AIAA 2001-2155
Time-Accurate Simulations and Acoustic
Analysis of Slat Free-Shear Layer
Mehdi R. Khorrami
Bart A. Singer
NASA Langley Research Center
Hampton, VA 23681-2199
Mert E. Berkman
High Technology Corporation
28 Research Drive
Hampton, VA 23666
7th AIANCEAS Aeroacoustics
Conference
28--30 May, 2001, Maastricht, Netherlands
For permission to copy or republish, contact the American Institute of Aeronautics and AstronauUcs
1801 Alexander Bell Drive, Suite 500, Reston, VA 20191-4344
AIAA-2001-2155
TIME-ACCURATE SIMULATIONS AND ACOUSTIC ANALYSIS OF SLAT
FREE-SHEAR LAYER
Mehdi R. Khorrami*
Bart A. Singer 1
NASA Langley Research Center
Ilampton, VA 23681-2199
Mert E. Berkmanl
High Technology Corporation
28 Research Drive
Hampton, VA 23666
A detailed computational aeroacoustic analysis of
a high-lift flow field is performed. Time-accurate
Reynolds Averaged Navier-Stokes (RANS) compu-
tations simulate the free shear layer that originates
from the slat cusp. Both unforced and forced cases
are studied. Preliminary results show that the shear
layer is a good amplifier of disturbances in the lo_-
to mid-frequency range. The Ffowcs-Williams and
Hawkings equation is solved to determine the acous-
tic field using the unsteady flow data from the RANS
calculations. The noise radiated from the excited
shear layer has a spectral shape qualitatively simi-
lar to that obtained from measurements in a corre:
sponding experimental study of the high-lift system.
Introduction
As part of a major effort to reduce aircraft noise
emission, airframe noise has received renewed at-
tention in the past few years. 1 To develop viable
noise reduction technologies, a concerted effort to-
ward isolating and understanding noise sources asso-
ciated with individual components of a high-lift sys-
tem has been undertaken. Experimental studies by
Hayes et al., 2 Dobrzynski et al., 3 Davy and Remy, 4
Grosche et al., 5 Michel et al., 6 Storms et al., 7 and
Olson et al., s along with the in-house measurements
at NASA Langley Research Center (LaRC), clearly
*Research Scientist formally with High Technology Corp.
Senior Member AIAA.
IAssistant Branch Head, Computational Modeling and
Simulation Branch. Member AIAA.
I Research Scientist; currently with ArvinMeritor Exhaust
Systems, Member AIAA.
Copyright C)2001 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 purposes. All other
rights are reserved by the copyright owner.
show the importance of a leading-edge slat as a ma-
jor contributor to overall airframe noise. The LaRC
tests, which are the focus of our attention, involved
a generic Energy Efficient Transport (EET) high-lift
model. The model is comprised of a slat, a main el-
ement, and a flap (fig. 1). Both aerodynamic and
acoustic measurements were obtained in the Low
Turbulence Pressure Tunnel (LTPT) during entries
in 1998 and 1999.
In the present paper we continue studying noise
sources associated with a leading-edge slat in a high-
lift setting. Our previous research focused on accu-
rate unsteady simulations of the slat trailing-edge
flow field and computation of the resulting acoustic
far field. 9' 10 Current research applies the framework
established in references 9 and 10 to the free shear
layer that originates at the slat cusp.
In the experiments, acoustic measurements were
made by a team from Boeing Commercial Airplane
Company using the Boeing microphone-array tech-
nique. The array was mounted roughly one meter
from the underside of the model. The setting for
the baseline case consisted of a main element angle
of attack that varied between 6 to 10 degrees, a flap
deflection angle of 30 degrees, and a slat deflection
angle of 30 degrees. For the angles of attack consid-
ered, with the exception of minor details, the EET
slat produces acoustic signatures that have similar
features.
Representative microphone-array measurements
for a 9-degree ease from the 1999 entry are shown
in figure 2. The plotted spectra are in 1/12th-octave
bands. The high-frequency microphone array had a
smaller aperture than the low-frequency array and
was better suited for resolving high-frequency noise.
The flow Mach number is 0.2, corresponding to a
typical approach condition. Two prominent features
1
American Institute of Aeronautics and Astronautics
AIAA-2001-2155
(a)
Cstowed (= Ccruise)
(b)
Figure 1. Three-element EET high-lift system. (a)
Three-dimensional model. (b) Cross-sectional view.
in the acoustic spectrum are a relatively high ampli-
tude peak near 50,000 Ilz and high sound levels in
the lower frequency range that drop abruptly be-
tween 4,000 Hz to 5,000 Hz.
