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AIAA 99-1802
Computational Aeroacoustic Analysis
of Slat Trailing-Edge Flow
Bart A. Singer, David P. Lockard,
Kenneth S. Brentner
NASA Langley Research Center
Hampton, VA 23681-2199
Mehdi R. Khorrami,
Mert E. Berkman,
Meelan Choudhari
High Technology Corporation
28 Research Drive
Hampton, VA 23666
5th AIAA/CEAS Aeroacoustics
Conference
10--12 May, 1999, Greater Seattle,
Washington
AIAA-99-1802
COMPUTATIONAL AEROACOUSTIC ANALYSIS OF SLAT TRAILING-EDGE FLOW
Bart A. Singer
,David P.Lockard
y
,
Kenneth S. Brentner
z
NASA Langley Research Center
Hampton, VA 23681-2199
Mehdi R. Khorrami
x
,
Mert E. Berkman
{
,
Meelan Choudhari
#
High Technology Corp oration
28 Research Drive
Hampton, VA 23666
An acoustic analysis based on the Ffowcs Williams
and Hawkings equation was performed for a high-lift
system. As input, the acoustic analysis used un-
steady ow data obtained from a highly resolved,
time-dependent, Reynolds-averaged Navier-Stokes
calculation. The analysis strongly suggests that vor-
tex shedding from the trailing edge of the slat results
in a high-amplitude, high-frequency acoustic signal,
similar to that whichwas observed in a correspond-
ing experimental study of the high-lift system.
Introduction
Airframe-generated noise is an imp ortant comp o-
nent of the total noise radiated from commercial
aircraft, esp ecially during the approach portion of
the ight path when the engines are run at reduced
power. Recent studies byDavy and Remy
1
on a
scale model Airbus aircraft indicate that the high-
lift devices and landing gear are the main sources
of airframe noise when the aircraft is congured
for approach. Earlier tests on a model of a DC-
10 also identied the high-lift system as an impor-
tant airframe noise source.
2
Dobrzynski, Nagakura,
Gehlhar, and Buschbaum
3
performed full-scale ex-
Research Scientist, Aero dynamic and Acoustic Metho ds
Branch.
y
Research Scientist, Aero dynamic and Acoustic Metho ds
Branch, Member AIAA.
z
Senior Research Engineer, Aerodynamic and Acoustic
Methods Branch, Senior Member AIAA.
x
Senior Scientist, Senior Member AIAA.
{
Senior Research Scientist, Senior Member AIAA.
#
Research Scientist, Member AIAA.
Copyright
c
1999 by the American Institute of Aeronau-
tics and Astronautics, Inc. No copyright is asserted in the
United States under Title 17, U.S. Code. The U.S. Govern-
ment has a royalty-free license to exercise all rights under the
copyright claimed herein for government purp oses. All other
rights are reserved by the copyrightowner.
perimental studies in an op en-jet wind tunnel of a
portion of a wing equipp ed with a high-lift system.
They found that b oth the leading-edge slat and the
side edge of the trailing ap contributed signicantly
to the airframe noise.
An extensive experimental and computational ef-
fort to study the various mechanisms associated
with airframe-generated noise is currently underway
at NASA Langley Research Center.
4
Considerable
progress has already been made in understanding
various asp ects of the noise-generation process on
the ap side edge.
5{11
More recently, attention has
focussed on noise generated in the vicinityofthe
leading-edge slat.
A co op erative test involving NASA's High-Lift
Program Element and NASA's Airframe Noise Team
was conducted in NASA Langley Research Center's
Low-Turbulence Pressure Tunnel (LTPT). Variation
of the pressure in the tunnel allows the Reynolds
number to be changed at constant Machnumber.
In these tests, the Reynolds number based on the
cruise-wing chord varied from 3.6 to 19 million. No
qualitativechanges were observed in the data for
Reynolds numbers above 7.2 million. The mo del
tested in the tunnel is known as the Energy E-
cientTransport (EET) model.
