American Institute of Aeronautics and Astronautics
1
An MDOE Investigation of Chevrons for Supersonic Jet
Noise Reduction
Brenda Henderson
*
and James Bridges
†
NASA Glenn Research Center, Cleveland, OH
The impact of chevron design on the noise radiated from heated, overexpanded,
supersonic jets is presented. The experiments used faceted bi-conic convergent-divergent
nozzles with design Mach numbers equal to 1.51 and 1.65. The purpose of the facets was to
simulate divergent seals on a military style nozzle. The nozzle throat diameter was equal to
4.5 inches. Modern Design of Experiment (MDOE) techniques were used to investigate the
impact of chevron penetration, length, and width on the resulting acoustic radiation. All
chevron configurations used 12 chevrons to match the number of facets in the nozzle. Most
chevron designs resulted in increased broadband shock noise relative to the baseline nozzle.
In the peak jet noise direction, the optimum chevron design reduced peak sound pressure
levels by 4 dB relative to the baseline nozzle. The penetration was the parameter having the
greatest impact on radiated noise at all observation angles. While increasing chevron
penetration decreased acoustic radiation in the peak jet noise direction, broadband shock
noise was adversely impacted. Decreasing chevron length increased noise at most
observation angles. The impact of chevron width on radiated noise depended on frequency
and observation angle.
I. Introduction
He application of chevrons (serrations applied to a nozzle trailing edge that protrude into the exhausting flow) to
military aircraft is particularly attractive because existing engines can be retrofitted rather than redesigned to
incorporate these devices. At takeoff, high performance tactical aircraft typically have overexpanded, supersonic
jet-exhausts that contain noise sources not present in the subsonic exhausts of commercial aircraft engines. As a
result, chevrons that have been optimized for noise reduction in commercial aircraft may not perform adequately on
tactical aircraft. While a reasonably large number of investigations have studied the impact of chevrons on subsonic
jets, similar studies for supersonic flows are limited. The present investigation uses a Modern Design of
Experiments (MDOE) approach to explore the impact of chevron design on the acoustic radiation of overexpanded
supersonic jets.
An overexpanded jet resulting from operating a convergent-divergent nozzle at a stagnation pressure below that
corresponding to the nozzle design Mach number contains a quasi-periodic shock cell structure that can persist for
several diameters downstream of the nozzle exit. The constructive interference of sound waves produced by the
interaction of large-scale jet disturbances with the shock waves within the shock cell structure results in broadband
shock noise
1,2,3
. Shock noise can dominate the acoustic spectra at upstream and broadside observation angles
relative to the nozzle exit. Additionally, mixing noise sources are present and are associated with large scale jet
disturbances (radiating in the downstream direction) that become very effective noise sources when their phase
speeds (relative to the ambient speed of sound) become supersonic
4
,
and with fine scale turbulence
5
(radiating in the
upstream direction). Mixing noise sources are also present in subsonic jets but the large-scale disturbances typically
have subsonic phase speeds.
In subsonic jets, properly designed chevron nozzles produce lower overall acoustic radiation levels than those of
a corresponding round nozzle
6,7,8,9
. Experiments have shown that increasing chevron penetration decreases low
frequency noise and often increases high frequency noise (sometimes referred to as high frequency crossover). The
number of chevrons also impacts the acoustic radiation but not as significantly as the penetration. Jet shear velocity
(the velocity difference between the inner and outer jet streams) impacts chevron acoustic performance with
increases in shear velocity increasing low frequency noise reduction but sometimes increasing high frequency noise
*
Researcher, Acoustics Branch, MS 54-3, 21000 Brookpark Rd., Cleveland, OH 44135.
†
Reseacher, Acoustics Branch, MS 54-3, 21000 Brookpark Rd., Cleveland, OH 44135, Associate Fellow.
T
16th AIAA/CEAS Aeroacoustics Conference AIAA 2010-3926
This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States.