Our previous efforts, 9'1° proved our first conjec-
ture that vortex shedding at the slat blunt trailing-
edge is the mechanism responsible for the tonal peak
in the acoustic spectra at high frequencies. During
the course of that study, our time-accurate solution
pointed to the presence of additional flow oscilla-
tions in the slat-cove region. The observed oscilla-
tions were associated with the slat free shear layer
and had frequencies between 2,000 Hz and 4,000 Hz.
This early simulation 9 also suggested that the
shear layer may self-excite and would not require
explicit forcing. Therefore, our preliminary time-
accurate simulations involved no forcing at the slat
cusp, relying instead oll the presence of numerical
perturbations in the initial solution to provide nec-
essary excitation for the cove shear layer. Initially
this natural forcing was adequate, as the shear layer
self-excited in the proper frequency band. Unfor-
tunately, the excitation did not last more than a
few periods before numerical dissipation damped the
shear layer instability modes and caused the flow
field to return toward its original quasi-steady state.
B5
80
75
"0
J
tt
(n
70
65
60
r L 1 , , , , I I , 1 t|lltlllttiLlllll
Frequency, Hz
Figure 2. Measured acoustic spectrum for slat in
1/12th-octave bands. Test parameters are: slat de-
flection angle of 30 degrees, main element angle of
attack of 9 degrees, flap deflection angle of 30 de-
grees, Mach number of 0.2, Reynolds number Of 7.5
million, low-frequency microphone array,
high-frequency microphone array.
Lack of sustained disturbance growth prompted us
to undertake a more thorough study. Ill this effort
we focused our attention on the role of large-scale
instabiliy modes of the slat shear layer in generating
noise. Therefore, goals of the present study are to
test our conjecture that amplified perturbations in
the free shear-layer are responsible for low-frequency
content of the acoustic spectra. While similar con-
jectures have been put forth by other investigators
(Dobrzynski et al.3), the issue remains unresolved.
Although our current simulations were started in
late 1998 and early 1999, two recent studies lend
added support to our conjecture. Using Particle Im-
age Velocimetry (PIV), Paschal et al. 11 were able
to map the flow field slightly downstream of the slat
trailing edge. At low angles of attack (4 degrees), the
PIV-generated images show the presence of large,
strong spanwise vortices in the slat's wake. Size and
location of these rollers, relative to the wake, pre-
clude the slat trailing edge as the source. |n all
likelihood, as pointed out by Paschal et al., these
vortices originate from the slat-cove region and then
are pumped through the gap. As the angle of attack
is increased, unsteadiness coming out of the cove is
diminished and the number of vortices ill the wake is
reduced significantly. Similarly, Takeda et al. 12 em-
ployed the PIV technique to map the flow field in-
side a slat-cove area. Growth of the shear-layer dis-
2
American Institute of Aeronautics and Astronautics
AIAA-2001-2155
turbances and their subsequent evolution into large-
scale structures are captured.
Computational Approach
The computational framework employed in the
present study was explained in detail in references 9
and 10. Only a brief overview is given below.
As in reference 9, the CFL3D solver is used
to perform time-accurate flow-field simulations.
CFL3D is a finite-volume formulation-based code
that solves time-dependent compressible thin-layer
Navier-Stokes equations. CFL3D offers a wide va-
riety of turbulence models, including 0-, 1-, and 2-
equation models. Based on our past experience, the
2-equation SST (k-w) Menter la model is selected and
preferred for the present problem.
All current computations are performed using the
second-order-accurate time discretization and the
"dual time stepping" method. Thirty subiterations,
in conjunction with 3-level V-type multigrid cycles,
are utilized to ensure approximately two orders of
magnitude drop in both mean-flow and turbulence-
model residuals during each time step.
A full account of the three-element high-lift EET
model and grid construction has been given by Khor-
ramiet al. 9 For the present work, it suffices to men-
tion that in the stowed position, the model has a
chord of 21.65 inches (0.55 m) with slat and flap
chords of 15 percent and 30 percent, respectively.
The geometrical settings associated with the slat and
flap (gaps 9, and 9f; overhangs o_ and ol) in the
baseline experiment are provided in table 1 where
the distances are given as a percentage of the stowed
chord. A graphical representation of the respective
gaps and overhangs are shown in figure lb. In the
1998 entry, angle of attack for the baseline experi-
ment was set at 10 degrees and the deployed flap was
part span. To match loading on the slat and the
main element, present two-dimensional (2D) simu-
lations are performed at 8 degrees angle of attack.
In the 1999 entry, the part-span flap was replaced
by a full-span flap with a slightly different profile.
The slat gap and overhang remained identical. The
new flap had little effect on relevant features of the
measured acoustic spectra. Therefore, current sim-
ulations, which are conducted using the original flap
profile, apply to both 1998 and 1999 experiments.