12
The EET model
tested includes a full-span leading-edge slat and a
part-span trailing ap. To obtain acoustic data,
members of Bo eing Commercial Airplane Company
designed and built a microphone array that was in-
stalled in the ceiling of the wind tunnel. The mi-
crophone array and the subsequent data pro cessing
followed techniques developed earlier at Boeing .
13
These techniques have previously b een used suc-
cessfully to determine the noise radiated from lo cal-
ized sources, even in hard-walled, non-anechoic wind
1
American Institute of Aeronautics and Astronautics
AIAA-99-1802
Centroid of
Acoustic Array
Wind-Tunnel Ceiling
Wind-Tunnel Floor
Flow Direction
0 deg.
270 deg.
Figure 1. Schematic of mo del in wind tunnel. Flow
from left to right. Acoustic directivity angles 0 and
270 deg. are indicated. View is rotated relativeto
experimental setup.
tunnels like the LTPT. To measure noise radiating
groundward in normal ight, the EET model was
mounted upside-down in the tunnel so that the pres-
sure surface faced the array in the wind-tunnel ceil-
ing. However, to reduce confusion, all references to
directions in this pap er will conform to the schematic
of the exp erimental setup shown in Fig. 1. The view
in Fig. 1 has been rotated from the physical orien-
tation to one that is more intuitive. An enormous
amount of data was collected and continues to b e
analyzed.
Figure 2 illustrates one unexpected and until re-
cently, perplexing feature of the exp erimental data.
For the case in which the slat deection,
s
,is30
degrees, a very large amplitude peak is observed in
the acoustic spectrum in the vicinity of 50 kHz. This
peak rises almost 20 dB above the signal observed
for the case in which the slat is deected 20 degrees.
During the course of the experiment, eorts to elim-
inate the high-frequency peak by altering the over-
hang of the slat were largely unsuccessful. Only for
cases in which the overhang b ecame unrealistically
large was a signicantchange in the high-frequency
acoustic peak observed. Increasing the congura-
tion's angle-of-attack from 10 to 15 degrees, reduced
the amplitude of the high-frequency peak by approx-
imately 10 dB. For some time, no consistent explana-
tion of the observed phenomena was available. The
focus of this paper and a companion paper
14
is to ex-
plain the observed large-amplitude, high-frequency
peak in the exp erimentally obtained acoustic spec-
1
0
2
0
3
0
4
0
5
0
6
0
7
0
Frequency (kHz)
70
75
80
85
90
95
SPL (dB)
30 deg.
20 deg.
Slat Angle
Figure 2. Acoustic sp ectrum based up on 1
=
12th o c-
tave bins with array focussed on slat region. Cong-
uration angle of attack is 10 deg., Reynolds number
is 7
:
2 million, Machnumber is 0.2.
trum.
Khorrami et al
14
provides details of unsteady,two-
dimensional (2D), Reynolds-averaged Navier-Stokes
(RANS) calculations designed to mimic the exp er-
imental conditions. In particular, the RANS com-
putation was specially designed to prop erly incor-
porate and resolve the small, but nite trailing-edge
thickness of the slat. Extremely small grid cells were
used in the vicinity of the slat trailing edge and the
time step was chosen to ensure more than 120 time
steps p er p erio d of a 50 kHz signal. Initially calcula-
tions were p erformed with a slat trailing edge thick-
ness
h
of approximately 0
:
07 p ercent of the cruise-
wing chordlength
C
, whichwas an estimate of the
actual slat trailing-edge thickness. Slat deections
of both 30 and 20 degrees were simulated. These
calculations clearly showvortex shedding from the
slat trailing edge for the case with a 30 degree slat
deection. Figure 3 shows a snapshot of the pressure
uctuations pro duced in the ow eld. For physical
reasons that are not yet clearly understo o d, the vor-
tex shedding virtually disappears for the case of a
20 degree slat deection. Acoustic analyses of the
rst set of data suggested that the initial grid dis-
tribution was insucient to completely resolve the
complex acoustic eld in the cove and other regions
in the vicinity of the slat. Later calculations with
an enhanced grid were performed for a 30 degree
slat deection with
h=C
0
:
0009. The slat thick-
ness was adjusted to more accurately represent the
measured slat thickness on the mo del. In all cases,
2
American Institute of Aeronautics and Astronautics
AIAA-99-1802
Figure 3. Instantaneous uctuation pressure, in
vicinity of leading-edge slat, from CFD calculation.
