Flow and Acoustics of Jets from Practical Nozzles for …munday/pubs/Munday_Dissertation.pdfFlow and...
181
Transcript of Flow and Acoustics of Jets from Practical Nozzles for …munday/pubs/Munday_Dissertation.pdfFlow and...
Flow and Acoustics of Jets from Practical Nozzles for High-
Performance Military Aircraft
A dissertation submitted to the
Graduate School of the University of Cincinnati
in partial fulfillment of the
requirements for the degree of
Doctor of Philosophy
in the Department of Aerospace Engineering and Engineering Mechanics
of the College Engineering and Applied Science
2010
by
David Munday
B.S. Mathematics, Northern Kentucky University, 1988
B.A. Physics, Computer Science and History, Northern Kentucky University, 1991
M.A. American History, Miami University, 1999
Dipl. Aeronautics and Aerospace, von Karman Institute for Fluid Dynamics, 2003
Dissertation Committee:
Dr. Ephraim Gutmark, Chair
Dr. Shaaban Abdallah
Dr. Paul Orkwis
Dr. James Bridges
Dr. Kailas Kailasanath
iii
Abstract
This research project examines supersonic jets from nozzles representative of the practical
variable-geometry convergent-divergent nozzles used on high-performance military aircraft. The nozzles
employed have conical convergent sections, sharp throats and conical divergent sections. Nozzles with
design Mach numbers of 1.3, 1.5, 1.56 and 1.65 are tested and the flow and acoustics examined. Such
nozzles are found to produce a double-diamond shock structure consisting of two overlapping sets of
shock cells, one cast from the nozzle lip and one cast from the nozzle throat. These nozzles are found to
produce no shock-free condition at or near the design condition. As a result they produce shock-
associated noise at all supersonic conditions. The shock cell spacing, broad-band shock-associated noise
peak frequency and screech frequency all match those of more traditional nearly isentropic convergent-
divergent nozzles.
A correlation is proposed which improves upon the Prandtl-Pack relation for shock cell spacing in
that it accounts for differences in nozzle design Mach number which the Prandtl-Pack relation does not.
This proposed relation reverts to the Prandtl-Pack equation for the case of a design Mach number of 1.0.
Chevrons are applied to the nozzles with design Mach numbers of 1.5 and 1.56. The effective
penetration of the chevrons is found to be a function of the jet Mach number. Increasing jet Mach number
increases effective penetration of the chevrons and increases the magnitude of all chevron effects.
Chevrons on supersonic jets are found to reduce shock cell length, increase mixing and spreading,
decrease turbulent kinetic energy at the end of the potential core and increase it near the nozzle.
Chevrons corrugate the shear layer but not the shock structures inside the jet which remain axisymmetric.
Chevrons thicken the shear layer, reducing the sonic diameter and reducing the diameter of the shock
cells. By reducing their diameter they also reduce the shock cell spacing. Chevrons reduce low-
frequency mixing noise near the end of the potential core, increase high-frequency noise near the nozzle
exit. They eliminate screech and reduce broad-band shock-associated noise and shift it to higher
frequencies.
iv
Fluidic injection is applied to the nozzle with design Mach number of 1.5. Fluidic injection
corrugates the shear layer, increases mixing and spreading, reduces low frequency mixing noise, increases
high frequency noise, reduces broad-band shock-associated noise and shifts its peak to higher frequency.
v
Copyright © 2010 by David Munday
vi
Acknowledgements
This work was sponsored two organizations under two programs. The first sponsor is the
Strategic Environmental Research and Development Program (SERDP) under project WP-1584,
―Mechanical Chevrons and Fluidics for Advanced Military Aircraft Noise Reduction‖ for which Kailas
Kailasanath was the project leader as well as a collaborator.
For this project our team collaborated with a numerical group at the Naval Research Laboratory
(NRL) who supplied numerous detailed simulations matching the experiments performed at UC. Results
of both experiment and simulation were regularly and fruitfully discussed with Kailas Kailasanath and
Jun-Hui Liu from NRL. Steve Martens of GE Global Research guided this project in ensuring that the
models and test conditions used corresponded to those in actual use in full-scale aircraft.
The second sponsor was the Swedish Försvarets materielverk (FMV) as joint project 311956-A1
722654 ―Active suppression of jet engine noise‖ under the direction of Erik Prisell. In this project our
team collaborated with a numerical group at Chalmers Technical University (CTH) where Lars-Erik
Eriksson and Markus Burak performed the matching simulations. Likewise with this project relied for its
success on discussions among all collaborators. Bernhard Gustafsson of Volvo Aero Corporation
provided technical guidance in the design of the nozzle and the determination of test conditions.
While completing this work I received additional support from the Jacob D. & Lillian Rindsberg
Fellowship program, which supplied additional stipend and a travel budget to expand the number of
opportunities to present this work at professional conferences and receive valuable feedback from the
broader community of aeroacousticians and fluid mechanics.
Russell DiMicco provided invaluable help in designing apparatus, preparing drawings and
overseeing the production of components by outside vendors. In addition he supports all the
instrumentation in the lab and ―makes the trains run on time.‖ Chief among our outside fabricators is Blue
Chip Tool, where Bill Riehle was a cooperative and creative partner in expanding the complexity of
vii
shapes they could make, particularly in the case of the chevron nozzles and plenums. For items fabricated
in-house, Doug Hurd provided patient instruction and guidance in making the odd bits that were needed.
Mihai Mihaescu aided greatly in my understanding of what is and is not possible with numerical
simulations. Curtis Fox was always helpful with trouble shooting Labview® codes. Jeff Kastner was of
constant assistance in issues of instrumentation setup and data analysis. Nick Heeb and Michael Perrino
worked closely with me on both SERDP and FMV projects and will carry these projects on after I leave.
Dan Cuppoletti, Seth Harrison, Andrew Regent, and Romain Girousse all provided help in running
experiments.
I would like to thank the members of my dissertation committee: Shaaban Abdallah and Paul
Orkwis of the University of Cincinnati; James Bridges of the NASA Glenn Research Center and Kailas
Kailasanath of the Naval Research Laboratory. I especially thank Ephraim Gutmark, my Ph.D.
dissertation and research advisor for putting me on this path and guiding me along it to a successful
conclusion.
Lastly, none of this would have been possible without my family, Joanne and Victor Abitabilo.
Their daily encouragement and loving support kept me going daily. Their sacrifice and forbearance
enabled me to concentrate my efforts to complete this endeavor.
viii
Table of Contents
List of Tables………….……………………………….……………...……………………………. x
List of Figures………….………………...…………………….…………………………………… xi
List of Symbols………….………………………………...…………….………………………..… xvi
Chapter 1—Introduction………....................…………………………………….…………..…….. 1
1.1 The Problem…………………………………………………………………………… 1
1.2 Project Structure……………………………………………………………………..… 6
Chapter 2 – Background…………………………….……………………………………………… 9
2.1 Supersonic Nozzles…………………………….…………………………………….… 9
2.2 Supersonic Jets Past the nozzle………………………….…………………………...… 11
2.3 Shock Cells……………………………………………………….……………………. 12
2.4 Large Scale Coherent Structures in the Shear Layer…………………….…………….. 13
2.5 Jet Noise from Supersonic Jets………………………………………………….……... 15
2.6 Mixing Noise……………………………….………………………………………….. 25
2.7 Chevrons… ………………………………………….………………………………… 29
2.8 Fluidic Injection……………………………………………….………………………. 32
Chapter 3 – Methodology………………………………………………………….……………….. 36
3.1 Models………………………………………………………………………….……… 36
3.1.1 Baseline Nozzles………………………….…………………………………. 36
3.1.2 Chevron Nozzles………………………………….…………………………. 38
3.1.3 Fluidic Chevron Nozzle Configurations………………….…………………. 40
3.2 Experimental Facility………………………………………………………….……….. 42
3.3 Instrumentation……………………………………………………...…………………. 43
3.3.1 Far-field Acoustic Measurement……………………….…………………... 43
3.3.2 Near-field Acoustic Measurement……………………………….…………. 46
3.3.3 Shadowgraph………………………….…………………………………….. 48
3.3.4 Particle Image Velocimetry…………………….…………………………… 50
3.3.5 Total Pressure Measurement…………………………….………………….. 56
3.4 Uncertainty Estimation…………………………………………………….…………... 56
3.4.1 Transducer Calibrations………………………………………………….….. 56
3.4.2 Set-point Variation……………………………….………………………….. 60
3.4.3 Repeatability of Acoustic Measurement………………….…………………. 61
3.4.4 Comparison of Acoustic Spectra to Measurements at Other Facilities……... 63
3.4.5 PIV Stokes Number Calculation……………………………………………. 64
3.4.6 PIV Comparison to Pressure Probe Data and LES………………………….. 66
Chapter 4 – Baseline Nozzle Results……………………………………………………………….. 68
4.1 Double Diamonds……………………………………………………………………… 68
4.2 Variation with Set-point……………………………………………………………….. 74
4.3 Shock Cell Spacing…………………………………………………………………….. 76
4.4 Influence of Secondary Flow…………………………………………………………... 77
4.5 Far-field Acoustics……………………………………………………………………... 78
4.6 Near-field Acoustics…………………………………………………………………… 81
ix
4.7 Baseline Summary……………………………………………………………………... 83
Chapter 5 – Chevron Nozzle Results……………………………………………………………….. 98
5.1 Gross Flow-field Changes………………………………………………………………98
5.2 Effective Penetration of Chevrons……………………………………………………... 101
5.3 Shock-cell Structures and Shear Layer Changes………………………………………. 101
5.4 Far-field Acoustics……………………………………………………………………... 110
5.5 Near-field Acoustics…………………………………………………………………… 113
5.6 Chevron Summary……………………………………………………………………... 117
Chapter 6 – Fluidic Chevron Results……………………………………………………………….. 133
6.1 Flow Field Changes Due to Fluidic Chevrons………………………………………… 133
6.2 Far-field Acoustics…………………………………………………………………….. 136
6.3 Comparison with Chevrons……………………………………………………………. 141
6.4 Community Noise Extrapolation………………………………………………………. 142
6.5 Fluidic Chevron Summary……………………………………………………………... 143
Chapter 7 – Contribution Summary………………………………………………………………… 149
7.1 Practical Supersonic Engine Nozzles…………………………………………………... 149
7.2 Chevron Nozzles……………………………………………………………………….. 151
7.3 Fluidic Chevron Nozzles……………………………………………………………….. 152
7.4 CFD Validation………………………………………………………………………… 153
7.5 Improved Correlation for Shock Sell Spacing…………………………………………. 153
Chapter 8 – Recommendations for Future Work…………………………………………………… 155
8.1 Two-Point Correlation Studies in the Shear Layer…………………………………….. 155
8.2 Screech Removal………………………………………………………………………. 155
8.3 Chevrons on Different Nozzles………………………………………………………… 156
8.4 Increased Mass Flow for Fluidics……………………………………………………… 156
8.5 Near-field Mapping of the Blowing Configuration……………………………………. 157
8.6 Cross-stream PIV of the Blowing Configuration………………………………………. 157
8.7 Centerline Static Pressure Measurements……………………………………………… 158
Bibliography………………………………………………………………………………………... 159
x
List of Tables
Table 5.1 – Shock properties, location ―c‖, Lip wave, inward running, r/De = 0.1……………….... 119
Table 5.2 – Shock properties, location ―f‖, Throat wave, second outward wave, r/De = 0.1………. 119
Table 5.3 – Spectral features from Far-field observation…………………………………………... 120
Table 6.4 Noise footprint values with and without fluidic injection in the 60-0 configuration
with a mass fraction of 1.4%............................................................................................................... 144
xi
List of Figures
Figure 1.1 – Conical C-D nozzle simulating the exhaust of a high-performance military
aircraft, with secondary flow nozzle for forward-flight simulation………………………………… 4
Figure 1.2 – A CF34-3B1 engine on a Mesa Airlines CRJ with chevrons on the core nozzle……... 5
Figure 1.3 – External blowing in the Md = 1.5 nozzle without forward-flight effects.
Secondary flow exit covered with a shroud………………………………………………………… 6
Figure 2.1 – Area-Mach number relation for isentropic quasi-1D flow. (Figure adapted
from Anderson, 1990.)……………………………………………………………………………… 9
Figure 2.2 – C-D nozzle conditions. a) overexpanded. b) overexpanded. c) perfectly
expanded. d) underexpanded………………………………………………………………………. 12
Figure 2.3 – Shock diamonds from a P&W J58 engine from SR-71 on a test stand at
Edwards AFB………………………………………………………………………………………. 13
Figure 2.4 – Supersonic Jet Noise, Md = 1.50 . (Figure adapted from Norum & Seiner,
1982.)……………………………………………………………………………………………….. 15
Figure 2.5 – BBSN Noise, Md = 1.50 . (Figure adapted from Seiner & Yu, 1984 by
Tam, 1995.)…………………………………………………………………………………………. 18
Figure 2.6 – Mach wave radiation due to a supersonic travelling wave component. (Figure
from Tam and Tanna, 1982)………………………………………………………………………... 20
Figure 2.7 – Screech tone frequency as the limit of BBSN peak. Squares and diamond,
Md = 2.0, Mj = 2.236. Circles and triangle, Md = 1.5, Mj = 1.802. (Figure adapted from
Tam, Seiner & Yu, 1986)…………………………………………………………………………… 22
Figure 2.8 – Strouhal number of fundamental screech. (Figure adapted from Tam, Seiner
& Yu, 1986)………………………………………………………………………………………… 23
Figure 2.9 – Broad-band amplification of mixing noise and BBSN by tonal excitation.