The present grid is identical to the "refined grid"
employed in reference 9. The 2D grid has 21 blocks
and approximately 433 K total nodes. More than
60 percent of the points are clustered in regions sur-
rounding the slat and leading edge of the main el-
ement. To illustrate this point, mesh distribution
in the slat's vicinity is shown in figure 3. For clar-
Slat angle, J_
Flap angle, _/
Slat gap, 9_
Flap gap, 91
Slat overhang, o_
30 deg
30 deg
2.44%
3.0%
-1.52%
Flap overhang, of 1.7%
Table i. Geometrical Settings
Figure 3. Grid distribution in vicinity of slat. Every
other point is shown.
ity, every other point is displayed. Notice that mesh
clustering occurs at the solid surfaces, trailing edge,
wake, and the cove. Deliberate concentration of
mesh points in the slat cove region helps ensure ac-
curately capturing the free shear layer that forms at
the slat-cusp region tip.
Forcing Strategy
As discussed in the introduction section and based
on our previous simulations, a decision was made to
introduce low levels of forcing into the flow field.
Controlled forcing helps to isolate and capture the
mechanism(s) responsible for low frequency oscilla-
tions observed in the slat cove region. After careful
consideration, the most appropriate forcing location
was selected oil the slat bottom surface, roughly two
to three local boundary layer heights upstream of the
finite thickness cusp (fig. 4). The forced quantity is
the vertical velocity, which at the forcing location,
closely approximates wall-normal velocity. A simple
harmonic function given by equations (1) and (2)
was chosen to represent the forcing function where t
3
American Institute of Aeronautics and Astronautics
AIAA-2001-2155
Probe4
( ( - Probe3
_Probe 1
Figure 4. Location of forcing and computational
probes.
and x denote time and streamwise direction, respec-
tively.
N
g(x,t) = -_h(x)_ sin(_,t + _b_) (1)
i=1
h(x) = - bl(x - b2) (2)
In equation (1), the summation is over N equally
spaced frequency bins, each with a center frequency
_i that differs by 93 Hz. To ensure the indepen-
dence of individual frequencies, a randomly gener-
ated phase, ¢i, is assigned to each bin. Also note
that in order to avoid forcing at a single point, am-
plitude of the source is distributed over several grid
nodes (seven in the present case) using a parabolic
variation in x. The constants bl and b2 are chosen
to ensure zero velocity at the edges of the forcing
region. Finally, A0 represents the root mean square
(rms) of the signal and is used to set desired ampli-
tude levels.
The time consuming nature of the unsteady sim-
ulations and the need to generate meaningful time
records limited the number of cases computed. The
present set of computations is focused on flow fields
forced over two different frequency bands. The first
simulation involves frequency band 1,200 Hz < f <
5,000 Hz corresponding to the observed range of fre-
quencies of interest in the measured spectra. Once it
became clear (from the simulated flow field) that the
shear layer is an emcient amplifier of disturbances
in the observed frequency range, frequency of the
forcing fnnction was expanded to encompass a range
approximately twice that of the initial distribution.
For the second simulation, the selected frequency
band is 700 Hz < f < 10,000 Hz. Widening the
frequency band was significant for two related rea-
sons. Given the shear layer's thinness near the cusp,
a wider frequency band allows a more natural se-
lection process for the most amplified disturbances.
In addition, it removes any ambiguity regarding the
effect of initial forcing distribution on the final out.-
come of the established flow field. We must also
mention that for both cases, the rms amplitude A0
is fixed at 3 percent of the freestream velocity.
Acoustic Procedure
Previously, Singer et al. 1°'14 explored the use
of unsteady computational results in acoustic-
propagation codes based on the Ffowes Williams and
Hawkings 15 (hereafter referred to as FW-H) equa-
tion. Such codes compute the acoustic signal at a
distant observer position by integrating the FW-H
equation. Following Brentner and Farassat, 16 the
FW-H equation may be written in differential form
as
05
- [T,-jH(I)]
- + (3)
1 0 2 _ _-12
where o2 -- _N-_- is the wave operator, c is am-
bient speed of sound, t is observer time, p' is acoustic
pressure, p' is perturbation density, p0 is free-stream
density, f = 0 describes the data surface, 6(f) is
the Dirac delta function, and H(f) is the Heaviside
function. The quantities Ui and Li are defined as
= (1- + P"_Apo (4)
and
= + - v,,) (5)
respectively. In the above equations, p is total den-
sity, pui is momentum in the i direction, vl is velocity
of the data surface f = 0, and Pij is the compressive
stress tensor. For an inviscid fluid, Pij = PC_ij where
p is the perturbation pressure and 6ij is the Kro-
necker delta.. The subscript n indicates projection
of a vector quantity in the surface-normal direction.
To obtain a solution to equation (3), the first term on
the right-hand-side must be integrated over the vol-
ume outside data surface f = 0 wherever Lighthill
stress tensor T/j is nonzero in this region. In the
work reported here, this term is neglected; however,
the main effects of nonzero T/j within the flow can
4
American Institute of Aeronautics and Astronautics