American Institute of Aeronautics and Astronautics
2
(relative to a round nozzle). Flow field measurements
7,10,11,12
have shown that chevrons produce streamwise vortices
that enhance jet mixing. Relative to a jet plume produced by a round nozzle, a chevron nozzle produces a jet plume
with lower peak turbulent kinetic (TKE) and higher TKE near the nozzle exit. The decrease in peak TKE
presumably leads to the observed reductions in low frequency acoustic radiation. High frequency noise is produced
near the nozzle exit so increases in TKE in this region of the jet can lead to increased high frequency acoustic
radiation.
Recent experiments using chevron nozzles for noise reduction on supersonic jets have focused on non-ideally
expanded jets with shocks. For underexpanded jets
13,14
, chevrons increased broadband shock noise over that of the
baseline nozzle for co-flow Mach numbers less than, or equal to, 0.5. Flow-field measurements showed that the
chevrons produced higher turbulence levels than the baseline nozzle near the nozzle exit and comparable shock
strengths, the combined effect possibly leading to increased shock noise. In the peak jet noise direction, the chevron
nozzle reduced low frequency noise relative to the baseline round nozzle. The application of chevrons to
overexpanded jets
15
resulted in reduced broadband shock noise and noise reduction at all frequencies in the peak jet
noise direction.
The present study investigates the impact of chevron design on the acoustic radiation of overexpanded jets.
Chevron penetration, length, and width were varied in a MDOE investigation that resulted in the development of
modeled noise reduction for a range of observation angles and jet operating conditions. The chevron designs were
guided by extensive prescreening computational fluid dynamics (CFD) results. The CFD studies showed that
altering the levels of the three selected parameters significantly impacted the jet plume TKE. The chevrons
appeared to have little impact on shock strength. The effects of forward flight, bypass flow, and nozzle design Mach
number on chevron acoustic performance are also presented.
II. Experimental Approach
The experiments were performed in the Aero-Acoustic Propulsion Laboratory (AAPL) at the NASA Glenn
Research Center shown in Fig. 1. The AAPL is a 20 m radius geodesic dome treated with acoustic wedges. The
AAPL contains the Nozzle Acoustic Test Rig (NATR), which produces a 53 inch diameter simulated forward flight
stream reaching Mach numbers of 0.35 and contains the High Flow Jet Exit Rig (HFJER), a dual-stream jet engine
simulator capable of replicating most commercial turbo-fan engine temperatures and pressures
16
.
The experiments used two representative military style nozzles with conical convergent and divergent sections,
nozzle area ratios corresponding to design Mach numbers (M
d
) equal to 1.51 and 1.65, and throat diameters equal to
4.45 inches. Facets were cut in the internal surfaces of the nozzles to simulate divergent seals as shown in Fig. 2.
Pockets were machined in each of the 12 nozzle facets to mount chevrons. For the baseline nozzle, blanks were
used in place of the chevrons. Unless otherwise stated, the results presented here are for the M
d
= 1.65 nozzle.
The nozzles were mounted on the fan stream of the HFJER as shown in Fig. 3. The fan-stream was used to
simulate the cooling flow in tactical aircraft nozzles. The area ratio of the fan and core streams at the exit of the fan-
core splitter was 0.2 which resulted in a bypass ratio of roughly 0.3.
The cycle conditions used in the investigation are shown in Table 1. The nozzle temperature ratio (NTR) is the
ratio of the jet stagnation temperature to the ambient temperature, the nozzle pressure ratio (NPR) is the ratio of the
jet stagnation pressure to the ambient pressure, and the free jet Mach number (M
fj
) is the Mach number of the
simulated flight stream. The subscripts “c” and “b” indicate the core and bypass streams, respectively. For the
normalized shear velocity shown in the last column of Table 1, ∆V is given by V
fe
– V
fj
, where V
fe
is the fully
expanded jet velocity and V
fj
is the free jet velocity.