(Figure from Jubelin 1980)…………………………………………………………………………. 24
Figure 2.10 – Tam’s similarity spectra, F and G for large and fine scale turbulence noise
respectively…………………………………………………………………………………………. 26
Figure 2.11 - Peak noise amplitudes. (a) large-scale noise. (b) fine scale noise Mj = 0.98,
T0/T∞ = 1. (Figure from Tam, 1998)………………………………………………………………... 28
Figure 2.12 - Peak frequencies for Tam's similarity spectra. (Figure from Tam, Viswanathan,
Ahuja and Panda, 1998)…………………………………………………………………………….. 29
xii
Figure 3.1 – Nozzles simulating the exhausts of tactical jets. (a) Cross sections of three
nozzles without forward-flight simulation, (b) Cross section of the Md=1.56 nozzle with
the secondary flow nozzle to simulate forward flight………………………………………………. 36
Figure 3.2 - Nozzle geometry for the Md = 1.3, 1.5 and 1.65 baseline nozzles………………….. 38
Figure 3.3 – Chevron nozzle arrangement. A cap holds chevrons to the existing nozzle
trailing edge. The internal flow lines of the nozzle are unmodified, (a) Exploded view,
(b) Chevron detail views, (c) Cross-section view of cap alone……………………………………. 39
Figure 3.4 – Md = 1.56 chevron nozzle. (a) Cross-section view of chevron nozzle.
(b) Detail of chevron shape…………………………………………………………………………. 40
Figure 3.5 – Convergent-divergent nozzle with 12 fluidic injection tubes, with 36° pitch
and 20° yaw. (a) perspective view. (b) upstream view. This configuration is referred
to as 36-20…………………………………………………………………………………………... 41
Figure 3.6 – Convergent-divergent nozzle with 12 fluidic injection tubes, with 60° pitch
and 0° yaw. This configuration is referred to as 60-0……………………………………………. 41
Figure 3.7 - Microphone locations for far-field and near-field acoustic measurements……………. 45
Figure 3.8 - Two-dimensional PIV arrangement for capturing PIV in axial planes. ………………. 52
Figure 3.9 - Stereo PIV arrangement for cross-stream planes……………………………………… 54
Figure 3.10 - Sample calibration data for pressure transducer……………………………………... 58
Figure 3.11 - Sample comparison of old and new calibration constants for a pressure transducer… 59
Figure 3.12 - Variation in jet velocity for the Md = 1.5 nozzle……………………………………... 61
Figure 3.13 - Back-to-back acoustic measurements of Md = 1.5, Mj = 1.56, ψ = 35°……………… 62
Figure 3.14 - Back-to-back acoustic measurements of Md = 1.5, Mj = 1.56, ψ = 150°…………….. 62
Figure 3.15 - variation from mean spectra for Md = 1.5, Mj = 1.56, ψ = 150°……………………... 63
Figure 3.16 - Comparison of measured spectra with measurements of similar nozzles at
other scales in other facilities, Md = 1.5, Mj = 1.56, ψ = 150°, scaled to R/D = 100……………….. 64
Figure 3.17 - Comparison PIV with LES and LES with pressure probe along the centerline
of the jet. Md = 1.5. Mj = 1.56……………………………………………………………………... 66
Figure 4.1 - Mach number contours inside the nozzle by LES (figure from Munday,
Gutmark, Liu and Kailasanath, 2009)………………………………………………………………. 85
Figure 4.2 - Flow field representations by shadowgraph, PIV for Md = 1.5 and Mj = 1.56.
a) Instantaneous shadowgraph. b) Average of 100 shadowgraph images. c) Instantaneous
PIV. d) Average of 500 PIV image pairs…………………………………………………………… 85
xiii
Figure 4.3 – Conical C-D nozzle (Md = 1.5) shadowgraph. One hundred images averaged
to suppress turbulence and emphasize stationary features………………………………………….. 86
Figure 4.4 - Width of the slip line, w, at x/De = 0.125. The diameter of the slip line indicates
the size of the internal Mach disk which shed it. It is dominantly a function of the design
Mach number of the nozzle, and weakly a function of the nozzle pressure ratio…………………... 87
Figure 4.5 - Axial position of first throat reflection, T0. The reflections for Md = 1.30 are
inside the nozzle. The reflections for Md = 1.50 are taken from shadowgraph. For Md = 1.65
they are taken from PIV…………………………………………………………………………….. 87
Figure 4.6 – Mean u/Ud for different nozzles, perfect expansion. a) Mj = Md = 1.3.
b) Mj = Md = 1.5. c) Mj = Md = 1.65………………………………………………………………... 88
Figure 4.7 – Mean v/Ud, for different nozzles, perfect expansion. a) Mj = Md = 1.3.
b) Mj = Md = 1.5. c) Mj = Md = 1.65………………………………………………………………... 88
Figure 4.8 – Mean u/Ud for the same nozzle with different conditions. Md = 1.5. a) Mj = 1.22,
overexpanded. b) Mj = 1.50, perfectly expanded. c) Mj = 1.71, underexpanded………………….. 89
Figure 4.9 – Mean v/Ud for the same nozzle with different conditions. Md = 1.5. a) Mj = 1.22,
overexpanded. b) Mj = 1.50, perfectly expanded. c) Mj = 1.71, underexpanded………………….. 89
Figure 4.10 -- Shock reflection locations for Mj = Md = 1.5……………………………………….. 90
Figure 4.11 -- Shock Cell size, Ls as a function of Mj……………………………………………... 90
Figure 4.12 - Shock cell spacing collapsed for all valued of Md…………………………………… 91
Figure 4.13 – Shadowgraph. One hundred images averaged to suppress turbulence and
emphasize shock cells. Mj = Md = 1.56, T0/Ta = 1.22. Solid lines descend from reflections at
the shear layer in M2 = 0.0. Dashed lines descend from waves crossing the centerline in
M2 = 0.0. Green lines pertain to the wave from the lip. Red lines pertain to the wave from
inside………………………………………………………………………………………………... 92
Figure 4.14 – Far-field spectra for Md = 1.50. a) Mj = 1.47, overexpanded. b) Mj = 1.50, perfectly
expanded. c) Mj = 1.56, underexpanded…………………………………………………………… 93
Figure 4.15 – Far-field SPL at ψ = 35°. a) Md = 1.3. b) Md = 1.5. c) Md = 1.65…………………. 93
Figure 4.16 -- Peak BBSN frequencies for an observer ψ = 90º……………………………………. 93
Figure 4.17 -- Strouhal number of screech peak……………………………………………………. 94
Figure 4.18 -- Variation in OASPL with βd = ±(|Mj2-Md
2|)
0.5………………………………………. 94
Figure 4.19 -- Near-field contour maps of OASPL and 50 Hz bands for a slightly
underexpanded case, Md = 1.50, Mj = 1.56. Levels are in dB. (a) Over All Sound Pressure
Level. (b) Mixing noise, St = 0.166. (c) Screech, St = 0.266. (d) BBSN, St = 0.566………………. 95
xiv
Figure 4.20 -- Near-field OASPL and 50 Hz band SPL in dB along a line beginning in
the exit plane of the nozzle at r/De = 0.85 and sloping outward with an angle of 10º from
the axis. (a) OASPL. (b) Low frequency screech, f = 1000Hz. (c) Screech peak frequency…….. 96
Figure 4.21 – Near-field pressure contours for the Md = 1.50 nozzle. Column 1 is a 50 Hz
band centered at each condition’s screech frequency. Column 2 is a 50 Hz band centered at
the BBSN peak frequency as it is observed at ψ = 90°……………………………………………... 97
Figure 5.1 – Instantaneous shadowgraph images, Md = 1.5, Mj = 1.56. a) baseline. b) chevron... 120
Figure 5.2 – Averaged shadowgraph images of nozzle with and without chevrons (100 images
averaged). The camera is in a plane passing through the two chevron tips. ………………………. 121
Figure 5.3 - PIV images for Md = 1.5, Mj = 1.56. Left image is the baseline nozzle. Middle
image is the chevron nozzle in a plane through the chevron tips. Right image is the chevron
nozzle in a plane through the valleys between chevrons…………………………………………… 122
Figure 5.4 – PIV of velocity modification due to chevrons, Md = 1.5, Mj = 1.47, x/De = 2.
Color map is axial velocity. Arrows show cross-stream velocity. The black circle has a
diameter equal to the nozzle exit. The missing data regions are due to hardware reflections
contaminating the PIV images of the seeded flow………………………………………………….. 122
Figure 5.5 – Shock reflection axial position with and without chevrons…………………………… 123
Figure 5.6 – Shadowgraph, 100 images averaged, Md = 1.56, Mj = 1.56, T0 = 367 K,
M2 = 0.1. (a) Baseline nozzle. (b) Chevron nozzle………………………………………………… 123
Figure 5.7 – Mean axial velocity from PIV of jet in axial planes. For all three cases:
Mj = 1.56, T0 = 367 K, M2 = 0.1, T0 = 300K. Contour interval is 10 m/s. Selected contours
have been labeled. a) Baseline nozzle. b) Chevron nozzle, plane through chevron tips.
c) Chevron nozzle, plane through chevron valleys. The letters in (a) are the locations
where shock strengths are determined……………………………………………………………… 124
Figure 5.8 – Axial velocity and Turbulent Kinetic Energy at x/De = 0.5, Mj = 1.56, T0 = 367 K,
M2 = 0.1, T0 = 300K. a) Mean Axial Velocity. b) Turbulent Kinetic Energy……………………. 125
Figure 5.9 – Mean axial velocity at an axial position. The contour interval is 20 m/s. Selected
contours are labeled in n/s. (a) x/De = 1.0. (b) x/De = 2.0. (c) x/De = 4.0………………………… 125
Figure 5.10 – Mean axial velocity along lines of constant radius. a) r/De = 0.0. b) r/De = 0.1.
c) r/De = 0.4…………………………………………………………………………………………. 125
Figure 5.11 – Far-field acoustic measurements of a Md = 1.50 nozzle with and without chevrons
at a distance of 47 exit diameters from the nozzle exit. a) ψ, of 35°. b) ψ, of 90°. c) ψ, of 150°… 126
Figure 5.12 – Far-field OASPL a Md = 1.50 nozzle with and without chevrons at a distance
of 47 exit diameters…………………………………………………………………………………. 126
Figure 5.13 – SPL Spectra in dB along a line just outside the jet, with and without chevrons…….. 127
Figure 5.14 – Maps of near-field SPL at 1000Hz representing low-frequency mixing noise……… 128
xv
Figure 5.15 – Maps of near-field SPL at the screech frequency for each condition………………... 129
Figure 5.16 – Maps of near-field SPL at the peak BBSN frequency for each condition…………… 130
Figure 5.17 – Maps of near-field SPL at the 30,000Hz for each condition. ………………………... 131
Figure 5.18 – Maps of near-field OASPL for each condition………………………………………. 132
Figure 6.1 – Shadowgraph images of Md = 1.5 nozzle alone, with fluidics and with chevrons,
Mj = 1.56. The camera is in a plane passing through the two fluidic nozzles or two chevron tips.
(a) (b) and (c) are single images. (d) (e) and (f) are each averages of 100 images. (a) and (d)
are baseline. (b) and (e) are with fluidics in the 60-0 configuration with a mass fraction of
1.4%, (c) and (f) are with chevrons…………………………………………………………………. 145
Figure 6.2 - Shadowgraph of fluidic injection with the main jet off. a) instantaneous image.
b) average of 100 images…………………………………………………………………………… 145
Figure 6.3 – As measured spectra with and without fluidic injection compared with the
spectra for the injection tubes operating without the main jet and the background spectra
for the room. The fluidic injection case shown is the 60-0 configuration with a mass
fraction of 1.4%.................................................................................................................................. 145
Figure 6.4 – Baseline far-field spectra compared spectra with the fluidic hardware mounted,
but turned off. Md = 1.5. Mj = 1.56………………………………………………………………... 146
Figure 6.5 – Baseline far-field spectra compared spectra similar nozzles at NASA, Glenn
and Penn State University. Md = 1.5. Mj = 1.56…………………………………………………... 146
Figure 6.6 –Spectra with and without fluidic injection. The fluidic injection case shown
is the 36-20 configuration supplied with 40 psig of air. Md = 1.5. Mj = 1.56…………………….. 146
Figure 6.7 – Spectra with and without fluidic injection. The fluidic injection case shown
is the 60-0 configuration with a mass fraction of 1.4%. Md = 1.5. Mj = 1.56…………………….. 147
Figure 6.8 – Community noise footprint plots with and without fluidic injection in the
60-0 configuration with a mass fraction of 1.4%. Md = 1.5. Mj = 1.56…………………………… 147
Figure 6.9 – OASPL and dB(A) plots for the jet scale up by a factor of 8 and taken at an
observer distance of 8m. Md = 1.5. Mj = 1.56……………………………………………………... 147
Figure 6.10 – Spectra with and without chevrons. Md = 1.5. Mj = 1.56…………………………... 148
xvi
List of Symbols
a Speed of sound
A Cross-sectional area
A* Throat cross sectional area
BBSN Broad-band shock-associated noise
D Diameter
fp Peak frequency of broad-band shock-associated noise
fs Peak frequency of screech
Ls Shock cell spacing
Md Design Mach number
Mj Fully expanded jet Mach number
M2 Secondary flow Mach number
npr Nozzle pressure ratio
OASPL Over-all sound pressure level
P Pressure
r Radial coordinate
R Ideal gas constant
Re Reynolds Number
SPL Sound pressure level
St Strouhal number
TKE Turbulent kinetic energy
u Axial velocity
v Radial velocity
w Width of slip line from internal Mach disk
x Axial coordinate
xvii
β Shock strength parameter
γ Ratio of specific heats
θ Angle from the downstream axis
ψ Angle from the upstream axis
ρ Density
subscripts
c Convective condition
d Design condition
e Exit condition
j Condition of perfect expansion
o Total condition
∞ Ambient condition
1
Chapter 1 – Introduction
1.1 The Problem
There has been a great deal of work done on jet noise from subsonic jets, both ideal subsonic
jets and jets from nozzles representative of those on commercial aircraft. Study of these nozzles has
advanced to the point that there is a general understanding of the mechanisms of noise production and
the application of noise reduction technologies have advanced to the point that some, such as chevrons,
have entered service in the fleet of aircraft in revenue-generating service.
There has been less work done on the noise production from supersonic jets. There is a body of
work on super-sonic jet noise from idealized nozzles, and a limited amount of work on noise from
nozzles like those on commercial aircraft operating slightly underexpanded. But until recently there has
been very little attention paid to jets from the kind of nozzles used in high-performance military aircraft.
These nozzles have unique features which cause them to differ from idealized nozzles in their shock
structures and thus in the production of those components of jet noise which are produced by
interactions with the jet’s shock structures.
