2D-3
9
June 30 - July 3, 2015 Melbourne, Australia
AN INVESTIGATION OF SONIC & SUPERSONIC AXISYMMETRIC
JETS: CORRELATIONS BETWEEN FLOW PHYSICS AND FAR-FIELD
NOISE
Andrew S. Magstadt, Matthew G. Berry, Zachary P. Berger, Patrick R. Shea, and Mark N. Glauser
Dept. of Mechanical & Aerospace Engineering
Syracuse University
Syracuse, NY 13244
asmagsta@syr.edu, mgberry@syr.edu, zpberger@syr.edu, prshea@syr.edu, mglauser@syr.edu
Christopher J. Ruscher, Sivaram Gogineni
Spectral Energies, LLC.
Dayton, OH 45431
christopher.ruscher.ctr@us.af.mil, sgogineni@spectralenergies.com
ABSTRACT
flow features in a cold, axisymmetric convergent jet; in particular, sonic and supersonic flows are investigated to further recognize differences in noise generation associated
with shocks. Particle imaging velocimetry (PIV) is simultaneously sampled with far-field pressures to allow for rigorous analyses. Reduced-order modeling (e.g. POD) of the
jet plume in the streamwise plane (complementing work by
Caraballo et al. (2003)), directivity and magnitude calculations of acoustic radiation, and correlations between the two
measurements are carried out. Flow physics are then related
to far-field noise signatures. Previously, subsonic test campaigns at Syracuse University’s Skytop Turbulence Laboratory by Low et al. (2013) and Berger et al. (2014) have presented evidence correlating deterministic spatial structures
in the near-field flow with far-field noise. At present, data
sets containing ideally and underexpanded jets (M j = 1.0 &
M j = 1.1) are presented to similarly locate noise generation
mechanisms.
An axisymmetric convergent jet is studied at ideal and
underexpanded conditions using velocity and acoustic data.
Time-resolved and large-window PIV capture near-field velocities and are simultaneously sampled with far-field microphones. POD is used to extract modes representative
of physical processes in the flow. Specifically, screechcontaining and turbulent mixing modes are isolated in the
supersonic case. The decoupled velocity fields are then correlated with acoustic data to identify modes related to specific noise spectra. Finally, selective flow reconstruction is
carried out to reduce flow features associated with an imperfectly expanded jet.
INTRODUCTION
Understanding and reducing jet noise are difficult problems due to the inevitable turbulence encountered. The
aerospace industry continues to invest considerable effort
into mitigating jet noise as it creates unwanted acoustic pollution near airports, generates negative health consequences
to flight deck crews, and compromises the stealth of military
aircraft. Today, supersonic flight is becoming a standard for
military aircraft and is being revisited for commercial applications. Furthering the understanding of turbulence in
supersonic flow is a critical step towards noise source identification and suppression for future aircraft.
While research in the area of aeroacoustics has progressed considerably since its introduction, Tam (1998), engine technologies are advancing at increasing rates, which
push aircraft to greater speeds. Advanced designs utilize
exotic nozzle and flow configurations to increase performance and abate noise generation in supersonic jets, Henderson et al. (2012). However, many of the heuristic solutions employed to date have been guided by partially anecdotal evidence, leaving incomplete understanding of the
fluid mechanics involved. Prior to studying such configurations, the axisymmetric nozzle is revisited to interpret
shock-turbulence interactions as anticipated in future designs. This prompted an investigation of supersonic noise
generation in Syracuse University’s anechoic chamber.
Current research is focused on identifying important
EXPERIMENTAL SETUP
The experimental results were acquired in the Skytop
Turbulence Laboratory at Syracuse University. The 206 m3
anechoic chamber is acoustically treated with fiberglass
wedges, achieving a cutoff frequency of 150 Hz. Within
the chamber is an axisymmetric 5th -order-polynomial convergent nozzle (Md = 1.0) with a diameter of D = 50.8mm,
described by Tinney et al. (2004). For the M j = 1.0 and
M j = 1.1 test cases discussed below, Re = 1.1 · 106 and
Re = 1.2 · 106 , respectively, are sustained. The anechoic
chamber and jet can be seen in Figure 1.
