 0
◦
. Noise spectra were also (prior to background noise subtraction)
corrected for convective amplification, source convection and shear-layer diffraction. Hereby, use of the
well-known shear-layer correction developed by Amiet
16
was made. Finally, sound pressure levels were
back-propagated to a reference distance of 1 m from the model.
IV. Flap tip noi se spectral shape
Based on the present measurements and also from previous measurements reported in Rossignol
13
an
empirical prediction model for flap tip noise was developed. Its formulation accounts for the influence
of both free-stream velocity (U
0
) as well as flap deflection angle (δ
f
) and also includes n oise source
directivity effects.
Noise intensity is assumed to follow a power law of the form p
2
∝ U
n
c
when plotted versus a Strouhal
number (St
c
= f · c/U
c
) based on flap chord (c) and the tip cross-flow velocity (U
c
) as the relevant local
velocity. U
c
is taken here as the spanwise component of velocity at the flap tip lower ridge level
13
and
x/c = 0.7. It is obtained from the following empirical relation:
U
c
U
0
=
0.0316 · δ
f
δ
ref
+ 0.1879. (1)
δ
ref
is a reference deflection angle (δ
ref
= 1
◦
). For noise spectral scaling, the cross-flow velocity is
non-dimensionalized by an arbitrary reference velocity of U
ref
= 100 m/s. The best collapse of the data
is obtained for an exponent of n = 5.5 (see figure 3). From the preceding arguments a normalized flap
tip noise spectra can be expressed as follows;
SPL
n
= SPL + 20 · log
10
(r/c) − 55 · log
10
(U
c
/U
ref
) (2)
From the theory of aeroacoustic noise the generation of noise through interaction of turbulence with
an infinitely thin edge should result in a velocity dependance to an exponent of 5.0. Higher exponent
were, however, also found in other experimental investigations.
4, 7
The first term on the right-hand side of equation 2 accounts for the geometrical extent (c) of the
model and its distance from an observer (r). It is assumed that noise intensity varies linearly with the
radiating surface (p
2
∝ c
2
). This assumption is based on the idea that p
2
should be proportional to the
length of the flap tip and to a characteristic length of the noise-generating flow mechanism. The vortex
size, which is proportional to the model chord length.
In figure 3, the scaled sound pressure levels (measured underneath the model) are plotted along with
a polynomial fit. The low Strouhal number range is fitted with a 6
th
order polynomial while for the high
Strouhal number range a polynomial of order 3 is used (see equations 3 and 4). The fitted polynomials
intersect at St
c
≈ 25. This defines the flap tip noise spectral shape, as measured underneath the model.
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10
0
10
1
10
2
10
3
St
c
60
70
80
90
100
110
SPL
+ 20
·
log
10
(
r/c
)
−
55
·
log
10
(
U
c
/U
ref
)
[dB]
3rd order
6th order
Measurement Least-squares fit
Figure 3: Scaled airfoil tip 1/3-octave band noise spectra measured underneath the model. The solid
line is a least-squares fit of the data.
This approximation is independent of δ
f
as well as U
0
. A listing of the coefficients values obtained from
the regression analysis is given in appendix A.
SPL
n
(St
c
)|
St
c
≤25
= l
0
+ l
1
· St
c
+ l
2
· St
2
c
+ l
3
· St
3
c
+ l
4
· St
4
c
+ l
5
· St
5
c
+ l
6
· St
6
c
(3)
SPL
n
(St
c
)|
St
c
>25
= h
0
+ h
1
· St
c
+ h
2
· St
2
c
+ h
3
· St
3
c
(4)
The spectral shape of figure 3 reveals a peak at St
c
≈ 9, in good agreement with experimental data
from Koop
7
and Brooks et al.
3
when using the same Strouhal number definition (St
c
). This, however,
differs from what is found by Guo et al.
5
(St
c
= 3.91). These discrepancies mightl, however, be due to
a wrong evaluation of U
c
at high flap deflection angle (δ
f
= 50
◦
in
5
) based on equation 1.
In figure 4 a comparison of flap tip noise spectra predictions made by three published empirical
models is shown (U
0
= 50 m/s, δ
f
= 25
◦
). In the low Strouhal number part of the spectrum all models
tend towards a similar prediction. The computed spectral levels agree to about 5 dB with slight shift
in peak frequency. Both Guo’s
6
and Brook’s
3
models predict, at high Strouhal numbers, a much more
rapid SPL decay compared to the model described herein.
10
0
10
1
10
2
S
t
c
30
40
50
60
70
80
SPL [dB]
Rossignol (2011)
Guo et al. (2003)
Brooks and Marcolini (1989)
Figure 4: Comparison of existing flap tip noise prediction models. δ
f
= 25
◦
, U
0
= 50 m/s
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