Commercial and regulatory pressures have driven interest in and funding of research in
commercial subsonic jet noise. The “community noise” problem of aircraft annoying airport neighbors,
driving down property values and leading to political pressure has led to the formalization of jet noise
regulation by the FAA in the United States, by ICAO internationally and by numerous local governments
in cities with major airports like London or New York. The necessity to meet the limits imposed by these
regulations has caused aircraft and engine manufacturers to be concerned with noise production and
mitigation and to fund research into these areas. This has also led to interest by and funding from
government (through NASA in the United States.)
2
Military aviation has historically been much less constrained by concerns with community noise
around air bases and naval air stations. One cause of increased interest in the problem of noise from
military jets was the Base Realignment and Closing process (BRAC) beginning in 1989 which caused some
flight training to be moved, and so caused some base neighbors to be exposed to a sharp increase in
community noise. Law suits were filed against the Navy between 2001 and 2005 on behalf of 3400
neighbors to Naval Air Station Oceana in Virginia Beach and eventually a settlement was reached for
34.4 million dollars. This brought attention and interest to the problem of community noise around air
bases and air stations and let to concern that increased noise from military aircraft would lead to
constraints on peace time training and testing by the armed forces. In an effort to find ways to mitigate
noise from military testing and training funding was made available from SERDP to the UC-NRL-GE
project which makes up part of this dissertation as well as a concurrent effort at Penn State University
with some testing taking place at NASA Glenn Research Center.
Interest in community noise from military activity is not confined to the United States, or to US
government or US defense contractors. Interest is also expressed by other countries including Sweden.
The Swedish government through its Defense Materiel Administration (Försvarets materielverk or FMV)
is interested in the problem of noise from military aircraft and has also funded a project in partnership
with Volvo Aircraft Corporation. This Swedish project also funds work that makes up a major portion of
this dissertation research.
Another motivation for jet noise research on the jets typical of military aircraft is more of a
concern of navies than of other services. In aircraft carrier operations there are numerous personnel
who work in the immediate region around high-performance aircraft while they operate at high power
settings. In a catapult launch from a carrier deck there are men working within a few meters of the
aircraft as it goes to high power just before the cat shot. Exposure to the high acoustic forcing is a
health risk for carrier deck crew more so than ramp crew on an airbase who are typically much farther
3
from the runway when the aircraft goes to high power. The most obvious risk from the high acoustic
forcing levels is hearing loss. Despite noise attenuating protective helmets and earphones hearing loss is
a growing problem. Disability due to hearing loss as a primary disability cost the US Navy 6.5 Billion
dollars between 1968 and 2006. All US military services were spending over 750 million dollars a year
on veterans disability benefits for hearing loss as a primary disability in 2005. Worse, the trend is
sharply upward. Less than half that amount was spent five years earlier.
Both community noise and noise exposure to personnel grow worse as each generation of
aircraft becomes more powerful and louder. This is a growing problem and the need to reduce the
noise of military aircraft has led to interest in study of noise from military aircraft with their supersonic
jets from nozzles different from those studied in nearly all previous work on supersonic jets.
The unique character of the nozzles employed for high-performance military aircraft and studied
in this program is driven by the fact that they must be convergent-divergent (C-D) in order to efficiently
produce high-Mach-number jets and also must be variable geometry so that the throat area may be
changed to match the atmospheric conditions over a wide range of altitudes and match the power
setting from ground idle up to full afterburner.
The typical military C-D nozzle is polyhedral in cross section, with a large enough number of
sides that the polyhedron roughly approximates a circle. Twelve is a typical number. At the upstream
end of the convergent section of the nozzle, then flat plates are hinged around the perimeter and forced
toward the centerline of the jet by hydraulic rams. Between these plates are sliding seals so that the
plates and their seals approximate a convergent conic surface. The downstream end of these plates and
seals are the nozzles throat where an additional set of plates is hinged and sealed to one another to
form a surface approximating a divergent conic surface. These divergent plates may in some cases be
driven independently by a second set of hydraulic rams, but are more often controlled by solid links so
their position is not independent of the position of the convergent section. The hinge joints between
4
the convergent plates and the divergent plates form a throat that is much sharper than the kinds of C-D
nozzles used in previous studies of supersonic jets and jet noise. Also in contrast to typical laboratory
nozzles these military nozzles do not have flow lines that
curve to have parallel slopes at the nozzle exit.
The research program covered by this dissertation
examines the flow and acoustic behavior of supersonic jets
from convergent-divergent nozzles with conical contractions,
relatively sharp throats, and conical expansion sections. The
static nozzles used in this study are representative of variable
geometry C-D nozzles used on high-performance military
aircraft. They are simplified in having circular cross sections rather than polyhedral ones. This is the
limiting case in the limit of large number of sides. One of the nozzles employed in this study is shown in
Figure 1.1.
Since most nozzles of this type do not provide independent control of the convergent and
divergent sections of the nozzle, they do not provide independent control of the throat and exit areas of
the nozzle. Since it is essential to set the area of the throat to adapt to the mass flow through the
engine, the lack of independence in setting the exit area means that the ratio of throat to exit areas
must be a compromise and will in most conditions not exactly match the fully expanded Mach number
of the jet. This implies that for the general case the nozzle will be operated off its design condition. This
makes off-design condition (underexpanded and overexpanded) important for the practical acoustics of
these nozzles and study of underexpanded and overexpanded conditions are a particular focus of this
study in addition to study of on-design condition.
Part of this project is to examine noise reduction techniques that have been found to be
effective for subsonic jets and determine how effective they are on supersonic jets from military nozzles.
Figure 1.1 – Conical C-D nozzle
simulating the exhaust of a high-
performance military aircraft, with
secondary flow nozzle for forward-flight
simulation.
Md = 1.56
5
The most effective method which has been applied to civilian engines is an increase in bypass ratio
(BPR). This is the ratio of mass flow that passes around the hot engine core to the total mass flow
through the engine. Increasing bypass ratio generally leads to larder diameter engines and increased
efficiency by accelerating a larger mass of air, but accelerating it to a lower velocity. Since mixing noise
scales with the eighth power of jet velocity this can produce substantial decrease in jet noise for
subsonic jets. The difficulty with this for the high-performance military aircraft is that the body of the
aircraft is built around the engine, and increasing engine diameter will increase the cross sectional area
of the aircraft fuselage. Increasing cross section will increase drag unacceptably. Early jet engines
(turbojets) had a bypass ratio that was essentially zero. Civilian engines today have bypass ratios greater
than eight, with manufacturers considering designs with BPR as great as fifteen. The requirement to
keep the engines slim, however, has kept engines for supersonic military aircraft low. The F404 for
example has a BPR of 0.27 and the EJ200 of 0.4.
Chevrons have been applied to civilian designs have proved successful enough that they are now
entering revenue-generating service on the commercial fleet (Figure 1.2). Chevrons are serrations along
the nozzle lip which introduce streamwise vorticity into the
shear layer, enhancing mixing. Previous studies of subsonic
jets typical of commercial aircraft have shown acoustic benefit
from chevrons at lower frequencies, but increased noise at
higher frequencies with a modest thrust penalty. Application
of chevrons to subsonic engines, therefore, requires a
balancing of the costs and benefits for the particular
application. We would expect similar balancing to be necessary for supersonic applications. This study
aims to aid our understanding of the behavior of chevrons in a supersonic context to inform design
decisions.
Figure 1.2 – A CF34-3B1 engine on a
Mesa Airlines CRJ with chevrons on the
core nozzle.
6
Noise abatement is most important in the airport or carrier environment, but is less critical for
the rest of the aircraft’s flight. One difficulty with chevrons
is that the small thrust penalty they impose is imposed
throughout the flight, not just in the take-off and landing
phases. This disadvantage motivates attention to
approaches which may be turned on when needed, and
turned off at other times. One such approach is to create
streamwise vortices by means other than chevrons. This
may be done by introducing small jets, sometimes called
micro-jets around the perimeter of the nozzle oriented at an
angle to the principal flow direction. In subsonic applications these small jets have been shown to
introduce streamwise vorticity as chevrons do, and to produce similar acoustic benefits and penalties.
This study aims to explore the application of such micro-jets to the supersonic jets from conical C-D
nozzles as a second noise-reduction approach.
1.2 Project Structure
This study was funded by two different organizations with slightly different interests and
requirements and that has limited the consistency among the data presented. If this was a unified
project one might have concentrated on a single nozzle for both studies of the influence of NPR or jet
Mach number and for the study of the influence of secondary flow Mach number. One study required
hot (or at least warm) jets and the other concentrated on larger jets which were run cold because we
didn’t have enough heating capacity to raise their temperature significantly. The two projects had
different industrial partners, and since it was important to avoid interchange of intellectual property
related to nozzle design the chevron geometries were deliberately made different between two of the
Figure 1.3 – External blowing in the Md =
1.5 nozzle without forward-flight effects.
Secondary flow exit covered with a
shroud.
Md = 1.5
7
nozzles. It would have been interesting to try the different chevrons on the same nozzle, but that was
not possible because of the differing requirements of the two projects.
The first project, sponsored by SERDP introduced an additional constraint by the fact that SERDP
sponsored two concurrent projects; one with University of Cincinnati and one with Penn State
University. The Penn State project concentrated on far-field acoustics and in order to avoid duplication
of effort imposed on University of Cincinnati an explicit de-emphasis on far-field. Though some far-field
measurements were taken, and proved to be important the emphasis of this project was on near-field.
Both projects were experimental/numerical collaborations, though with different numerical
collaborators for each. They were both conceived as relying heavily on interaction between the
experiments and simulations. This interaction stretches far beyond a one-way effort where the
experimental portion provides validation data to the numerical effort. Results of measurement and
simulation are both shared and examined regularly with an eye towards finding those areas where each
technique excels. For example measurement within the nozzle itself is difficult without disturbing the
flow excessively. This is not a problem for simulation. On the other hand it is expensively time
consuming to run many cases in simulation on the same geometry, but for experiment it is a simple
matter of changing the set point and continuing the run.
While this dissertation is a presentation of individual effort and contribution, the nature of the
collaborative investigation means that inevitably some insights into the physics under study will have
come from the numerical portion of the program which is not the author’s individual effort. There will
necessarily be some points that will be reliant on simulation for explanation. Two examples will be the
understanding of what is happening upstream of the nozzle exit and the validation of the PIV system.
The PIV measurements were not validated by comparison with some other velocity measurement
system. Both PIV and pressure measurements are compared to simulation and since all three agree,
one may have confidence in the results of any of them.
8
The first project was funded by SERDP, an organization jointly supported by the Department of
Defense, Department of Energy an Environmental Protection Agency. SERDP’s aim is to mitigate the
environmental influence of military testing and training activities. The environmental influence of
interest here is jet noise. As noted above SERDP funded two projects in this area and as a result UC’s
project had an explicit de-emphasis on far-field acoustics. This project was jointly awarded to UC, to a
group at the Naval Research Laboratory (NRL) and to GE Global Research (GEGR). UC provided the
experimental portion. NRL provided the numerical portion in the form of LES. GEGR provided technical
guidance in nozzle design and selection of test cases in order to ensure that the cases studied were
relevant to actual practice. The SERDP project employed jets where jet total temperature was
approximately equal to the atmospheric temperature. Three C-D nozzles were constructed with design
Mach numbers, Md, of 1.3, 1.5 and 1.65. One chevron geometry supplied by GEGR was affixed to the Md
= 1.5 nozzle and blowing by microjets in place of chevrons was employed on the Md = 1.5 nozzle. There
were other components of the project, but they are outside the scope of this dissertation. No
secondary jet was applied in the SERDP project.
The second project was funded by Försvarets materielverk (FMV), the Swedish Defense Materiel
Administration. This project did emphasize far-field acoustic effects. This project was jointly awarded to
UC, Chalmers University of Technology (CTH) and Volvo Aero Corporation (VAC). UC provided the
experimental portion of the project. CTH provided the numerical work in the form of LES with
extrapolation to the far-field by the Kirchoff Integral method. VAC provided the nozzle design and test
conditions in order to insure relevance to current practice. The jets in the FMV project were heated,
though not to the temperatures found in real engines. One baseline and one chevron nozzle were
constructed with a design Mach number (Md) of 1.56. In order to insure that GEGR’s chevron designs
were clearly not copied the chevron designs were taken from a set of published NASA chevrons. There
was also a blowing component to this program but it is beyond the scope of this dissertation.
9
Chapter 2 – Background
2.1 Supersonic Nozzles
Convergent-divergent nozzles are used to accelerate fluid to supersonic speeds. The area-
velocity relation for quasi-1D flows,
, tells us that to accelerate a subsonic flow (M < 1)
we must decrease the area of the duct. For M = 1 we can see that the area must be at a maximum or
minimum. In order to accelerate a supersonic flow (M > 1) we must increase the area of the duct. A
convergent-divergent nozzle with sufficient total pressure
will therefore accelerate the flow to a sonic condition at the
throat, and if there is sufficient pressure it will further
accelerate the flow supersonically beyond the throat to an
exit Mach number determined by the ratio of areas
between the throat and the exit. Examining the Area-Mach
number equation, and its solution in Figure 2.1, we can see
that if we know the nozzle geometry and if we know that
there is sufficient pressure to sustain supersonic pressure
downstream of the throat we can determine the Mach
number for any axial position. Knowing the Mach number and the stagnation conditions we can find the
local thermodynamic properties from the isentropic stagnation relations:
.
From T we can then find the local sound speed, , and from this we can find the local velocity
u. Note that we can determine the conditions for any point within the nozzle without reference to the
conditions outside the nozzle exit.
Figure 2.1 – Area-Mach number relation
for isentropic quasi-1D flow. (Figure
adapted from Anderson, 1990.)
10
This approach relies on a number of assumptions about the flow. It ignores boundary layer
growth, though that can be got around by considering a virtual nozzle with radius everywhere reduced
by the displacement thickness, δ*. It assumes quasi-1D flow which is a reasonable approximation if the
nozzle isn’t too short so the flow directions aren’t too far from parallel. Finally it assumes that the flow
through the nozzle is isentropic, which may be close to true for a well designed nozzle. Designing
nozzles for nearly isentropic flow is a subject unto itself. Here let us say only that nearly isentropic
nozzles can be designed by the method of characteristics, or by more modern computational methods.