Particle Image Velocimetry
Near-field velocity measurements were acquired using
two different PIV setups. A time-resolved PIV (TRPIV)
system was used to gather the M j = 1.0 data. This system
was unavailable when the M j = 1.1 test campaign was underway, thus large-window PIV (LWPIV) was utilized to
capture data for the supersonic case.
The TRPIV system operates a 10 kHz Quantronix
Hawk-Duo Nd:YAG laser. In combination with a Photron
1
Table 1.
FASTCAM CCD, two-component velocity measurements
were taken along the jet centerline (i.e. the r − z plane) in
approximately 1.5 x 1.5 diameter separate windows. Samples were acquired from (z/D = 0) to (z/D = 7.8) downstream with 0.5 diameter overlap. The LWPIV utilized
a standard 4 Hz New Wave Nd:YAG Gemini laser that
triggered three Dantec HiSense cameras simultaneously.
The laser sheet and cameras were oriented to take twocomponent measurements along the centerline of the jet
axis. Each camera’s field of view slightly overlapped the
neighboring one’s to ensure appropriate merging of velocity vectors. Using a least squares algorithm as described
in Shea et al. (2014), the PIV images were stitched together to achieve a single streamwise velocity window from
2.5 < z/D < 9.4 and −1.0 < r/D < 1.0.
Proper Orthogonal Decomposition (POD) is a method
for decomposing a flow into its energetic building blocks
first introduced by Lumley (1967). Sirovich (1987) made
the POD method more tractable for data with large spatial
resolution, such as PIV, and is the method used in this paper.
(n)
The decomposition give spatial modes, φi (⃗x), and temporal coefficient, an (t), which allow the reconstruction of the
flow using
N
(n)
∑ an (t)φi
(⃗x).
Mj
fPIV
NPIV
fMic
NMic
1.0
10 kHz
8623
40 kHz
4x105
1.1
4 Hz
2500
25 kHz
2.5x107
With the time-varying component of the modal decomposition calculated, an (t), cross-correlations can be
computed to relate the simultaneously sampled far-field
noisePi (t) to each spatial mode. This is accomplished by
creating a range of time lags, τ , around the average acoustic
propagation time (approximately 10 ms) and generating a
correlation matrix for each time lag, microphone, and mode
number. The maximum correlation values in each time lag
series are then extracted for relation to flow physics.
Figure 1. Anechoic chamber showing far-field microphone array (left), near-field pressure ring and PIV instrumentation (center), and axisymmetric jet (right).
ui (⃗x,t) =
Data acquisition parameters.
RESULTS
Ideally Expanded Jet
The data from the M j = 1.0 case was originally reported by Berger et al. (2012). Here, important results are
summarized. Averaged velocities from four (of seven) camera locations are shown in Figure 2. Since the data are not
phase-locked, a merged instantaneous flow-field is not possible. Initial analyses were thus focused on the velocity
fields from individual camera locations.
1
r/D
0.5
0
−0.5
−1
0
1
2
3
4
x/D
5
6
7
8
Figure 2. Ensemble average of time-resolved data from
four separate camera locations. An additional three locations were taken, to give overlap of each flow-field.
(1)
n=1
Far-field Acoustics
Far-field acoustics were simultaneously sampled with
each PIV setup. The setup uses two arrays of six G.R.A.S.
free-field condenser microphones positioned in an arc,
(z/D = 75) away from the nozzle lip. One arc of six microphones is located in-plane with the jet (as shown in Figure
1), while the second arc is positioned approximately one
meter above, angled down at 15°. The microphones are
spaced in 15°increments from 90°to 165°with respect to the
jet axis, where the jet axis, +z, corresponds to 180°.