Acoustic measurements were made with the far-field array shown in Fig. 1. The array contains 24 microphones
located on a 45 foot constant radius arc covering polar angles between 45
o
and 160
o
, where angles greater than 90
o
are in the downstream direction relative to the nozzle exit. All data were corrected for atmospheric absorption
17
and
wind tunnel shear layer effects
18
and are presented on a one-foot lossless arc. Data are acquired using ¼” Bruel and
Kjaer microphones without gridcaps, pointed directly at the nozzle exit. Microphone sensitivity and frequency
response have been applied to all measurements. Narrowband results are presented as power spectral density and
one-third octave band results are presented as sound pressure levels within the band.
A full-factorial, three-parameter, two-level Modern Design of Experiments (MDOE) investigation was conducted
using the parameters shown in Fig. 4 and the parameter levels given in Table 2. Also shown in Table 2 are the
configuration designations (quantities in parentheses) used to identify each chevron configuration. The chevrons are
identified by two digits following the penetration (P), length (L), and width (W) so a chevron designation of
P03L08W06 indicates a chevron with 0.30 inches penetration, 0.75 inches length, and 60% width. As shown in Fig.
4, the penetration is defined as the distance from the line extending along the inner facetted surface of the M
d
= 1.65
American Institute of Aeronautics and Astronautics
3
nozzle to the chevron tip. The length is defined as the distance from the nozzle trailing edge to the chevron tip
parallel to the facet surface. Lastly, the width is equal to the chevron base width divided by the nozzle facet width
and represented in percentage form. All configurations used 12 chevrons to match the number of facets in the
nozzle. All combinations of the parameters were tested, resulting in the design space shown in Fig. 5. The chevrons
shown in Fig. 5 are edge-point designs. A center point design (represented by the black dot in Fig. 5) was also
tested and used to identify curvature in the resulting models, quantify error, and identify block effects (effects due to
acquiring data on different days). The center chevron was tested two times during each data acquisition block (each
night of testing) for a total of eight repeat acquisitions. Details of MDOE analysis are found in Montgomery
19
.
III. Results
The impact of operating condition, forward flight, bypass flow, and the nozzle area ratio (nozzle design Mach
number) on the chevron acoustic performance will be presented first. These effects were not part of the MDOE
analysis. For some of the experiments, only the center point chevron was used. The MDOE analysis will be
presented in Section B. Only the chevron configuration order was randomized during the experiments so the jet
operating condition was not a parameter in the MDOE analysis. Separate models were developed for each operating
condition which means that applying the MDOE analysis to operating conditions not contained in Table 1 requires
model interpolation.
A. Effect of Operating Condition, Forward Flight, Bypass Flow, and Nozzle Area Ratio on Chevron Acoustic
Performance
Plots of the noise produced by the chevron nozzles and the baseline nozzle are shown in Fig. 6 for setpoint
44543 and observation angles equal to 80
o
and 160
o
. The baseline average spectra were obtained by averaging the
data obtained from three individual acquisitions. The observation angles in Fig. 6 have been chosen to show the
impact of chevrons on broadband shock noise [evident in the Fig. 6 (a)] and mixing noise in the peak jet noise
direction [see Fig. 6 (b)]. Broadband shock noise dominates the acoustic spectra obtained at an observation angle of
80
o
. In the peak jet noise direction [Fig. 6 (b)], peak acoustic levels exceed those at 80
o
by roughly 10 dB. While
most chevron configurations increase broadband shock noise over that of the baseline average, peak noise level
reductions of up to 3 dB are achieved in the peak jet noise direction with many of the chevron designs. At the 80
o
observation location, most chevrons increase noise relative to the baseline average for frequencies above 3000 Hz.
Similar results to those shown in Fig. 6 were obtained for setpoint 44103 probably due to the fact that both setpoints
had spectra dominated by broadband shock noise for observation angles less than roughly 100
o
.
The upturn in the data of Fig. 6 at frequencies greater than 30,000 Hz may be the result of nonlinear
propagation
20
due to the high sound pressure levels produced in the experiments and the presentation of the data in
lossless format. As-measured data at the far-field microphone locations did not display the upturn. Since
propagation of the lossless data to the far field will result in recovering the measured spectra, models adequately
describing the one-foot lossless spectra can be used for predicting far-field noise.