The nozzles we are concerned with in this study are not designed for nearly isentropic expansion, and
we examine the consequences of this throughout, but the isentropic 1-D method outlined above is
commonly used for C-D nozzle analysis and it defines a number of the parameters of interest so we will
continue to use it while recognizing that its application requires some important caveats for the conic C-
D nozzles we study here.
The most important parameter of the geometry of a C-D nozzle is its area ratio, , where
the subscript e denotes the exit condition. If we use this ratio as the right side of the equation in Figure
2.1 for the supersonic case we will find the design Mach number, Md , where the subscript d denotes
design. This is purely a function of the nozzle, and is commonly used to describe the nozzle geometry.
Another commonly used parameter for the nozzle geometry is the design nozzle pressure ratio,
.
The design npr is so called because when the nozzle pressure ratio, , takes on this value
the exit pressure and the surrounding ambient pressure match, and the nozzle is said to be operating at
its design condition. If, as is common in nozzle design, the flow exiting the nozzle is nearly parallel a C-D
nozzle operating on-design will produce a supersonic stream which is shock free. This shock-free
condition is important when considering the acoustics since the shock induced components of noise will
be absent. The flow from our conic C-D nozzles will never be parallel, so this is an area in which the
11
common nozzle theory falls short in describing our case, but again we will proceed with the usual theory
and note the consequences of differences in the results section.
2.2 Supersonic Jets Past the Nozzle
Whatever the design of the nozzle, C-D, convergent, or some other design, we commonly
describe the operating point of the nozzle in terms of the nozzle pressure ratio, npr, between the total
pressure supplied to the nozzle and the ambient pressure into which the jet exhausts. This parameter
gives rise to a family of parameters based on the isentropic 1-D theory, and denoted by a subscript j.
The fully expanded jet Mach number is determined by the isentropic stagnation relation:
.
This is a function solely of the nozzle pressure ratio, npr. If we also know the stagnation conditions at
the nozzle inlet, we can also find Tj from
, and , and the jet velocity
. Despite the several limitations of the isentropic-1D theory for our cases, uj is still a
reasonable approximation of the exit velocity for all of our nozzles, and is a very useful parameter for
non-dimensionalization. One further parameter useful for nondimensionalization is Dj. This is the
diameter for perfect expansion. It is a function of npr and throat diameter. It is determined by the
equation in Figure 2.1 with M = Mj. Dj is related to D by
As noted above, if npr = nprd we will have , and Mj = Md and the nozzle is said to be
perfectly expanded. If the nozzle is well designed, this will result in a shock-free supersonic jet. This is
the condition c) in Figure 2.2. If the total pressure supplied to the nozzle is reduced, or the ambient
pressure is increased, npr and Mj reduce as well, and . This is referred to as an overexpanded
12
condition. The mismatch in pressure at the exit cannot be sustained in the jet, so the flow must turn
radially inward to become less expanded. This forms an oblique shock anchored at the nozzle exit and
the shock increases the pressure to match . This condition
is denoted on Figure 2.2 as b).
For low enough npr, a normal shock forms near the
jet center connecting the oblique shocks from the lip. This
normal shock is called a Mach disk, and the perimeter of the
Mach disk creates a slip line downstream of it between the
subsonic flow downstream of the Mach disk and the
surrounding supersonic flow downstream of the oblique shock. This is a) in Figure 2.2.
Still lower npr will produce a normal shock at the nozzle exit or inside the nozzle creating a
wholly subsonic jet outside the nozzle. These subsonic jets are outside our range of interest in this
study.
If the npr is raised above nprd then and . This is unsustainable so the flow
expands by turning radially outward creating a Prandtl-Meyer expansion fan anchored at the nozzle lip.
This expansion reduces the pressure so that it matches . Such a condition is called underexpanded,
and is depicted as d) in Figure 2.2. This underexpanded condition is not unique to convergent-divergent
nozzles. This is what happens with a simple convergent nozzle if operated at a pressure above the sonic
npr.
2.3 Shock Cells
Whether the jet is overexpanded, or underexpanded the downstream development is much the
same. Figure 2.2b shows the case of an overexpanded jet. A shock wave shown as a single solid line
forms at the exit lip turning the flow inward and matching pressure along the slip line, shown as a
Figure 2.2 – C-D nozzle conditions. a)
overexpanded. b) overexpanded. c)
perfectly expanded. d) underexpanded.
13
dashed line. This shock reflects from the centerline as it would from a solid boundary creating an
outward running shock. This outward running shock then reflects off the slip line in opposite manner,
producing an inward running Prandtl-Meyer expansion fan. This then reflects from the centerline in like
manner creating an outward running Prandtl-Meyer fan. This outward running wave reflects from the
slip line as a compression wave, which coalesces into an inward running shock like the one produced at
the nozzle lip. The process then repeats. If the jet is underexpanded, as in Figure 2.2d the process starts
with an inward running Prandtl-Meyer fan, and the cycle of reflections is the same. In either case the
shocks and expansions form a diamond pattern, called variously shock diamonds, or shock cells, or a
shock train. The repeating pattern continues until shear layer growth consumes the potential region in
which these shock and expansion structures form. Figure 2.3
shows an example of shock diamonds from a high-
performance military engine on a test stand. The repeating
pattern of the shock diamonds is clearly evident. An
important parameter for the acoustics is the length of the
shock cells, Ls. The Prandtl-Pack model of the shock train (Pack, 1950) models the flow as a weak wave
inside a shear layer modeled as a linear vortex sheet is found by:
, where
This model does not account for the thickening of the shear layer, so it is strictly only valid near the
nozzle.
2.4 Large Scale Coherent Structures in the Shear Layer
The predominant noise sources particular to shock containing jets involve interactions between
the shocks and the large scale structures in the shear layer surrounding the jet. Our experiments are
with jet Reynolds numbers on the order of 107, but most of the early work on jet shear layers is much
Figure 2.3 – Shock diamonds from a
P&W J58 engine from SR-71 on a test
stand at Edwards AFB
14
lower. Crow & Champagne (1971) used low-level excitation to examine large scale structures in jets up
to Re = 105. Previously the view had been that turbulence was composed of random, disorganized flow.
They were able to produce quite vivid images of large scale, organized, axisymmetric structures in the
fully turbulent shear layer of round jets. They found that there was a “preferred mode” with an
excitation Strouhal number of 0.3 if their excitation velocity was above 2% of the main jet velocity. The
response to the excitation was at a maximum near four jet diameters downstream.
Brown & Roshko (1974) studied large scale structures at higher Reynolds numbers, up to 106,
and with one case supersonic. They also employed forcing. They found that the thickening of turbulent
shear layers was caused by the pairing of eddies, and that entrainment and mixing is dominated by
engulfment, not molecular diffusion.
Eddys form in the shear layer out of the response to instabilities in the flow. The large sale
structures are often discussed in the literature as comparable to, or equivalent to instability waves in
the shear layer. The growth of these mathematical instability waves had been analyzed previously by
Michalke, (1965), who found that the growth of these waves could best be described by spatial
linearized inviscid instability analysis, and that this better modeled measured data than temporal
linearized analysis. Instability waves are often used in models of jet noise production, and large-scale
structures are measured in its investigation. It is convenient to consider these as generally
interchangeable, one describing observable eddies, and one describing the instabilities that give rise to
them.
Both of the above experimental studies employed forcing to line up the eddies in phase, making
them directly observable. Zaman and Hussain (1984) used conditional phase locking to examine forced
and unforced jets to look for large-scale structures in the latter. They found no significant difference
between the statistical measures of forced and unforced cases, lending considerable support to the
15
notion, that orderly, large scale structures naturally occur in turbulent jet shear layers, that they are not
called into being by forcing, but rather that the forcing merely locks them in phase.
Crow & Champagne and Brown & Roshko examined large scale structures of significant cross-
stream extent. They were essentially 2-D features. These initial 2-D features eventually further evolve
into randomly oriented large eddies as the flow transitions to isotropic turbulence. Yule, A. J. (1978)
examined this process and found that the axial distance over which toroidal structures exist is a function
of Reynolds number, and that this distance decreases as Reynolds number rises. By Re = 105 the
distance was less than a diameter. As this distance shrinks, the process of toroidal vortex merger
becomes insignificant. He further found that the randomly oriented eddies generated by the
breakdown of the initial 2-D structures could remain coherent to the end of the jet’s potential core.
Large scale structures were shown to exist in high-Reynolds-number, supersonic jets by
Lepicovsky, Ahuja, Brown & Burrin (1987). They
used excitation on a perfectly expanded jet with a
Mach number of 1.4 and Re = 1.6 x 106. They found
that large-scale structures definitely do exist for this
case with a preferred mode Strouhal number of 0.4.
2.5 Jet Noise from Supersonic Jets
Noise from supersonic jets is dominated by
three mechanisms, turbulent mixing noise, broad-
band shock associated noise (BBSN) and screech.
The far-field spectral signatures of the three
mechanisms were thoroughly documented by
Norum & Seiner (1982). Figure 2.4 was adapted from their report by Tam (1995). The lower trace in
each pair is a perfectly expanded case. Screech and BBSN are absent for perfect expansion and these
Figure 2.4 – Supersonic Jet Noise, Md = 1.50 . (Figure
adapted from Norum & Seiner, 1982.)
16
lower spectra show only the turbulent mixing noise. This source is identical to subsonic turbulent mixing
noise, and is not central to this study, since we are chiefly interested in off-design operation of
supersonic nozzles.
The upper trace in each pair is for a C-D nozzle operated off-design, in this case it is operated
underexpanded. For the off-design case, the jet produces shock cells and the two shock associated
mechanisms come into play. These are the principal subject of this study. The screech presents itself as
a narrow peak, sometimes with higher harmonics, with the frequency unchanged by direction of
observation. It propagates most strongly into the upstream quadrant, and becomes weaker as you
approach the downstream jet axis. BBSN is identified by a broader spectral peak, which is strongest and
narrowest at upstream angles, and changes frequency with angle of observation. The frequency is
lowest at the most upstream angles, and becomes higher as the angle of observation moves toward the
downstream axis. The peak frequency shifts as a Doppler effect would, leading to the supposition that it
is produced by moving sources. As we move closer to the downstream direction, the spectral peak also
becomes broader and lower. This implies that BBSN also propagates most strongly into the upstream
quadrant.
The production of screech was first documented by Powell (1953) both for round jets and 2D
jets. Based on Schlieren photographs of his 2D jets and the strong acoustic waves they produced, he
introduced a feedback theory of screech production. In this theory, “disturbances” shed from the nozzle
lip travel in the shear layer and interact with the shock cells “probably with the shock waves near the
end of the cells” and so produce sound waves which propagate upstream outside the jet. Finally “the
sound waves passing the exit give rise to the stream disturbances.” If we take these “disturbances” to
be instability waves or large scale structures induced by tonal forcing by the upstream propagating
wave, we have essentially the present understanding of screech production. The identification between
the “disturbances” and instability waves was made by Yu & Seiner (1983).
17
Screech has been shown to have multiple modes, giving rise to multiple screech frequencies.
These arise from different toroidal or helical modes in the instability waves shed from the jet. For
convergent nozzles up to five modes have been identified (Norum, 1983). For C-D nozzles Yu & Seiner
(1983) found that only two screech modes dominate depending on the nozzle condition. Overexpanded
conditions generate a toroidal mode, and underexpanded conditions generate a helical mode. Near
perfect expansion, both of these modes have been observed.
Both toroidal and helical modes arise from symmetric nozzles. It has been shown by many
researchers than a small break in symmetry at the nozzle, as by adding a small bump or tab, will
suppress screech. This has the potential disadvantage of reducing the symmetry of the mean jet as well.
The peculiar directional nature of BBSN was first documented by Harper-Bourne & Fisher (1974).
They proposed a phased emitter model for BBSN which modeled the shock cells as an array of acoustic
sources separated by the shock cell spacing Ls and assumed that these sources emitted correlated
acoustic signals delayed by the convection time of an eddy in the shear layer which they took to have a
convective velocity . Their prediction of BBSN peak frequency was
Where Mc is a convective Mach number based on uc. This relationship with n = 1 correlates well with
measured data for jets without forward flight simulation. Harper-Bourne & Fisher also found that the
overall sound pressure level (OASPL) due to BBSN was proportional to β4 where this is
consistent with assuming a source strength related to the pressure difference across a normal shock
since for a normal shock
.
This view of BBSN production implies that the noise is produced by the interaction of large scale
structures with the shock cells as they convect downstream in the shear layer. Pao & Salas (1981)
simulated the interaction of a shock wave with a single vortex using a Euler solver. Pao & Seiner (1983)
18
integrated the results of this simulation into a theory of BBSN production. They expanded the findings
to oblique shocks, and applied the findings to the shock pattern present in shock cells. They found that
most of the acoustic radiation from the shock vortex interaction radiated along the downstream side of
the shocks and emerged from the jet at the shock reflections with the shear layer, generating the
apparent sources correlated by the convection velocity described by Harper-Bourne & Fisher’s model.
Pao & Seiner found that the intensity of the BBSN emissions will rise with vortex size and strength and
also with oblique shock strength. These predictions were compared to measured data for a convergent
nozzle and for Md = 1.5 and 2.0 with good agreement.
Seiner & Yu (1984) used correlations between a wedge probe in the flow and near-field
microphones to attempt to locate the sources of BBSN. After accounting for propagation delay time
their correlations were highest along curves parallel to the shocks in the flow, lending credence to the
notion that shock-vortex interaction is the source of BBSN, but they do have an issue with probe noise
contaminating their measurements. Without the
probe in place they found strong evidence that most of
the BBSN comes from the later shock cells, and they
also found indications of Doppler shift in the acoustic
near-field. Doppler shift thus could not occur due to
the constructive interference effect included in the
Harper-Bourne and Fisher model. Such near-field
effects would have to come from actual moving
sources.
A relatively complete theory of BBSN
production is presented by Tam & Tanna (1982). They Figure 2.5 – BBSN Noise, Md = 1.50 . (Figure adapted
from Seiner & Yu, 1984 by Tam, 1995.)
19
examined noise from a C-D nozzle with Md = 1.67 and operated from Mj = 1.1 to 2.0 producing noise
from overexpanded perfectly expanded and underexpanded jets.