National Instruments’ PXI and SCXI systems were
used for synchronization and acoustic data acquisition.
Upon test initialization, PIV triggers were sampled and used
to match the appropriate acoustic signatures for data analysis. The number and frequencies of PIV snapshots and
microphone samples (found in Table 1) were determined by
hardware restrictions and run times. TRPIV experiments
were limited to less than one second (due to bandwidth limitations from the large amount of data acquired), while the
LWPIV setup allowed for much longer simultaneous acoustic sampling. TRPIV offers great temporal resolution, but
sacrifices the field of view due to large laser power requirements. LWPIV can capture a much greater interrogation region, but does not contain useful temporal information for
this flow.
The final camera location of the TRPIV setup, 6 <
z/D < 7.8, is selected to investigate since much evidence
has been found to suggest a major source of noise is near
the collapse of the potential core (e.g. Seiner (1998) and
Hall (2008)). Snapshot POD is applied as a reduced-order
model. The resulting streamwise POD modes are shown in
Figure 3. These first 18 modes possess 45 % of the data’s
energy. Modes 1 & 2 contain large structures, indicative of
the greatest coherent structures. As the subsequent less energetic modes are examined, the structures begin to breakdown. The symmetric modes (i.e. 3-6) are likely associated
with column modes in the jet (m = 0 in the r − θ plane). The
even less dynamical modes lose symmetry and the smaller
structures become more poorly organized (e.g. 9-14), presumably capturing the collapsing mixing layers which introduce further turbulence in the center of jet. Thus, it is
believed that these higher modes are responsible for much
of the acoustic radiation propagated to the far field.
Far-field data are next consulted. Spectral content are
not of particular interest for the M j = 1.0 case, but may be
found in the report by Berger et al. (2012). Typical acoustic signatures were observed, with turbulent mixing being
the prime source of noise and spatially-varying magnitudes
2
0.2
2
u
φ
0.15
0
−0.5
4
5
u
0.5 φu
6
u
φ
a (t),P
o
a (t),P
o
a (t),P
o
a (t),P
o
10
3
u
φ
Correlation Coefficient, ρ
1
0.5 φu
φ
0
−0.5
12
15
0.1
16
165
165
165
165
0.05
0
−0.05
7
8
u
0.5 φu
9
u
φ
φ
0
−0.1
r/D
−0.5
8
10
12
14
τ (ms)
10
11
u
0.5 φu
Figure 4.
12
u
φ
φ
Loud modes at the 165°microphone.
0
underexpanded jets. The jet is then further analyzed via a
reduced order model.
−0.5
13
14
u
0.5 φu
15
u
φ
φ
1
r/D
0
−0.5
0
a)
-1
16
17
u
0.5 φu
18
u
φ
φ
0.5
r/D
0
−0.5
0
-0.5
7
6
7
6
7
|U|CL (m/s)
6
b)
z/D
Figure 3. First spatial modes of the M j = 1.0 data, taken
near the collapse of the PC.
obeying refraction Atvars et al. (1965). However, the timevarying pressure signals were used to compute correlations.
As discussed in the Experimental Setup section, correlations can be computed to draw conclusions between the spatial functions and far-field acoustics. Calculations of such
yielded significance between a select few modes and the
165°microphone, shown in Figure 4. Specifically, modes
15 & 16 are found to have the greatest correlations, consistent with the findings of Berger et al. (2012). The isolation
and control of these ”loud” modes is then used in attempts
to reduce the noise. No other outstanding correlations were
found at other microphones.
350
325
300
LPC = 7.12
3
4
5
6
z/D
c)
7
8
9
Figure 5. Streamwise velocity component of the M j = 1.1
jet. Separate instantaneous flow-fields (a) are merged and
averaged (b), and the centerline velocity is then extracted (c)
to illustrate shock cells and define the potential core length.