The acoustic spectra for setpoint 44053 are shown in Fig. 7. The results are typical for conditions where
broadband shock noise does not dominate the acoustic spectra (NPR < 2.5). At the 80
o
observation location, long
chevrons with low penetration (P03L18W10 and P03L18W06) have little impact on the acoustic radiation. Short
chevrons with high penetration (P06L08W10 and P06L08W06) decrease low frequency noise and increase high
frequency noise over that of the baseline average. Comparable low frequency noise reduction was not observed for
the higher operating conditions (setpoints 44103 and 44543). Additionally, the spectral peak shifts (relative to the
baseline nozzle) associated with some of the chevrons shown in Fig. 7 (a) are much greater than those occurring at
setpoints 44103 and 44543. Near the peak jet-noise angle [see Fig. 7(b)], most chevrons produced lower acoustic
levels than the baseline average at all frequencies with the lowest peak levels (6 dB below the baseline average)
occurring for the P06L08W10. Unfortunately, P06L08W10 chevron also produced the highest noise levels at 80
o
.
Larger peak noise reductions at the peak jet noise angle were achieved at setpoint 44053 than 44543, a result
somewhat inconsistent with chevron investigations conducted on subsonic jets
8
although the differences in
normalized shear velocity in the current study (see Table 1) are much smaller than those used in the subsonic
experiments.
The effect of operating condition on the resulting noise reduction for the chevron designs with the lowest and
highest penetration, length, and width (P03L08W06 and P06L18W10) are shown in Figs. 8 and 9, respectively.
Results for the P6L08W10 chevron are shown in Fig. 10. The data have been plotted against Strouhal number
calculated from the fully expanded jet velocity. The corresponding normalized shear velocities are given in Table
1. Only the spectra obtained at the peak jet noise angle are compared since the acoustic performance of the chevrons
American Institute of Aeronautics and Astronautics
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at small angles to the jet is different when broadband shock noise dominates the spectra than when it does not.
Additionally, the jet shock cell spacing changes with NPR so the chevron penetration location within the shock cell
will depend on the jet operating condition. Therefore, chevron performance at small and broadside angles to the jet
where broadband shock noise radiates should depend on operating condition. Noise reduction was obtained by
subtracting the chevron spectrum from the average baseline spectrum so positive values indicate lower noise levels
relative to the baseline average. The data indicate that the noise reduction associated with any chevron design is
highly dependent on the jet operating condition although the noise reduction trends for the two highest NPRs
(setpoints 44103 and 44543) are similar. It should not be surprising that chevron performance depends on jet
operating condition since the effective jet diameter, and therefore the actual chevron penetration into the jet, changes
with NPR
21
.
The impact of forward flight on chevron performance is shown in Fig. 11 for the chevrons with the lowest and
highest values of penetration, length, and width (P03L08W06 and P06L18W10). Forward flight has little impact on
chevron noise reduction except for frequencies between 2000 and 7000 Hz at observation angles near the peak jet
noise angle [see Fig. 11(b)]. The results in Fig 11are representative of those obtained for other chevron designs.
The impact of bypass flow on chevron performance was determined by acquiring data with and without the fan-
stream flow. For the no-bypass-flow experiments, the fan stream was shut off and the core-stream pressure was
adjusted back to the specified value, filling the nozzle with core flow as if the nozzle had been mounted to the core
stream duct. The plots in Fig. 12 show a comparison of the noise reduction achieved for the center chevron design
with and without bypass flow. The noise reductions for both conditions are similar at the 80
o
observation location.
Near the peak jet noise angle [see Fig. 12 (b)], the noise reductions for the no-bypass flow condition are slightly
lower than those for the jet operating with bypass flow.