They modeled the jet as a standing wave in a waveguide with diameter Dj. They model the
streamwise oscillations as a cosine series, and build up the radial component with a series of Bessel
function through a radial function:
Where J0 and J1 are the zeroth and first order Bessel Functions and μn is the nth root of J0 so
. This function is orthonormal, satisfying:
where is the Kronecker delta. The complete series for the shock structure is:
, where
,
,
The shock cell spacing can be found from the first term alone:
, .
Tam and Tanna model the large scale turbulent structures as in Tam & Chen (1979) as:
Where Re indicates the real part of the quantity in braces. In this equation u is any quantity
disturbed by the passage of a large scale structure. The function a(x) is a streamwise amplitude function
that grows slowly in the x direction, as the structures grow, then it reaches a maximum where the
structures peak, then it diminishes slowly as the structures decay. The important attributes of a(x) are
that it is a slowly varying function in comparison to the other parts of the model. The radial function
20
ψ(r) is the eigenfunction of the wave mode. k is the wave number and is the radian
frequency, so the convection velocity, .
The pressure fluctuation disturbance due to the interaction of the large scale structures with
the shock cells is then modeled as the product:
Examining the term in brackets we see
that this is a superposition of traveling waves with
velocities of
and
for the first and
second terms. Note that the traveling wave
represented by the second term may be
significantly faster than uc and may in fact be
supersonic even if uc is not. It is Tam and Tanna’s
thesis that BBSN is produced from the Mach wave
radiation of these supersonic traveling waves in the shear layer.
Any of the traveling wave components will create irregularities in the outer edge of the shear
layer, which will translate downstream at the wave component’s propagation velocity. These
irregularities will behave like the classical wavy wall case, producing Mach wave radiation as sketched in
Figure 2.6. The case shown, is the case responsible for BBSN production. It is the n = 1 case for the
negative λ term, with convection velocity . From the wavy wall analysis we have:
Solving this for f we get:
Figure 2.6 – Mach wave radiation due to a supersonic
travelling wave component. (Figure from Tam and
Tanna, 1982)
21
Which differs from Harper-Bourne and Fisher’s result only by the choice of direction from which
to measure angles. If we supstitute we will have the same result for the first peak.
Tam and Tanna argue that all the positive λ traveling wave components are subsonic, and
therefore produce no Mach wave emissions. It remains to deal with the negative λ components. Tam
and Tanna argue that the ratio of intensities radiated between the n= 1 and n= 2 components would be
or a reduction of 7.2dB. This is substantially weaker than the first peak
and can be considered negligable. By this theory the frquency of the second peak would be
above the first, or 2.29 as compared to 2 for Harper-Bourne and Fisher’s result.
Tam and Tanna’s theory also provides a relationship for the BBSN intensity. To a first
approximation . We have relations relating the exit pressure (P∞+ΔP) and the
atmospheric pressure P∞ to the reservoir pressure PR.
Taking the ratio of these we have:
For , , and
, the right hand term in the last brace is less than 0.17
so we may expand the right had side as a binomial expansion. So we have
, or
22
We keep only the first two terms of the expansion and simplify, so we have
Which agrees with Harper-Bourne and Fisher’s β4 relationship for the case where Md = 1.
Tam’s theory differs from Harper-Bourne &
Fisher’s in the prediction of the higher frequency
peaks of BBSN. Harper-Bourne & Fisher’s theory
predicts that the higher peaks will be simple
harmonics of the fundamental. Tam’s theory predicts
that the spacing between peaks will decrease as peak
number increases.
Tam, Seiner and Yu (1986) make comparisons
with the higher peaks and find that Tam’s theory
provides better agreement with experimental
evidence. Tam’s theory of 1986 also accounts for the spectral broadening of the BBSN peak as the
observer moves to the downstream direction. By differentiating the equation for peak frequency by
convection velocity we find that if the variation in emitted sound frequency is taken to be due to
variation in the convection velocity, the spectral broadening is neatly accounted for.
The spectral width is a function of the angle of observation and further when the observer is directly
upstream the peak becomes quite narrow. This coupled with the observation that the screech
frequency is always lower than the BBSN suggests that screech may be a special case of BBSN.
Figure 2.7 – Screech tone frequency as the limit of
BBSN peak. Squares and diamond, Md = 2.0, Mj =
2.236. Circles and triangle, Md = 1.5, Mj = 1.802.
(Figure adapted from Tam, Seiner & Yu, 1986)
23
Experimental support for this view is shown in Figure 2.7. The open symbols show the broad-
band shock associated noise frequencies expressed as Strouhal numbers for a range of observation
angles, shown as cosθ. The lines are fit through these, and it can be seen that the screech frequencies,
depicted as solid symbols at θ = 180° (ψ = 0°) match the extended lines well, supporting the theory.
Tam, Seiner and Yu go on to propose two
prediction models for the screech fundamental.
One, fully analytical, but without closed form
solution, and a second, closed in form, but
including empirical assumptions that Uc = 0.7 Uj
and that the diameter near the end of the
potential core where the shear layer has
thickened will be 0.8 Dj. This second semi-
empirical relationship is valid for hot as well as cold jets and is given by:
Both relationships are shown in Figure 2.8. The solid line is the wholly analytical relation and
the dashed line is the semi-empirical relation.
Tam’s theory of BBSN and screech has been extended to account for forward flight effects in
Tam (1995). For BBSN the relationship is:
Which reduces to the prior relation as M∞ goes to zero, and if we take the case where ψ goes to zero we
come to a relationship for the screech frequency with forward flight effects:
Figure 2.8 – Strouhal number of fundamental
screech. (Figure adapted from Tam, Seiner & Yu,
1986)
24
This relationship has been compared to measured data for convergent nozzles up to M∞ = 0.4 by Norum
and Shearin (1986). The agreement was only fair, but the trend towards reduced frequency with
increasing M∞ was captured.
Since jet noise is generated by large scale structures, it is reasonable to think that introducing
more large scale structures will increase noise. Large scale structures can be induced by pressure
forcing from within the nozzle or near the nozzle lip.
It has been found for subsonic and supersonic jets
that such forcing generates a broad-band
amplification of the over-all spectrum including
BBSN. Broad-band amplification by forcing was first
reported by Bechert (1975) who forced cold high-
subsonic jets with a pure tone. Jubelin (1980)
extended this to shock containing jets. Figure 2.9
shows results for a supersonic jet with BBSN and
mixing noise. This broad-band amplification
introduces a difficulty for interpretation of noise reduction data. Since a screech tone introduces
periodic forcing near the nozzle lip, it also provides the consequent broad-band amplification. This
implies that if screech is eliminated there will be a consequent reduction in mixing and BBSN due to the
removal of the broad-band amplification alone. This reduction may be indistinguishable from any
reduction in BBSN or mixing noise independent of the elimination of the screech tone.
Since full-scale jet engines generally do not screech, the presence of screech in model scale jets,
and of the broad-band amplification of other noise components presents a difficulty in extrapolating
model-scale results to full scale. It is presently not settled whether the absence of screech in full-scale
Figure 2.9 – Broad-band amplification of mixing
noise and BBSN by tonal excitation. (Figure from
Jubelin 1980)
25
engines is due to physical scale (as compared to boundary layer thickness) to heating or to other factors
in the full-scale engine case.
2.6 Mixing Noise
Though this study has concentrated on the shock-related aspects of jet noise, this is always
mixed with the mixing noise which is common to both subsonic and supersonic jets. The study of mixing
noise dates from the early 1950’s when jet engines were making it plain to any observer just how loud a
high-speed jet could be. The founding theory was put forth in a pair of papers by Lighthill (1952, 1954)
in which he cast the governing equations for any liquid in the form of a wave equation in density, ρ:
where
is called the Lighthill stress tensor, , p and are the velocity, pressure and viscous stresses and is
the Kronecker delta. Since the left hand side of the equation propagates as a wave, it must be that the
right hand side must therefore be the source of the wave. By applying green’s functions to this wave
function Lighthill was able to arrive at a relation that acoustic power radiated from a jet should raise
with the eighth power of jet velocity. Sources in a jet must reasonably be assumed to convect with the
jet. This leads to an asymmetry in the radiated power. Moving sources will propagate sound more
strongly in the direction of travel. Ffowcs-Williams (1963) extended Lighthill’s theory to account for the
motion of the sources.
Refraction influences the directional distribution of sound from a jet. Any sound radiated by a
source within the jet will in general be turned by refraction as it crosses the jet boundary. The
propagating sound waves move with at the local speed of sound plus the velocity of the medium they
pass through. This has a strongest effect on sound propagating at an angle close to the downstream axis
26
of the jet. A wave propagating nearly axially lies nearly perpendicular to the jet. It lies across a gradient
in axial velocity. That part of the wave closer to the axis convects faster than the part of the wave
farther from the axis. This has the effect of turning the wave’s propagation direction farther from the
axis. For the typical case of a jet that is hotter than its surroundings the wave lies across a gradient of
temperature and sound speed as well. This also causes the part of the wave closer to the axis to travel
faster than the part farther out, so this refraction effect is stronger for hot jets than for cold ones. As a
wave propagates at an angle farther from the axial direction this refraction effect becomes weaker the
farther the wave turns, but refraction occurs for all angles except the direction parallel to the gradient.
A consequence of this refraction effect is that little sound propagates in the downstream axial direction
outside the jet. This creates a “zone of silence” in the downstream direction.
Lilley (1974) extended the Lighthill-Ffowcs-Williams theory further by accounting for this
refraction effect. The approaches of Lighthill is originally put forth, and as later modified by Ffowcs-
Williams and Lilley are referred to as acoustic analogy approaches. All these approaches were
developed against an understanding of turbulence which conceived of turbulent eddies as random and
uncorrelated phenomena. New and different views arose in reaction to the discovery of the organized
structure of large-scale turbulence by Crow and
Champagne (1971), and Brown and Roshko (1974)
discussed in section 2.4.
Tam argues that the lack of length scales and
time scales within a mixing layer tells us that the
spectra produced by the motions within that mixing
layer must be self-similar. In Tam, Golebiowski and
Seiner (1996) he examined a large number of spectra
for perfectly expanded supersonic jets and arrived at Figure 2.10 – Tam’s similarity spectra, F and G for
large and fine scale turbulence noise respectively.
27
two different similarity spectra which each dominate the acoustic emissions in different directions. They
are shown in Figure 2.10. One, shown as G in Figure 2.10, is associated with fine scale turbulence which
radiates in all directions equally, though it is refracted as described above. This spectrum dominates at
angles of ψ ≤ 90°. The second is associated with large-scale turbulence and it propagates most strongly
in a downstream direction. This spectrum dominates at angles ψ ≥ 125°. This large scale spectrum is
shown as F in Figure 2.10.
Any general spectrum, S, is then given by
Where F and G are the similarity spectra shown in Figure 2.10 for which F(1) = G(1) = 1, and fF and fg are
the peak frequencies of the fine scale and large scale spectra, and A and B are the peak sound levels.
The parameters fF and fg and A and B are functions of Vj/a∞, To/T∞ and ψ. At side and forward angles the
fine scale noise dominates and A is negligibly small. At aft angles the large scale noise dominates and B is
negligibly small. In an intermediate region both sources must be accounted for. Figure 2.11 shows the
variation in amplitudes with ψ. The large-scale levels increase linearly and then plateau at the after
angles. The fine-scale levels also rise linearly, but at a slower rate. At after angles they are dominated
by the large-scale noise.
Tam supplies empirical correlations for the magnitude parameters A and B. For large scale
turbulence, expressed in dB/Hz he has
where
.
and for fine scale
28
where
Figure 2.11 - Peak noise amplitudes. (a) large-scale noise. (b) fine scale noise Mj = 0.98, T0/T∞ = 1. (Figure
from Tam, 1998).
Tam’s theory has been further extended to subsonic jets and supported by measurements in
Tam (1998) and Tam, Viswanathan, Ahuja and Panda (1998). In this last the authors offer data on fF and
fL shown in Figure 2.12. The peak frequencies for the large scale spectra show little dependence on Mj
or temperature ratio beyond the scaling implicit in Strouhal representation.
29
Figure 2.12 - Peak frequencies for Tam's similarity spectra. (Figure from Tam, Viswanathan, Ahuja and
Panda, 1998).
2.7 Chevrons
When noise from jet engines first became a problem in the era of turbojet engines efforts to
reduce noise centered on enhancing mixing through the use of chutes, corrugations or even by dividing
up the engine exit into a number of physically separate exits. (See Gliebe, Brausch, Majjigi, Lee, 1995
and Gutmark, Schadow, and Yu, 1995). Between the 1950’s and 1980s corrugated nozzles became the
norm. For civil aircraft these were superseded by a change in the fundamental design of the engines.
Accelerating more mass to a lower velocity produced the same thrust while making dramatically less
noise and improving the thermodynamic efficiency at the same time. This was accomplished by
bypassing a portion of the air from the compressor around the hot section. Extracting more of the core
energy as shaft power rather than thrust allowed larger and larger compressors to compress a greater
mass of air increasing the bypass ratio until today we have commercial turbofan engines with bypass
ratios of greater than eight.
30
Military engines have come to bypass a portion of the air around the hot section as well, but the
large bypass ratios employed on civilian transport engines lead to substantial increases in engine
diameter. Since high-performance military aircraft are built around their engines this would mean an
increase in the aircraft cross sectional area and an increase in form drag that would be unacceptable so
military aircraft have come to have bypass ratios well below two.
As noise regulations have become more stringent civilian aircraft have begun adopting noise
reduction treatments even to the high-bypass engines in present use. Corrugated nozzles are heavy so
approaches have been tried which corrugate the shear layer without adding a large, heavy corrugated
nozzle. Initial studies employed tabs which protruded into the nozzle at its trailing edge. The effect of
tabs on the shape of the jet were studied by Bradbury and Khadem (1975). Tabs were found to eliminate
screech from supersonic jets by Tanna (1977). Ahuja documented noise reduction due to tabs with
Manes, Massey and Calloway (1990) after examining the flow-field effects with Brown (1989). Samimy,
Zaman, Reeder (1993) determined that introduction of streamwise vortices were responsible for the
changes in both subsonic and supersonic jets.