POD is again implemented and the velocity is decomposed into basis functions. The most energetic of these spatial modes are found in Figure 6. Some distinct features
of the jet are highlighted in these spatial modes, and they
are classified into three main groups based on specific energy content and shape. The lowest modes (1-3) exhibit
large-scale structures near the collapse of the potential core,
modes 6-9 possess strong streamwise oscillations within the
supersonic core, and the higher modes (i.e. 11-14 & 17-20)
contain smaller organized structures embedded in the mixing layers. Each group is believed to be associated with a
particular physical feature of underexpanded flow. Modes
Underexpanded Jet
The multiple-camera setup of the LWPIV captures
phase-locked velocity data at three separate location and allows the merging of instantaneous vector fields. Figure 5
shows a snapshot of the jet’s streamwise instantaneous (a),
mean (b), and centerline (c) velocities. Fluctuating mean
velocities indicate the existence of shock cells typical of
3
noise generation through the oscillation of the jet and unsteady entrainment. Both theories offer reasonable explanations.
Regions of compression and decompression are
thought to be associated with the shock cell-like modes
6-9. Fluctuating velocities contained within the potential core are apparently tied to axisymmetric structures in
the shear layer, likely vortex rings. Dominant wavenumbers are calculated in the shear layer and potential core as
ν = 18.6m−1 . Based on a local wavespeed of (c − uconv ),
where uconv is taken in the shear layer to be 114m/s, these
lead to an average frequency of 4550 Hz. As will be seen,
this is close to the fundamental screech frequency. Additionally, the vortex rings are almost exactly 180°out of
phase with the potential core fluctuations, suggesting that
the vortices are driven by their adjacent downstream shock.
These interactions at least partially illustrate the feedback
mechanism responsible for screech tones Tam (1995). The
slower-convecting shear layer acts as a waveguide and allows Mach wave radiation at specific frequencies, generated from vortex-shock interactions, to propagate upstream
to the nozzle lip.
Finally, the mixing layer modes (n > 10) capture
smaller eddies. Specific spatial functions qualitatively
match well with the lower modes of subsonic jets Berger
(2014), and are believed to be associated with turbulent
mixing noise as in the M j = 1.0 case. More evidence is
sought to reinforce the relations to noise production, hence
the far-field noise data are next considered.
The acoustic spectra of the M j = 1.1 are presented in
Figure 7 as contours in polar coordinates. Sound pressure
levels (SPLs) are plotted as a function of Strouhal number
fD
(St = U
) and microphone angle relative to the jet. Suj
personic noise is well documented, see Tam (1995), and
the results found here are consistent with previous findings.
Narrow bands of intense SPLs (e.g. St ∼ 0.6) are identified as screech tones ( fs0 = 4545Hz & fs1 = 9101Hz), the
peak from 0 < St < 0.3 and directed towards the shallow
microphones is characteristic of turbulent mixing, and the
weak gradients from 150°to 120°extending across a range
of St are considered to be associated with broadband shockassociated noise (BBSAN). For this jet, the BBSAN is weak
and thus does not show up strongly in the spectra.
As with the M j = 1.0 data, correlation coefficients are
computed for each microphone, POD mode, and time lag.
In contrast to the sonic case though, the underexpanded jet
has significant correlations at multiple microphones. To display the multidimensional data, the maximum values of the
correlations are plotted in Figure 8. The orientation is the
same as the frequency spectra presented in Figure 7, with
the radial coordinate exchanged for the normalized crosscorrelation coefficient.
Figure 8 demonstrates the directional dependence of
the most highly connected velocity-acoustic correlations. A
threshold of ρ > 3σ was chosen as the minimum value
of significance, where σ is the standard deviation of the
maximum correlation coefficients. Comparing Figures 6,
7, and 8, one can immediately see which modes overlap
particular noise signatures. The high correlation coefficients of the shock-containing modes (6-9) align with the
screech tone propagation to the microphones at 90°, 105°,
and 165°. While the fundamental screech frequency is
greater at the shallower angle, the presence of the 1st at the
90°and 105°microphones apparently results in higher correlations. This provides additional evidence that modes (6-9)
r/D
15 & 16 appear to capture smaller events at the collapse
of the potential core. The unmentioned eigenfunctions are
to thought to be transitional states and may or may not be
mathematical constructs necessary to satisfy the equations.