Slat deection is 30 deg. Wiggles at edges of dark
and light bands are contouring artifacts.
the high cost of the calculations limited the duration
of the temporal sample that was obtained. Here we
discuss the use of that limited sample of unsteady
computational data to perform acoustic analyses of
the generated noise.
Acoustic Pro cedure
Previously Singer et al
15
explored the use of un-
steady computational data in acoustic-propagation
codes based on the Ffowcs Williams and Hawk-
ings
16
(hereafter referred to as FW-H) equation.
Such co des compute the acoustic signal at a dis-
tant observer position byintegrating the FW-H
equation. Following Brentner and Farassat,
17
the
FW{H equation may b e written in dierential form
as
2
p
0
(
x
;t
)=
@
2
@x
i
@x
j
[
T
ij
H
(
f
)]
,
@
@x
i
[
L
i
(
f
)] +
@
@t
[(
0
U
n
)
(
f
)] (1)
where:
2
1
c
2
@
2
@t
2
,r
2
is the wave op erator,
c
is
the ambient sp eed of sound,
t
is observer time,
p
0
is
the acoustic pressure,
0
is the p erturbation density,
0
is the free-stream density,
f
= 0 describ es the
integration surface,
(
f
) is the Dirac delta function,
and
H
(
f
) is the Heaviside function. The quantities
U
i
and
L
i
are dened as
U
i
=(1
,
0
)
v
i
+
u
i
0
(2)
and
L
i
=
P
ij
^
n
j
+
u
i
(
u
n
,
v
n
) (3)
respectively. In the above equations,
is the total
density,
u
i
, is the momentum in the
i
direction,
v
i
is the velocity of the integration surface
f
=0,
and
P
ij
is the compressive stress tensor. For an in-
viscid uid,
P
ij
=
p
0
ij
where
ij
is the Kronecker
delta. The subscript
n
indicates the pro jection of a
vector quantity in the surface-normal direction. To
obtain a solution to Eq. (1), the rst term on the
right-hand-side must be integrated over the volume
outside the integration surface
f
= 0 wherever the
Lighthill stress tensor
T
ij
is nonzero in this region.
In the work reported here, this term is neglected.
However the main eects of nonzero
T
ij
within the
ow can be included bycho osing an integration sur-
face that contains all of the volume with signicant
T
ij
contributions.
The other terms on the right-hand-side of Eq. (1)
include terms that are determined by the unsteady
ow-eld data on the integration surface. Provided
that the unsteady ow data on the integration sur-
face
f
= 0 is correct, Reference 15 demonstrated
that the FW-H equation correctly propagates the
acoustic radiation from several source regions, in-
cluding the complex signals asso ciated with acoustic
scattering from sharp edges.
The extremely small time step required in the
RANS calculation to adequately resolve the high-
frequency owphysics resulted in a limited temp o-
ral duration of the data. The total time represented
by the unsteady calculation was 0.68 ms, approxi-
mately long enough for an acoustic wave generated
at the leading edge of the main element to propa-
gate halfwaydown the cruise-wing chord
C
. Because
of the short time duration, the initial transientis
importanteven when attention is restricted to the
vicinity of the slat. Figure 4 shows the p erturba-
tion pressure signal at the slat trailing edge, the slat
cusp, and the slat leading edge. To account for the
rapidly decaying amplitude of the uctuating pres-
sure, relative to the scale of the pressure uctuations
at the slat trailing edge, the scale of the pressure
uctuations is magnied by a factor of 40 at the slat
cusp and a factor of 200 at the slat leading edge.
Although the data at the slat trailing edge is quasi-
perio dic from the start, over 0.2 ms pass before the
transientgoesby the slat cusp and almost 0.38 ms
pass before the transient propagates past the slat
leading edge. After passage of the initial transient,
3
American Institute of Aeronautics and Astronautics
AIAA-99-1802
time, s
p, relative scale
0 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006 0.0007
Figure 4. Perturbation pressure as function of time.