The impact of nozzle area ratio on the resulting noise reduction for the center point chevron is shown in Figs. 13
and 14 for setpoints 44543 and 44103, respectively. For small angles to the jet [see Figs. 13 (a) and 14 (a)] and
frequencies below the broadband shock noise peak, noise reductions for the M
d
= 1.65 nozzle were slightly greater
than those for the M
d
= 1.51 nozzle. For frequencies above the broadband shock noise peak, noise reductions were
nearly the same for both nozzles. In the peak jet noise direction, noise reductions for the M
d
= 1.65 nozzle were
greater than those for the M
d
= 1.51 nozzle at all frequencies. The results of Figs. 13 and 14 indicate that chevrons
applied to a variable area nozzle will not achieve the same noise reduction at all area ratios. The change in chevron
performance with area ratio should not be surprising since the chevron penetration is different for the M
d
= 1.51 and
M
d
= 1.65 nozzles due to differences in the nozzle conical angles and the dependency of the jet diameter on the fully
expanded and design Mach numbers.
B. MDOE Analysis
The intent of the MDOE analysis was to identify the significant chevron parameters and parameter interactions
leading to noise reduction and to develop a chevron design tool for noise prediction codes. Models for the noise
reduction from a chevron with a specified penetration, length, and width were developed through the MDOE
analysis for each one-third octave band for observation angles between 45
o
and 160
o
and the operating conditions
shown in Table 1. To recover absolute noise spectra, predicted or measured spectra for the baseline nozzle can be
combined with the noise reduction models. The modeled absolute spectra presented here were obtained by
subtracting the modeled noise reduction from the average baseline data measured in the experiments.
The eight center-point chevron measurements were used to quantify experimental error. It is assumed that the
error associated with the center point chevron is the same as the error for any configuration tested. The spectra for
the center-point chevron and the average baseline are shown in Fig. 15 for setpoint 44543. The spread in the data
for the 80
o
observation angle is roughly the same for all frequency bands up to a frequency of 50,000 Hz where the
data spread increases. For the 160
o
observation angle, the spread in the experimental data increases slightly with
increasing frequency. An acceptable noise reduction model will agree with the measured data obtained for any
configuration within the experimental error obtained from the center point chevron measurements.
As mentioned previously, the increase in sound pressure levels with increasing frequency above 30,000 Hz does
not occur with the as-measured data but rather is the result of propagating the measured levels back to the one-foot
lossless arc. Since the intent of the current investigation is to produce models to predict far-field noise reduction, the
sound pressure levels in bands above 30,000 Hz will still be modeled because a model that adequately replicates the
spectra at the one-foot lossless arc will recover the as-measured spectra when propagated to the far-field.
Comparisons of the modeled and measured spectra for the chevrons with the lowest and highest penetration,
length, and width (P03L08W06 and P06L18W10) are shown in Fig. 16. The baseline average spectra are also
shown in the figure. The models produce levels close (within experimental error) to the measured levels at both
American Institute of Aeronautics and Astronautics
5
observation angles and in all frequency bands. The results in Fig. 16 are similar to those obtained at other
observation angles and for other edge point chevron configurations.
In addition to quantifying error, the center point chevron measurements are used to identify curvature. If
curvature does not exist, the modeled spectra will agree (within experimental error) with measured spectra for the
center point chevron. While the center point chevron can be used to identify curvature, quantifying curvature
requires testing additional chevron configurations and is not a part of the experiments described here. If a model has
curvature, the predicted acoustic spectra for chevron designs falling within the box in Fig. 5 will not agree with
measured data.
The measured and modeled spectra for the center point chevron as well as the baseline average spectra are
shown in Fig. 17. For most one-third octave bands at the 80
o
observation angle, the model produces slightly higher
levels than the measured data indicating curvature. For the peak jet noise direction [see Fig. 17 (b)], the modeled
data falls within the measured data for most one-third octave bands. Curvature was identified in most models
developed for small and broadside angles to the jet.