2
u
1
u
1
0
−1
φ
φ
1
0
−1
φ3
u
φ4
1
0
−1
φ
5
u
φ
1
0
−1
1
0
−1
φ
7
u
φ
9
u
φ
1
0
−1
φ
11
u
φ
1
0
−1
φ
13
u
φ
1
0
−1
φ15
u
φ16
1
0
−1
φ
17
u
φ
1
0
−1
φ
19
u
φ
u
6
u
8
u
10
u
φ
3
Figure 6.
5
12
u
14
u
u
18
u
20
u
7
9 3
z/D
5
7
9
First spatial modes of the M j = 1.1 data.
The first modes of Figure 6 are now discussed in detail. Near the collapse of the potential core, vortices breakdown (from mode 1 → 2), a wave-like feature is found
and the vortices increase in size (mode 3), followed by further vortex breakdown (mode 3 → 5). The enlarged length
scale found in mode 3 is atypical, as structures in isotropic
homogeneous turbulence should be less energetic with decreasing size. Many jet flow models have been nominated
over the years to describe large-scale structure, but two particular theories match well the results here. Bishop et al.
(1971) found experimental evidence of large-scale eddies,
i.e. larger than the width of the shear layer, oscillating near
the collapse of the potential core in a manner similar to
instabilities found in laminar flow. A separate model proposed by Tam (1972) suggests helical instabilities of the jet
structure resonate with the shock disturbances, resulting in
4
1.8
o
90
flow structure and noise generation. To make such a comparison, the LWPIV data must be truncated and interpolated
to match the spatial locations of the TRPIV data before executing POD. This is done on the flow field, and the principal
modes are then compared via a spatial cross-correlation coefficient between the LWPIV and truncated LWPIV. These
data are omitted for brevity, but the large-scale structure are,
not surprisingly, lost in the operation of truncation. The
higher modes of the LWPIV, however, correlate to the lower
modes of the truncated data (e.g. modes 23 and 10), consistent with the window dependent relations found by Shea
et al. (2014) and Berry et al. (2015). Screech modes’ (69) correlation to the far-field noise are entirely lost due to
the truncation process at this location, but turbulent mixing remain. These newly computed eigenfunctions are then
compared to the M j = 1.0 jet.
o
Mic Angle ( )
o
105
1.6
120o
1.4
o
135
1.2
St
1
150o
0.8
0.6
165
0.4
o
0.2
o
0
180
0
0.5
1
1.5
25
St
Figure 7. Frequency and directional dependence of SPLs
for M j = 1.1. The max intensity is approximately 80dB/Hz.
90o
o
105
φi,u (~x), M = 1.1
0.5
20
a (t), Pi (t +
o τ)
Mic6 Angle
( )
a7 (t), Pi (t + τ)
Correlation Coefficient, ρ
120o a (t), P (t + τ)
8
i
0.4
a9 (t), Poi (t + τ)
135
a15 (t), Pi (t + τ)
0.3
a16 (t), Pi (t + τ)
o
a18 (t), Pi (t150
+ τ)
0.2
a23 (t), Pi (t + τ)
15
10
5
5
165
o
0.1
0
180
0
0.1
0.2
0.3
0.4
Correlation Coefficient, ρ
10
15
20
25
φi,u (~x), M = 1.0
Figure 9. Spatial correlation between the first modes of
M j = 1.0 and the truncated M j = 1.1 data at 6 < z/D <
7.8. Contours range from no correlation (white) to highly
correlated (dark red).
o
0.5
Figure 8. Directional dependence of the maximum
velocity-acoustic correlations for M j = 1.1.