Small tabs normal to the flow direction were later replaced by larger delta tabs at an angle of 30
to 45° to the flow and still larger chevrons which typically have a small angle to the undisturbed flow
direction on the order of 5°. In the public literature these were both tested in a large systematic study
at NASA on subsonic coaxial jets from the kind of separate flow exhaust nozzles typical of civilian
aircraft. (Saiyed, Mikkelsen and Bridges (2000), Bridges and Wernet (2002)). Both delta tabs and
chevrons were found to reduce low frequency noise, but to increase noise at high frequencies. The
increased mixing imposed by the chevrons reduced velocities along the centerline and introduced a
radial component to the velocity that peaked in one direction in line with the chevron tips and in the
opposite direction in line with the valleys between chevrons. Chevrons reduced the level of TKE in the
jet mixing region, which had been the peak region of TKE for the baseline jet, but they introduced a new
31
region of elevated TKE in the first two diameters. Chevron with no angle to the undisturbed flow were
found to have little or no effect implying that a degree of boundary layer penetration is necessary for
the chevrons to work.
Callender, Gutmark, Martens (2004) performed a parametric far-field study of chevrons applied
to the core flow of a subsonic separate flow exhaust system and replicated the finding that chevrons
produce a low frequency benefit balanced by a high frequency penalty. They found that both of these
phenomena increase with chevron penetration and with increase in the shear velocity across the
chevrons. They found that for sufficiently high shear velocity the high-frequency effect comes to
dominate. A later study by the same authors (2008) applied near-field acoustic mapping to the same
chevron cases and found that The low frequency benefit occurs downstream in the region associated
with the jet mixing region (around six equivalent diameters), while the high-frequency increase occurred
much farther upstream at a distance of 2-3 equivalent diameters.
Bridges and Brown (2004) performed parametric testing on a single-flow convergent nozzle at
an acoustic Mach number of 0.9 both on a heated and unheated jet. The peak noise levels were the
same for both cases indicating that jet velocity is the critical parameter. The directional distribution of
sound was altered by temperature by virtue of increased refraction across the shear layer. They showed
that the trends with increasing chevron penetration are the same for the single hot jet as Callender
found them to be for coaxial jets, shorter potential core, acoustic benefit at low frequencies and
acoustic penalty at high frequencies. They found these trends to hold for heated jets as well as
unheated. They further found that changing chevron length while holding penetration and chevron
number constant makes no significant difference in the acoustic behavior or much difference in the flow
field.
Opalski, Wernet and Bridges (2005) applied stereo PIV to a subset of the same nozzles and
found that changing the length of a chevron when the number of lobes and the penetration is held
32
constant has only a small effect on the downstream flow field. They found that for the same acoustic
Mach number the temperature of the jet did not significantly change the trends among the nozzles.
Alkislar, Krothapalli and Butler (2007) applied both chevrons and microjet blowing to a Mach 0.9
jet from a convergent nozzle. For chevrons they found the same trends with respect to far-field sound
as above. They also employed a phased array to map the source locations and found that the
application of chevrons moves the apparent source location of each frequency upstream. They also
applied stereo PIV and found that chevrons increase turbulence in the initial shear layer peaking at x/D =
2 which matches the location of peak high-frequency noise source.
Chevrons were applied to an underexpanded jet (Mj = 1.18) from the core nozzle of a
commercial type separate-flow exhaust nozzle with centerbody by Rask, Gutmark and Martens (2006,
2007). Tests were run with and without secondary flow from the fan nozzle. Shock cell spacing was
reduced and BBSN peak frequencies were increased by chevrons. For the no secondary flow case shock
noise was increased, but when secondary flow was applied shock noise was reduced. Chevrons reduced
the axial extent of the source region. For the no secondary flow case chevrons increased TKE near the
nozzle exit and reduced the TKE level downstream.
2.8 Fluidic Injection
Jet mixing enhancement and noise reduction has been attempted by injecting a variety of fluids
into the jets near the nozzle exit. Different embodiments of this approach have variously been called
“fluidic injection,” “microject injection,” or “fluidic chevrons.” Henderson (2010) provides an overview of
the literature on injection by a number of fluids including the air injection that concerns this
dissertation.
When examined locally or in the limit of large main jet radius, the behavior of a microjet around
the exit of a nozzle behaves as a jet in cross flow. The penetration of round jets into a supersonic cross
33
flow have been found to scale most strongly with momentum ratio,
where the cross
flow in our case is the main jet indicated by j and the microjet condition is indicated by μ. The
penetration, , is weakly dependent on Mj and not dependent on the pressure ratio or microjet
Mach number if J is held constant. This scaling is consistent with the relationship for a subsonic jet in
subsonic cross flow which is
where r is the ratio of velocities. (Papamoschou and
Hubbard 1993).
A detailed RANS study Chauvet, Deck and Jacquin (2007) shows that each microjet induces a pair
of counter-rotating vortices which are driven by their mutual induction toward the main jet axis. As
they penetrate deep enough they move toward the pair from the neighboring jet until come under the
influence of a new partner. When the influence of the new partner becomes strong enough the new
pairings are driven outward by their mutual induction. The resulting radial trajectory of each vortex is
then a motion into the high-speed side of the shear layer, followed by an outward motion into the low
speed side.
Circular microjets have been shown to increase the length of potential by reducing mixing in
subsonic jets (Alkislar, Krothapalli and Butler, 2007; Arakeri, Krothapalli, Siddavaram, Alklislar and
Louranco, 2003; Laurendeau, Bonnet and Delville, 2006; Aberg, Szasz, Fuchs, Gutmark, 2007). The effect
on turbulence intensities is not consistent among the studies. Arakeri et al., Laurendeau, et al. and
Callender, Gutmark and Martens (2007) have shown a reduction in peak TKE when fluidic injection has
been applied. Alkislar, Krothapalli and Butler (2007) and Alklislar, Krothapalli, Lourenco, Butler (2005)
found an increase in TKE levels. The differences in the reported effects warn that the results well may
depend on number of injectors, the angle of injection, microjet diameter, or other factors.
The influence on the flow field of microjets and chevrons have been compared by Alklislar with
Krothapalli and Butler in 2007, and in a sole author paper in 2008. High quality stereo PIV has been
taken in planes normal to the jet axis and the vortex pairs produced by chevrons or microjets were
34
tracked as they evolved downstream. The microjet case produced vortex pairs that were closer to the
high-speed side of the shear layer than those produced by the chevrons. Microjet produced vortices
persisted for several diameters, while chevron produced vortices dissipated more quickly, but chevrons
produced vortices were more effective at entraining mass into the shear layer. One should be cautious
about generalizing from a comparison between a single chevron geometry and a single injection
arrangement, but Alklislar observes that the sense of the rotation of the microjet vortices was opposite
that of the chevrons leading to an argument about the difference arising out of the mutual induction
between members of a vortex pair. The chevron vortex pairs were driven radially outward by mutual
induction while the microjet pair were driven radially inward.
Injection angle, measured from the jet axis, has a role similar to penetration depth for chevrons.
Callender, Gutmark and Martens (2007), Camussi, Guj, Tomassi and Sisto (2008) found that increasing
this angle decreases low frequency noise, but increases high frequencies as measured in the far field.
Angles from 45° to 60° have been shown to produce a net reduction on an OASPL basis. Callender et al
further found that much of the high frequency penalty is due to the noise of the microjets themselves.
Many studies do not separately control microjet injection pressure and mass flow rate so it is somewhat
difficult to separate these effects. Zaman (2007) increased microjet pressure while decreasing mass
flow and microjet diameter and found that this could reduce the noise radiated in the peak noise
direction. The largest peak noise reduction by microjets reported for subsonic cold jets was 1.4 dB with
a microjet mass flow of 1.6% of the main jet flow with 16 microjets with diameters of 2% of the main jet
diameter (Castelain, Sunyach, Juve, Bera, 2006 and 2008). Microjet numbers from 3 to 36 have been
examined, and it is found that with the largest numbers, the microjets interfere with one another,
spoiling any benefit.
Microjet injection into supersonic jets has been found to reduce screech, and broadband shock
associated noise. (Krothapalli, Greska and Arakeri, 2002) The highest reductions reported for supersonic
35
cold jets was 8 dB with a microject injection pressure of four atmospheres and a microjet mass flow of
1.2% of the main jet (Henderson and Norum, 2008).
Fluidic injection in full-scale engine tests has shown the capacity to reduce noise (Greska,
Krothapalli and Arakeri, 2003 and Greska, Krothapalli, Burnside and Horne, 2004). At a jet Mach number
of 0.9 noise reductions of two dB were attained using 2.3% of a YJ97 engine’s mass flow. At a
supersonic condition 1 dB was attained with 1% mass flow.
36
Chapter 3 – Methodology
3.1 Models
3.1.1 Baseline Nozzles
Four baseline C-D nozzles were constructed for this study. They have area ratios of 1.067, 1.181,
1.231 and 1.295, giving design Mach numbers (Md) of 1.3, 1.5, 1.56 and 1.65 respectively. The nozzle
geometries are shown in Figure 3.1.
The Md = 1.56 model has a throat diameter of 2.040” and has an outer contour determined in
consultation with Volvo Aero Corporation to represent the outer flow contour of the aft fuselage and
nozzle outer contour of a representative aircraft. This nozzle is mounted in a concentric jet rig with a
concentric secondary flow nozzle surrounding it. This secondary nozzle is to provide a secondary jet
simulating the flow over the outer contour of an aircraft. This is an imperfect forward flight simulation
because the secondary jet is smaller than would be desired for full forward flight simulation. To
properly simulate forward flight a secondary jet mist be much larger than the inner jet so that the inner
Figure 3.1 – Nozzles simulating the exhausts of tactical jets. (a) Cross sections of three nozzles without
forward-flight simulation, (b) Cross section of the Md=1.56 nozzle with the secondary flow nozzle to simulate
forward flight.
Md = 1.30
Md = 1.50
Md = 1.65
Md = 1.56
37
jet’s region of interest lies wholly within the potential core of the secondary jet. The fact that this jet is
not that large means that the shear layers of the outer and inner jets will merge at some point, but
limited forward flight simulation is achieved over the axial range where the inner and outer shear layers
remain distinct. Another limitation imposed by the size of the secondary shear layer is acoustic. If a
secondary jet is large enough, its acoustic spectrum will be shifted far enough to lower frequencies that
its noise can be separated from that of the primary jet spectrally. For jets closer in size as are used here,
this is not possible. For this reason acoustic measurements were limited to secondary flow Mach
numbers for which the sound level of the secondary jet is negligible when compared to the primary jet
noise.
The Md = 1.56 nozzle has a diameter upstream of contraction of 3.123”, a contraction section
angled 33.16° towards the jet centerline and a throat diameter of 2.040”. The radius of curvature at the
throat is 0.020” giving a very sharp throat. The expansion section axial length is 2.296” and the lip
thickness at the trailing edge is 0.020”. The outer diameter of the nozzle at its greatest is 4.25”. The
inner diameter of the secondary flow nozzle is 5.8” and the secondary flow nozzle is very slightly
convergent at the exit.
The three other baseline nozzles with Md = 1.3, 1.5 and 1.65 are identical to one another save
for the exit diameter, De. The diameter upstream of the convergent section is 3.123”. The convergent
section is 0.384” in axial length and the throat diameters are all 2.640”. The throat radius of curvature is
sharper than the one on the Md = 1.56 nozzle. The radius was specified to the machinist as a sharp
corner so the sharpness is limited only by the capacity to machine the steel. The divergent section was
2.896” in axial length and the exit diameters for the three nozzles were 2.728”, 2.868” and 3.006” for Md
= 1.3, 1.5 and 1.65 respectively. The thickness of the nozzle lip was 0.020” for each nozzle. The details
of the nozzle shape are shown in Figure 3.2. No secondary flow was applied with these three nozzles
38
and the exit to the secondary flow was covered by a shroud to prevent the presence of the opening to
produce any cavity tones or otherwise influence the acoustic measurements.
Figure 3.2 - Nozzle geometry for the Md = 1.3, 1.5 and 1.65 baseline nozzles.
3.1.2 Chevron Nozzles
Two chevron geometries were studied. Unfortunately the two geometries fit different nozzles
with different design Mach numbers so the results are not perfectly comparable. The Md = 1.5 nozzle
has a cap which fits over the external surface, supporting twelve chevrons extending from the trailing
edge lip. When the chevrons are installed, the internal flow lines of the nozzle are unaltered. The inner
surface of the chevrons are flush and tangent with the inner contour of the nozzle at the nozzle’s trailing
edge. This chevron design is based on chevrons tested at larger scale by GE, though the results were not
published. The inner and outer flow lines of the chevrons are circular arcs. The profile of the chevrons is
approximately triangular with a tip half angle of 35°. The axial length of the chevrons is 0.696”. The
chevrons penetrated 0.098” into the jet. The chevrons have their inner surfaces beveled to that there is
a sharp edge where the bevel meets the outer surface. There is a gap between the chevrons comprising
4.75° of circumference. This gap simulates the gaps between flat panels making up the divergent
section of a real engine nozzle. The design of the Md = 1.5 chevrons is shown in Figure 3.3.
39
The second chevron geometry was intended for testing with secondary flow on the Md = 1.56
nozzle. Since the baseline Md = 1.56 nozzle already had important outer contours it was not possible to
apply the chevrons by way of a cap affixed to the outside of the nozzle. Instead an entirely new nozzle
was constructed with internal flow lines identical to the Md = 1.56 baseline nozzle (2.040” throat, 2.263”
exit) and outer flow lines nearly so. In order to provide sufficient strength to support the chevrons it
was necessary to increase the thickness of the material near where the baseline nozzle ended and the
chevrons began. It was necessary to insure that the chevrons on this project did not use any intellectual
property from GE and GE’s chevron design so it was decided to copy the chevrons for this nozzle from a
published chevron case. The case chosen was the SMC009 nozzle used at NASA Glenn Research Center
on a subsonic convergent nozzle by Bridges, Wernet and Brown (2003). The nozzle had twelve chevrons
The chevrons extended 0.508” axially beyond the baseline nozzles exit plane and penetrated 0.099” into
the jet. Unlike the Md = 1.5 chevrons the Md = 1.56 chevrons are beveled on the outside so that the
bevel makes a sharp corner with the inside surface of the chevron. The Md = 1.56 chevron nozzle is
shown in Figure 3.4.
Figure 3.3 – Chevron nozzle arrangement. A cap holds chevrons to the existing nozzle trailing edge. The
internal flow lines of the nozzle are unmodified, (a) Exploded view, (b) Chevron detail views, (c) Cross-
section view of cap alone.