The model obtained from the MDOE analysis uses the equation
ܴܰ
ଵ
ଷ
ൗ
ൌ ܥܱ
ெ
ܥܱ
כ ܣ ܥܱ
כ ܤ ܥܱ
כ ܥ ܥܱ
כ ܣܤ ܥܱ
כ ܣܥ ܥܱ
כ ܤܥ ܥܱ
כ ܣܤܥ,
where ܴܰ
ଵ
ଷ
ൗ
is the noise reduction in the specified one-third octave band, CO are the coefficients determined from
the MDOE analysis for the term indicated by the subscript, Mean is the average noise reduction obtained from the
eight edge-point chevrons in Fig. 5 (data from the center point chevron is not included in the average), A is the
penetration, B is the length, and C is the width. The equation uses coded (normalized) values for A, B, and C which
means that the lowest value for each variable (column two in Table 2) is equal to -1 and the highest value for each
variable (column three in Table 2) has a value of 1. The values for A, B, and C are equal to 0 for the center point
chevron. The coded variables for each chevron configuration are shown in Table 3. In general, only terms shown
by the MDOE analysis to have a 94% (or greater) probability of effecting the response (noise reduction within the
one-third octave band) are included in the final model. The inclusion of interaction terms (AB, AC, BC, ABC)
indicates that the effect one variable on NR
1/3
depends on the level of the other variable so the inclusion of the AC
term indicates that the effect of A on the noise reduction is different for a high level of C (1) than for a low level of
C (-1). The lack of quadratic terms in the equation prevents quantifying curvature.
Plots of the coefficients obtained from the MDOE analysis at setpoint of 44543 and an observation angle equal to
80
o
are shown in Fig. 18. Also shown in the figure are piecewise curve fits for each coefficient. The different
segments used in the curve fits can be determined from the plot legends. Caution should be used when applying the
models to chevron designs within the box in Fig. 5 since curvature is present for most frequency bands. The
frequency band for the baseline spectral peak (3162 Hz) is labeled in the figure. The mean is positive for all
frequency bands below the baseline spectral peak frequency (the broadband shock noise peak frequency) indicating
that the center point chevron reduces noise (positive values of noise reduction) in these bands. The coefficients for
the penetration and width (C0
A
and C0
C
) are positive indicating that increasing the values of penetration and width
above those used for the center point chevron will increase noise reduction over that of center point chevron since A
and C will be positive. For frequencies above the baseline spectral peak frequency band, the mean is negative
indicating the center point chevron increases noise over that of the baseline average (negative noise reduction) and
the coefficients for the penetration and width (C0
A
and C0
C
) are also negative so further increases in the values of A
and C (penetration and width) will increase noise. The parameter having the largest impact on noise reduction is the
penetration. Significant parameter interactions are also present in the models [see Fig. 18 (b)].
A plot of the coefficients and piecewise curve fits for setpoint 44543 and an observation angle equal to 160
o
are
shown in Fig. 19. The only significant interaction identified in the analysis was AC (penetration and width). For all
frequencies, the mean is positive indicating that the center point chevron reduces noise over that of the baseline
average (positive noise reduction). In all frequency bands, the coefficients for penetration (CO
A
) and width (CO
C
)
are positive indicating that increasing the values of penetration and width (A and C are positive) increase noise
reduction. Since the length coefficient (CO
B
) is negative, increasing chevron length decreases noise reduction. The
parameter having the largest impact on noise reduction is penetration. The interaction term (CO
AC
) slightly impacts
the acoustic radiation at frequencies near 10,000 Hz.
Plots of the measured and modeled (from the curve fits in Figs. 18 and 19) spectra are shown in Fig. 20 for the
P03L08W06 and P06L18W10 chevrons at setpoint 44543. Also shown in the figure are the average baseline data.
The spectra obtained from the curve fits agree (within experimental error) with the measured data for both chevrons.
The results shown in Fig. 20 are representative of those obtained for other edge point chevron configurations used in
the experiments. The curve fit coefficients are given in Table 4. The values for f in the equations are the one-third
octave band center frequencies in the frequency ranges indicated at the top of columns two and three. The selection