Figure 9 demonstrates the similarity of the lowest
modes. The spatial mode switching observed also matches
the recomputed velocity-acoustic correlations. Mode 10
of the M j = 1.1 coincides spatially well with mode 12 of
M j = 1.0, and both show significant correlations to the microphone at 165°. Similarly, modes 12 & 14 interchange,
15 remains the same, and 17 & 16 reciprocate. Each has
a far-field correlation coefficient, ⟨an (t), Pi (t + τ )⟩, close to
that of its partner. This suggests similar events are recurrent
across the two different Mach numbers and are captured by
unique POD modes. Some further, qualitative, verification
is found through the reconstruction of the velocity fields.
By removing the screech-containing modes, the remaining modes (shown to be highly spatially-correlated
to the sonic case) ought to reproduce a flow-field similar
to the M j = 1.0 jet. Figure 10 shows instantaneous flow
fields from the M j = 1.0 case using reconstructed TPRIV
data, (a), and the M j = 1.1 data as produced from selective
reconstruction of the LWPIV (b), where modes 6-9 have
been omitted. The TRPIV data uses velocity information
from seven different cameras and merges the fields together
through a POD modal basis, discussed in a paper by Berger
correspond to screech production. The angles where turbulent mixing noise exist (i.e. 150°and 165°) also have high
correlations to the lower energy modes (n = 15, 16, 18 and
23), associated with the collapse of the potential core. This
evidence is in good agreement with countless research on
subsonic axisymmetric jets, where turbulent mixing is the
primary component of noise generation and propagates into
the cone of coherence, Atvars et al. (1965) and Tam (1998).
Though not presented, data collected from a second microphone array (positioned above the one shown in Figure 1)
are consistent with the current results. Regions of higher
and lower acoustic patterns in the offset array result in the
expected change in correlation coefficients.
Similarities across Mach numbers
Comparison between the two cases is difficult due to
differences in instrumentation used, as discussed by Berry
et al. (2015). However, some similarities are expected in
5
a)
0.5
0
-0.5
1
2
r/D
0
3
4
5
6
REFERENCES
7
Atvars, J, Schubert, LK, Grande, E & Ribner, HS 1965 Refraction of sound by jet flow or jet temperature. Institute
for Aerospace Studies, University of Toronto.
Berger, Z.P., Berry, M.G., Shea, P.R., Glauser, M.N., Jiang,
N., Noack, B.R., Gogineni, S., Kaiser, E. & Spohn, A.
2014 Analysis of high speed jet flow physics with timeresolved piv. 52nd AIAA Aerospace Sciences Meeting
(1226).
Berger, Z.P., Low, K.R., Kostka, S., Gogineni, S. & Glauser,
M.N. 2012 Investigation of an axisymmetric transonic jet
with high resolution time-resolved piv. 48th AIAA Joint
Propulsion Conference (3822).
Berger, Zachary P 2014 The effects of active flow control on
high-speed jet flow physics and noise. PhD thesis, Syracuse University.
Berry, M. G., Magstadt, A. S., Berger, Z. P., Shea, P. R.,
Glauser, M. N., Ruscher, C. J. & Gogineni, S. P. 2015
Comparison of spatial and temporal resolution on high
speed axisymmetric jets. 53rd AIAA Aerospace Sciences
Meeting .
Bishop, K A, Williams, Ffowcs & Smith, W 1971 On the
noise sources of the unsuppressed high-speed jet. Journal of Fluid Mechanics .
Caraballo, E., Samimy, M. & Scott, J. 2003 Application
of proper orthogonal decomposition to a supersonic axisymmetric jet. AIAA Journal .
Hall, A. M. 2008 An experimental investigation of lowdimensional techniques for large scale noise source characterization in a heated jet. Ph.D. dissertation, Syracuse
University .
Henderson, B., Bridges, J. & Wernet, M. 2012 Jet noise reduction potential from emerging variable cycle technologies. 48th AIAA Joint Propulsion Conference .