(
c)
Baseline nozzle Md = 1.5
Chevron cap Shroud
(
a)
40
3.1.3 Fluidic Chevron Nozzle Configurations
Two configurations of fluidic injection with microjets were tested on the Md = 1.5 nozzle in
attempts to create noise reductions similar to those produced by chevrons. Both of these aim to
introduce streamwise vortices by blowing into the shear layer. Chevrons do this, but they also impose a
thrust penalty throughout the flight envelope, including those portions of the flight in which noise is of
reduced concern. Fluidic injection with microjets holds the prospect of a technique that can be turned
on in noise sensitive portions of the flight, such as take-off and landing, and then turned off for the
remainder of the flight, thus substantially reducing the performance impact on the over-all flight profile.
The first configuration examined follows a blowing geometry used by Callender, Gutmark and
Martens (2007) in which paired jets with opposite yaw angles were injected into subsonic primary jets
with centerbodies. An analogously paired arrangement is shown in Figure 3.5. In this configuration six
pairs of tubes are applied with each member of a pair angled towards its partner at an angle of 20°. All
the tubes are also angled toward the jet axis at an angle of 36°. This configuration is referred to as 36-
20.
The second configuration examined is after Alkislar (2009) who used jets with no yaw angle, but
pitched deeply into the primary jet. These he employed alone and also with chevrons on a jet with Mj =
0.9. A similar configuration is shown in Figure 3.6. The tubes are evenly spaced and have no yaw angle
whatsoever. They are all pitched toward the jet axis at an angle of 60°. The injection tubes are
Figure 3.4 – Md = 1.56 chevron nozzle. (a) Cross-section view of chevron nozzle. (b) Detail of chevron shape.
a) b)
41
displaced axially 0.6 inches from the nozzle exit. This was done to make room for the addition of
chevrons in order to examine the effect of chevrons and injection together. The configuration with
chevrons and blowing together is outside the scope of this dissertation and will not be discussed here.
This configuration is referred to as 60-0.
Both fluidic injection arrangements were tested on a convergent-divergent nozzle with a design
Mach number of 1.5 and flow lines typical of a variable-geometry nozzle from a high-performance
military aircraft.
Figure 3.6 – Convergent-divergent nozzle with 12 fluidic injection tubes, with 60° pitch and 0° yaw. This
configuration is referred to as 60-0.
Figure 3.5 – Convergent-divergent nozzle with 12 fluidic injection tubes, with 36° pitch and 20° yaw. (a)
perspective view. (b) upstream view. This configuration is referred to as 36-20.
(
a)
(
b)
42
3.2 Experimental Facility
When measuring sound waves it is important to avoid multi-path interference. One is trying to
measure the sound that travels directly from the source under study to the microphone. One wishes to
avoid contaminating this measurement with noise from other sources, of course, but the more subtle
issue is that one wants to avoid contaminating the measurement with noise from the source under
study that has arrived at the microphone by a route other than the direct one. One wants no sound that
has reflected from the laboratory wall, for example. In order to avoid this multi-path interference as
well as to shield out sources other than the source under study, acoustic testing is often carried out in
an anechoic chamber, which is a test chamber in which the walls, ceiling and floor are treated with a
covering which limits the reflection of sound.
For the acoustic testing in this dissertation, all the models were mounted in the University of
Cincinnati’s Aeroacoustic Test Facility (UC-ATF) which is an anechoic room 24’ x 25’ x 11’ which has been
acoustically treated to be anechoic down to 500 Hz. This chamber has removable anechoic tiles on the
floor which can be removed when anechoic conditions are not needed. This allows ample floor space to
install a large computer-controlled three-axis traverse upon which near-field arrays, measurement
probes or PIV cameras and laser may be mounted.
Within this chamber there is a coaxial nozzle rig which supports the models. This rig includes
flow straightening hardware and screens feeding into a stilling chamber for each flow where stagnation
properties are measured. From each stilling chamber there is a smooth contraction to the nozzle inlet.
For the Md = 1.56 model, the nozzle is mounted to the inner, primary supply which is fed from a
1” piping system connected to a 1500psi air supply and passes through a steam-to-air heat exchanger
which at the mass flow rates appropriate to this nozzle has been found to be able to heat the air to a
stagnation temperature of 367K giving a temperature ratio of 1.22.
43
For the Md = 1.56 nozzle, on which secondary flow effects are studied, an outer nozzle has been
fitted to the outer, secondary supply. This outer, secondary flow nozzle is very slightly convergent in
order to assure that the throat is at the exit. The outer, secondary flow is fed by a 6” piping system
connected to a 150psi air supply. In this configuration the secondary flow is not heated. Secondary flow
stagnation temperatures measured in the rig’s stilling chamber are 300K. A total pressure survey at the
secondary flow exit shows that the exit flow is nearly uniform to a radius of 2.9”.
For the Md = 1.3, 1.5 and 1.65 nozzles no secondary flow effects are intended and the secondary
flow exit can be covered by a shroud to prevent the open cavity from influencing the acoustics. The
models are mounted to the primary flow exit which is connected by a 6” piping system to the 1500psi air
supply. In this configuration the flow is heated with a steam-to-air heat exchanger, but at these large
mass flows the system can only heat the air enough to make up for the decompression cooling so the
stagnation temperatures measured in the stilling chamber are typically 300K.
3.3 Instrumentation
3.3.1 Far-field Acoustic Measurement
Far-field acoustic measurement provides the ultimate test of a noise reduction approach. The
ultimate question: “Is it less noisy?” is usually assessed by an observer on the ground near the airport
and far-field acoustic measurement is the sub-scale equivalent measure that answers the same
question.
Sound from jets has a directional character. Different components of jet noise tend to
propagate in different directions. Refraction across the jet’s shear layer tends to turn propagating
sound away from the downstream axis so all components of jet noise become weaker when observed
from near the downstream axis. Mixing noise from small scale turbulence tends to propagate in all
directions. Mixing noise from large-scale structures tend to propagate most strongly into the aft
44
quadrant. Noise associated with shocks in the jet tends to propagate most strongly into the upstream
quadrant.
Since the noise measured changes with the direction of observation, we define a parameter ψ
to be the direction to the observer, or in a laboratory setting, the angle to the far-field microphone. We
measure ψ from the upstream axis as shown in Figure 3.7, so a position directly downstream of the
nozzle exit is ψ = 180° and a position in the nozzle’s exit plane is ψ = 90°. Since we are dealing with jets
which are nearly symmetrical about the nozzle axis this one parameter is sufficient. Chevrons and
blowing are not completely symmetrical, of course, but when viewed from far away, as from the
distances at which far-field measurements are taken, the small variations between chevron tip and
chevron valley, or the equivalent variations around a blowing jet are negligible. The proper definition of
the acoustic far-field includes the requirement that the observer be far enough away that the acoustic
sources may be considered to be compact. The spatial distance between sources should be small so
that the source region may be approximated by a point. This presents a practical difficulty in a
laboratory setting. The size of the test chamber is limited and this limits how far away the far-field
microphones may be placed.
For far-field acoustic measurements the anechoic floor tiles are installed in the test chamber
and eight or ten B&K ¼” microphones are mounted in a permanent microphone array which positions
them along a circular arc 149” from the center of the nozzle exit plane. The microphone holders are
positioned at ψ = 35°, 50°, 70°, 90°, 100°, 110°, 120°, 130°, 140° and 150° where ψ is defined as the
angle from the upstream direction along the axis of the jet. Older measurements were taken with eight
microphones, in which case the microphones at 100° and 130° were omitted. Measurements at ψ < 35°
are not practical because the piping system supplying the test model blocks the line of propagation.
Measurements at ψ > 150° risk placing the microphone in the jet flow as it spreads against the
downstream wall of the chamber.
45
Figure 3.7 - Microphone locations for far-field and near-field acoustic measurements.
The microphones are sampled at 200 kHz for 10 seconds giving a Nyquist limit of 100kHz to
avoid anti-aliasing. In earlier measurements the microphones are used with their grid caps attached and
the effect of the grid caps accounted for by a correction curve provided by the manufacturer. The grid
cap correction becomes large above 80 kHz so normally spectral data from 0.5 to 80 kHz have been
used. Blocks of 4096 samples are individually converted to spectra giving a frequency resolution of 50
Hz and these spectra from all blocks are then averaged. Whenever possible measurements of chevron
or blowing configurations were taken back-to back with measurements of the corresponding baseline
case. This was made possible by the design of the models to allow rapid changes. This eliminated day-
to-day variations from the comparison and made atmospheric correction unnecessary in most cases.
Atmospheric correction and scaling apply a constant gain to any given frequency bin, so they apply a
constant addition or subtraction in dB. If the desired measurement is a comparison between chevron
and baseline cases, the scaling and atmospheric correction will affect both spectra equally.
46
When it was necessary to scale the data atmospheric absorption was accounted for by use of
ISO 9613-1 (1993). This standard accounts for atmospheric absorption and accounts for variations in
atmospheric temperature, pressure and humidity. These atmospheric parameters were recorded during
the test in order to allow for the application of ISO 9613. The resulting lossless spectra were then scaled
to 100 Dj by the geometric 1/r2 law and then the spectra were nondimensionalized in both frequency
and amplitude. Nondimensionalization in frequency is achieved by multiplication by Dj/Uj giving Sj a
Strouhal number based on fully expanded jet diameter. The amplitude is nondimensionalized by
dividing the SPL by the frequency spacing do eliminate the variation due to frequency bin size. This
yields dimensional amplitude in SPL/Hz. This amplitude is the nondimensionalized by multiplying by
Uj/Dj giving amplitude in SPL/Stj. Scaling to full scale is then the reverse process. The spectra are
redimensionalized using the value of Dj for full scale. The observer radius is scaled from 100 Dj to the
desired value by the geometric 1/r2 law and atmospheric losses are reintroduced using ISO 9613 using
whatever atmospheric conditions may apply. The default conditions are standard day temperature and
pressure and 70% humidity.
3.3.2 Near-field Acoustic Measurement
If Far-field measurement answers the question “Is it less noisy” then near-field measurement is
used to answer more of the “Why?” questions. We would like to know how noise is produced and how
chevrons or blowing change this production. Part of this investigation is source location, ie. “Where is
the sound coming from?” or “Where is some particular frequency of noise coming from?” When the
source location of a particular frequency of noise has been identified, one can use flow measurement
techniques described in the following sections to see what is happening in the flow at the source
location. When examining chevrons and blowing, near-field measurements directly show how source
locations are changed by the application of chevrons or blowing.
47
Since near-field acoustic measurements are chiefly concerned with the spatial distribution a
sizable array of measurement locations is needed. Figure 3.7 shows the measurement locations relative
to the Md = 1.5 nozzle. By measuring acoustic spectra at each of these locations contour maps may be
constructed of the overall sound pressure level or for particular frequency bands. These intensity maps
will be strongest nearest the sound source and the shapes of the high-intensity lobes give an indication
of propagation direction.
It is necessary to keep the microphones out of the jet shear layer so that flow over the
microphone itself does not generate noise and contaminate the measurement. The measurement
location nearest the nozzle exit is in the exit plane of the nozzle, but is one inch radially outside the
nozzle lip inner surface. Since the jet spreads as it moves downstream a radial location so close to the
centerline will be within the flow for regions farther downstream. To avoid this, the array is installed at
an angle to the axis so that its downstream end is farther from the jet axis. The angle of divergence
from the jet axis is 10°.
Multi-path interference is not a significant concern for near-field measurement because the
microphones are close to the sources. The path length for a wave to travel to a particular microphone is
an order of magnitude smaller than the distance for a wave to travel to the floor, reflect, and then travel
to the same microphone. Since the sound pressure level falls of faster than 1/r2 the reflected wave will
be negligibly weak compared to the wave traveling directly to the microphone. Since multipath
interference is not a concern, near-field measurement may be taken without the anechoic tiles on the
floor of the test chamber. These tiles are removed and the large three-axis traverse is installed below
the jet.
A rake array with thirty-two microphones spaced at one inch intervals is mounted on the
traverse and positioned along the inner-most row of positions shown in Figure 3.7. The upstream
microphone is placed one inch radially outward from the inner surface of the nozzle exit and aligned
48
axially so that it lies in the nozzle exit plane. The rake is angled 10° from the jet axis. During acquisition
five seconds of data are acquired and the computer-controlled traverse moves the rake one inch in a
direction normal to the row of microphones. This process repeats for 13 locations so that a region of 32
inches by 12 inches is swept out. This region is shown by an array of circles in Figure 3.7. If a greater
axial length is to be surveyed the rake is then moved to a position in which the upstream-most
microphone begins in the place where the downstream-most microphone began before and the process
is repeated sweeping out another 32 inch by 12 inch region shown by an array of “x”s in Figure 3.7. The
combined grid thus gives a 63 inch by 12 inch contour plot of OASPL or SPL.
Earlier measurements taken when only eight microphones were available were taken by
mounting the eight microphones at six and one quarter intervals on a rake array. It was then necessary
to move the rake five times along its own length by steps of one and one quarter inch to fill in the
missing locations before the traverse moved radially outward. This obviously made the near-field
measurements take five times as long and limited the amount of data acquired.
Once acquisition was complete the resulting acoustic files were processed in a manner identical
to the far-field acoustic records. Blocks of 4096 samples were converted to spectra and then averaged
to give a spectrum at each location with 50 Hz spacing. Either OASPL or SPL at a chosen frequency were
then plotted as contour plots to find the regions of higher noise, which were taken to be near the source
locations within the jet.
3.3.3 Shadowgraph
The Shadowgraph technique is a quick and easy nonintrusive flow visualization technique which
provides vivid depiction of flows with high density gradients. Shadowgraph and Schlieren techniques
have traditionally been used to image shock containing flows for over one hundred years. They give
immediate information on the position and angles of shocks and Prandtl-Meyer expansion fans and the
49
Schlieren technique may be integrated to arrive at density values. The turbulence may be readily
observed in instantaneous images, or averaged images may be used to bring out the stationary features.
Both techniques were applied to this project, but the Schlieren technique is more complicated,
more sensitive to alignment and provides a smaller field of view, so it was abandoned in favor of the
simpler and more robust shadowgraph technique which gives a large field of view.