Slat deection is 30 degrees.
slat trailing
edge, slat cusp, slat leading
edge. Vertical scale for data at slat cusp is mag-
nied by factor of 40 and shifted. Vertical scale for
data at slat leading edge is magnied by a factor of
200 and shifted.
a quasi-p erio dic condition prevails at all locations.
To limit the eect of the transient, the rst 25 p er-
cent of the data record is not used to pro duce the
results presented here. Auxiliary calculations sug-
gest that the use or nonuse of the rst 25 percent
of the data record produce relatively small quanti-
tativevariations in the results. All of the qualitative
results are unchanged. To preclude any confusion,
hereafter the term \data record" or any equivalents
should be construed to refer to only the portion of
the data that is actually used.
To deal with the limited data time series, a mo d-
ied Hanning window is applied to the data. The
modied Hanning window includes a standard Han-
ning lter for the rst and last 12.5 p ercent of the
data and a boxcar lter for the middle 75 percent.
The windowed data is scaled to preserve the original
energy in the signal. The resulting data sequence is
then implicitly rep eated as needed to provide an in-
put signal of arbitrary duration. The windowing cre-
ates an articial p erio dicity at approximately 1960
Hz, but b ecause this frequency is muchlower than
the vortex shedding frequency, the articial perio d-
icity do es not introduce any problems.
The application of acoustic theories to 2D ow
data is a problem that is likely to become more visi-
ble as computational uid dynamics (CFD) is relied
upon more regularly to provide unsteady ow data
for use in acoustic calculations. Time-dep endent,
3D, CFD data is extremely expensive to pro duce.
In many applications, as in the current problem,
the primary aero dynamic phenomena that generate
noise are essentially 2D. The 3D eects are largely
restricted to the fact that the true 3D unsteady ow
structure is not completely correlated in the third
direction. Cox et al.
18
computed 2D and 3D vortex
shedding over circular cylinders and then used the
results to calculate the acoustic pressure at an ob-
server lo cation. To use the 2D CFD computations,
the acoustic calculations were performed by assum-
ing p erfect spanwise correlation of the owover a
nite span. They found that the acoustic ampli-
tude could increase byasmuch as 20 dB simply by
extending the nite span from 5 to 100 cylinder di-
ameters.
As a rst approximation, a 2D version of the FW-
H equations is used to predict the sound eld. Here
we use the code developed byLockard
19
for com-
puting the 2D acoustic eld from 2D CFD data.
As noted above, we expect the 2D results to have
greater amplitudes than those observed in the exp er-
iment, but the qualitative features of the acoustics
are not expected to dier substantially.To study the
eects of the spanwise correlation length, a limited
number of 3D acoustic calculations are p erformed
using the same FW-H code as was used in Ref. 15.
As input to the 3D co de, the 2D CFD data is re-
peated for a nite distance in the spanwise direc-
tion. Previous tests on idealized problems conrm
that the 3D FW-H code and the 2D FW-H code
give identical results for mo del problems when the
spanwise extent is suciently long.
For consistency, all of the acoustic calculations are
performed for observers located a xed distance from
the trailing edge of the slat. The xed distance cor-
responds to the distance from the slat trailing edge
to the centroid of the acoustic array. Directivity
angles are indicated in Fig. 1; 0 degrees is in the
downstream direction, 270 degrees is groundward in
normal ight, towards the microphone arrayinthe
wind tunnel.
Another imp ortant issue involves the choice of in-
tegration surface for the FW-H calculation. Figure 5
illustrates the twointegration surfaces that have
been used for the FW-H calculations for the cases
with a slat trailing-edge thickness
h=C
0
:
0007.
The solid lines correspond to the comp onent surfaces
that lie on the solid b o dies of the slat and main ele-
ment. This combination of surfaces is designated the
\on-bo dy surface." Because the limited time sam-
ple is insucient for acoustic signals to propagate
from the leading-edge slat to the trailing ap, the
4
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