Low, K.R., Berger, Z.P., Kostka, S., El Hadidi, B., Gogineni, S. & Glauser, M. 2013 A low-dimensional approach to closed-loop control of a mach 0.6 jet. Experiments in Fluids pp. 1–17.
Lumley, J. L. 1967 The structure of inhomogeneous turbulent flows. Atm. Turb. and Radio Wave Prop. ed. by A.M.
Yaglom and V. I. Tatarsky, (Nauka, Moscow) pp. 166–
178.
Seiner, J. M. 1998 A new rational approach to jet noise reduction. Theoretical and Computational Fluid Dynamics
10 (1-4), 373–383.
Shea, P.R., Berger, Z.P., Berry, M.G., Gogineni, S. &
Glauser, M.N. 2014 Low-dimensional modeling of a
mach 0.6 axisymmetric jet. 52nd AIAA Aerospace Sciences Meeting (0245).
Sirovich, L. 1987 Turbulence and the dynamics of coherent
structures, part i,ii, and iii. Quarterly Applied Mathematics 45.
Tam, C. K. 1972 On the noise of a nearly ideally expanded
supersonic jet. Journal of Fluid Mechanics 51, 69–95.
Tam, C. K. 1995 Supersonic jet noise. Annu Rev of Fluid
Mech .
Tam, C. K. 1998 Jet noise: Since 1952. Theoretical and
Computational Fluid Dynamics 10 (1-4), 393–405.
Tinney, C. E., Hall, A. M., Glauser, M. N.and Ukeiley, L. S.
& Coughlin, T. 2004 Designing an anechoic chamber for
the experimental study of high speed heated jets. 42nd
AIAA Aerospace Sciences Meeting and Exhibit (0010).
b)
0.5
0
-0.5
3
4
5
6
7
8
9
z/D
Figure 10. Reconstruction of fluctuating velocities for
snapshots of (a) M j = 1.0 from TRPIV data and (b) M j =
1.1 from LWPIV data with the shock modes omitted.
et al. (2014). The chart used, (a), is borrowed from this
work. Identical matching would be lucky given the nature
of turbulence, yet similarities between the two data sets do
exist such as activity near the potential core. Most importantly, shock-related features of the underexpanded jet are
almost entirely absent. Vortices clustered around the collapse of the potential core and located in the shear layer are
essentially all that remain, akin to a sonic or subsonic jet.
CONCLUSIONS
POD and velocity-acoustic correlations have been carried out on data taken from an axisymmetric jet operating at ideal and underexpanded conditions. Specific POD
modes were found to contain important physics of the problem. Specifically the large-scale structure of the jet, shockrelated fluctuations, and turbulent mixing regions of the
flow were isolated through POD in the supersonic case. By
computing cross correlations, particular modes were found
related to noise spectra. Strong evidence links modes 69 to screech production. Velocity-acoustic correlations associate these modes with the tonal patterns, and the spatial analysis suggests that vortex-shock interactions produce
Mach waves which can propagate upstream through the
shear layer at screech frequencies. Additionally, turbulent
mixing noise was isolated. By comparing to the sonic case,
where turbulent mixing is the sole source of noise, similar
mode shapes were found across both Mach numbers.
The distinct features of supersonic flow create an opportunity to classify particular sources of acoustic spectra
through reduced-order models. For example, POD modes
15 and 16 of the TRPIV and truncated LWPIV data sets
presented herein appear to represent structures indicative
of noisy turbulent flow events. These occur near the collapse of the potential core, yet the cause of such events may
be elsewhere in the flow. Time-resolved data allows one
to watch the evolution of the flow and identify a particular event. The large-window can then be looked at using
similarities between POD modes to learn more about the
flow and ascertain the behavior of the more energetic modes
which may influence the loud modes. Insight into screech
production is believed to have increased, but the cause for
noisy turbulent events remains under investigation.
ACKNOWLEDGMENTS
Thanks are given to Spectral Energies, LLC. and
AFRL, with Dr. Barry Kiel as project monitor, for the
continued support in this research.
6