An Oriel 66056 arc lamp was used for illumination. The light from the lamp was passed through
a pin-hole orifice in order to approximate a point source of light. The center of the orifice was placed at
the seventy-two inch focal length of a twelve-inch, parabolic, first-surface mirror. This renders the
reflected light rays parallel creating a twelve-inch diameter beam of collimated light. The light, orifice
and mirror were placed on heavy optical stands in such a way that the collimated beam passes through
the jet at an angle normal to the jet axis. The nozzle was allowed to intrude slightly into the collimated
beam so that its shadow shows near the edge of the resulting images. A second twelve-inch, parabolic,
first-surface mirror with a seventy-two inch focal length was placed on another heavy optical stand on
the other side of the jet in such a way that the collimated beam filled it completely and it focused the
reflected beam to a point. A camera was placed on near the focal point of the focused beam to capture
the resulting image. The camera used was a LaVision Imager Intense cross-correlation CCD camera with
1376 x 1040 pixel resolution and 12-bit intensity resolution. This gave a spatial resolution on the order of
0.01” or 0.004 throat diameters. A 28-300 zoom lens was mounted to the camera which allowed
optimization of the field of view. The aperture was left completely open and exposure was controlled
by mounting neutral-density filters. One hundred images were taken of each condition.
Individual images reveal details of the turbulence in the shear layer and reveal some of the
initial shock-cell structures, but the presence of the turbulence obscured later shock cells. This is
because the shadowgraph technique is line integrating. As a ray of light in the collimated beam passes
through density gradients in the jet, corresponding gradients in refractive index cause the beam to turn.
50
Regions of high gradient cause the light to turn leaving a dark region where the undisturbed ray would
have arrived. Since strong turbulence can create this effect a ray passing through the middle of the jet
may be influenced at the first shear layer before it reaches any shock structures inside. The turbulence
around the circumference of the jet may obscure any details in the interior of the jet. This may be
avoided by averaging images. Since the turbulent structures are randomly oriented, an averaged image
will tend to average out their effects. This leaves only the influence of stationary features visible, and
makes the relatively stationary shock cells clearly visible.
3.3.4 Particle Image Velocimetry
Shadowgraph gives clear views of the stationary structures in the flow, giving high resolution
spatial information about the position and angles of the shocks and Prandtl-Meyer fans, but it is
otherwise qualitative. Particle Image Velocimetry provides a quantitative measure of velocities in a
planer section of the jet while being only minimally invasive. It is a technique which may be described as
almost noninvasive. The qualification “almost” being required to acknowledge that microscopic seed
particles are added to the flow to serve as tracers for the fluid motion.
PIV is the principal tool used to study the details of the flow field. It is a technique used to
measure two or three components of velocity simultaneously within a planer region illuminated by a
laser sheet. Seed particles within this plane are illuminated by the laser and their motions are tracked
by one or more cameras. A one camera configuration yields velocity components within the plane while
a two camera system arranged with both cameras capturing the same region in stereoscopic fashion
yields three components of velocity.
Two PIV arrangements were used in this dissertation. In both arrangements the anechoic tiles
were removed from the floor of the test chamber and the large computer-controlled traverse was
installed below the jet. Mounting the laser sheet forming optics and the cameras on the same traverse
51
allows the system to be moved undisturbed to multiple locations saving the time required to align and
calibrate between locations.
For measurements in a plane containing the axis of the jet a two dimensional PIV arrangement is
used to capture axial and radial velocities. This arrangement is shown in Figure 3.8. An 19 inch by 23
inch optical breadboard is rigidly fixed to the second level of the three axis traverse allowing it to be
translated in the direction parallel to the axis of the jet. A 500 mJ New Wave Research nd:YAG double-
pulse laser is mounted on this breadboard so that it projects its beam parallel to the jet axis pointing
upstream. Also on the breadboard are a turning mirror to turn the beam vertical, focusing optics to
adjust the beam waist to occur as the beam crosses the jet centerline and a cylindrical lens to spread the
beam into a sheet. If left uncovered the laser and optics would become covered in oil. To prevent this
the entire optical arrangement is covered by a shroud with a hole cut for the light sheet to escape. This
hole is then covered with a piece of high-quality glass which may be removed and cleaned between
tests.
The camera or cameras are supported by a 90mm x 90mm Bosch rail which is mounted on the
vertical third element of the traverse so that it may be moved in three axes. The camera or cameras
used are LaVision 1376 x 1040 12-bit PIV cameras. These are usually arranged to point at right angles to
the light sheet. When two cameras are used they are arranged such that their fields of view overlap
only slightly so that the second camera is used to capture a larger total field of view, not as in a stereo
arrangement where both cameras point at the same field of view from different angles.
Interchangeable lenses and in some cases zoom lenses are used to adjust field of view.
The flow is seeded with olive oil droplets with diameters on the order of 1 μm. For coaxial jets a
number of seeders may be used and independently controlled. A single seeder feeds the main jet
stream and as many as four seeders feed the secondary stream at top, bottom and both sides.
52
The distinguishing characteristic of PIV cameras is the ability to take pairs of images closely
spaced in time. The cameras used in this study are capable of taking pairs of images separated by a dt of
only 0.6 μs. Any subsequent image pair must wait another 200 μs giving a sampling rate of 5 Hz, but
allowing high speeds to be measured.
Figure 3.8 - Two-dimensional PIV arrangement for capturing PIV in axial planes.
In addition to this typical streamwise two-dimensional arrangement a special case is used to
measure velocities very near the nozzle exit. The complicating issue with near-nozzle measurement is
that light from the laser sheet reflected from the nozzle itself will be much brighter than the light
reflected from the seed particles. This very bright light saturates the camera and may in some cases
even burn pixels out of the camera’s CCD. To avoid this a single camera is used and instead of orienting
the camera to view the light sheet at a normal incidence the camera is turned until the view from the
left edge forms a plane parallel to the nozzle exit plane. When the nozzle lies within the field of view in
such an orientation both the near and far edges of the nozzle exit appear to overlap. The location of the
nozzle exit is photographed on order to establish the camera position, and then the traverse is moved a
53
known axial distance far enough downstream that the nozzle does not appear in the field of view. In
this position no light reflected from the nozzle will reach the camera’s CCD. With this orientation of the
camera it is possible to measure to within a small fraction of an inch from the nozzle exit.
For measurements in a plane normal to the jet axis of the jet a three dimensional stereo PIV
arrangement is used. In a stereo PIV arrangement two cameras have oblique views of the same field of
view. Each camera’s images are processed into two components of velocity normal to the camera’s line
of sight. These two 2D measurements are then resolved into one 3D measurement providing all three
components of velocity.
Since the goal is to obtain velocities normal to the light sheet as well as the two within it, it is
necessary to change the focal length of the beam so that the beam waist is no longer near the
measurement region. An infinite focal length was used thickening the beam in the region where it
crosses the jet. The thicker light sheet is necessary to avoid lost tracer particles. Those seed particles
which pass completely out of the light sheet between images will not be usable to the PIV algorithm.
Thickening the light sheet extends the time any given seed particle is illuminated as it is transported
downstream, thus reducing the number of lost seed particles. The cylindrical lens is then rotated 90° so
that the light sheet lies in a plane normal to the jet axis.
A second vertical traversing stage is added to the end of the y axis stage and a 90mm x 90mm
section of Bosch rail is supported between the two vertical stages. One end is supported with a hinge
joint and the other end is simply supported so that the heights of the vertical stages can be adjusted
independently without putting strain on the system. When in position the Bosh rail is level, but it
deviates from level during adjustment.
Two cameras are mounted on the Bosh rail so that they each point in a horizontal plane at an
angle of 45° from the jet axis and so that their fields of view overlap completely. In order to have a
skewed plane be in focus it is necessary to install a Scheinflug adapter between the camera and the
54
focusing optics. This adapter tilts the lens and changes the angle of the focal plane. Without it only a
small portion of the field of view will be in focus when the camera faces the light sheet at a significant
angle. The arrangement for taking stereo cross planes sufficiently far from the nozzle is shown in Figure
3.9.
Figure 3.9 - Stereo PIV arrangement for cross-stream planes.
For planes sufficiently far downstream this arrangement is oriented to that the cameras point
downstream. This is desirable so that light reflected off the nozzle and associated hardware do not
contaminate the images. For the most upstream planes, this is not possible because the presence of the
nozzle obstruct the line of sight to the measurement plane. For these cases the arrangement is oriented
55
so that the cameras point upstream, and additional measures must be taken to avoid contamination by
hardware reflections.
The first and best way to avoid hardware reflections is to not have any hardware lying along any
line of sight of either camera. This is not possible for the most upstream cross planes. The next best
way to avoid hardware reflections is to avoid illuminating the hardware. Great care must be taken not
to allow direct illumination of the hardware. When the laser sheet was near the nozzle an extension on
the laser shroud was added to raise the exit of the sheet by 20 cm. The exit from this raised shroud was
covered with a pair of knife-edge blocks so that only a very narrow opening was available for the light
sheet and by making the opening from knife edges reflections from the sides of the slot were
eliminated.
This extended shroud served to eliminate direct illumination of anything outside of the plane of
the light sheet. The problem of indirect illumination remained however. Some light reflects off of the
seed particles in a direction towards the hardware and this reflected light can then make the hardware
visible, contaminating the PIV images. No amount of masking will avoid this problem of indirect
illumination by the scattered light from the seed particles. In order to mitigate this problem the
hardware is painted with an enamel paint saturated with rhodamine B. Rhodamine B is a
phosphorescent molecule which has an absorption peak at 543 nm, which is broad enough to make it a
good absorber at the 532 nm wavelength of the laser illumination. The molecule then fluoresces over a
broad range at wavelengths greater than 550 nm. By mounting narrow 532 nm band pass filters on the
cameras the emissions are eliminated from the PIV images and the absorption reduces the amount of
light reflected from the hardware. It should be noted that while the rhodamine B reduced the intensity
of reflected light at 532 nm is does not eliminate it because firstly the quantum yield of absorption is
less that 100%, and secondly some light is reflected from the surface of the paint before it would even
56
encounter the rhodamine. The rhodamine paint is a last line of defense to be used only to deal with the
light that cannot be eliminated by careful masking of the illumination or the field of view of the camera.
3.3.5 Total pressure measurement
Point measurements of static pressure and Mach number were performed using a supersonic
five-hole conical probe. The probe, a United Sensor model SDF-15-6-15-600, has a truncated cone with
a half angle of 15°, a total pressure port is located at the tip of the truncated cone and four side ports
are evenly spaced around the conic surface. Such a probe will create a probe shock in front of it, but the
flow-field between this conic shock and the conic surface of the probe may be solved for, and the shock
angle and upstream (freestream) Mach number determined. The freestream Mach number is a
monotonic function of the pressure ratio between the tip of the probe and the sides. The shock in the
immediate vicinity of the probe tip is normal and since the total pressure behind this shock is directly
measured and the Mach number is known one can determine total and static pressures before the
shock. One difficulty with this technique is to determine the location of measurement, both because
the stand-off distance of the bow shock is not known a priori and because some probe flexure under
aerodynamic loading was noted. To eliminate this uncertainty shadowgraph pictures of the probe and
probe shock were taken as the probe was used and the position of the bow shock, measured by
shadowgraph was taken as the measurement location. When the side port pressure values are
averaged the Mach number result is insensitive to yaw angle changes up to 10° (Cooper and Webster,
1951).
3.4 Uncertainty Estimation
3.4.1 Transducer Calibrations
The set-point of the jets are maintained by reference to pressure and temperature sensors in
the stilling chamber of each air stream jet Mach number is a function of the nozzle pressure ratio (NPR)
57
between the jet total pressure (P0j) and the atmospheric pressure into which the jet exhausts Patm by the
relation
where γ is the ratio of specific heats for the jet gas, in this case air. The sound speed in the jet is a
function solely of the jet static temperature, Tj, which is controlled by setting the jet total temperature,
T0j, so the sound speed is found by
,
where γ is again the ratio of specific heats and R is the gas constant, 287 J/kg·K for air. The jet velocity,
uj is then given by the product,
,
and may be controlled by controlling P0j and T0j.
The ratio of areas between the throat and the stilling chamber is 4.822 so the Mach number in
the stilling chamber will be 0.121 for all operating conditions. The total pressure ratio, P0/P for this
Mach number is 1.010 so we assume that the static pressure in the stilling chamber is the total pressure
in the jet. This introduces only a 1% error.
Measurement of the pressure in the stilling chamber is thus the principal measure of the jet
Mach number. The transducer attached to the stilling chamber by a flexible plastic tube is calibrated
periodically against a Druck model DPI 510 Pressure Controller/Calibrator. This device is connected to a
bottle of pressurized nitrogen which serves as pressure source, and it can vent gas to the atmosphere.
The transducer under test is connected to this device and a desired pressure is set. The device
automatically controls internal valves admitting more pressurized nitrogen if the pressure applied to the
attached transducer is too low, and venting gas to the atmosphere if it is too high. The Druck calibrator
58
also includes a reference pressure transducer which is periodically sent out for recertification. The
reference pressure is output on an LED display on the front of the calibrator.
The pressure transducer is calibrated in situ in the sense that it remains attached to the same
data acquisition system which is used during all tests. A series of pressures are set on the Druck
Controller/Calibrator and the data acquisition code is triggered to record several seconds of data. The
resulting time trace for the transducer channel is then extracted from the data file and averaged. The
averaged output voltage is then plotted against the pressure values presented by the Druck
Controller/Calibrator and a best fit line is fit through the resulting plot by the method of least squares.
The slope and intercept of this line are then taken to be calibration constants that are loaded into the
data acquisition code as the function to convert from raw Volts to engineering units, in most cases psig.
A sample of calibration data is shown in Figure 3.10. The rms error for this curve is 0.14 psid.
Figure 3.10 - Sample calibration data for pressure transducer
After each calibration, the new calibration constants are compared to those being superseded.
A large change would be taken as an indication of damage to the transducer, and would cast doubt on
measurements taken with the superseded constants. In every case the change in the calibration
59
constants has been found to be small. A sample comparison is shown in Figure 3.11. The rms error for
the old constants as compared to the new calibration measurements is 0.97 psid. The difference
between the points associated with the new constants and the old constants is not large.
Figure 3.11 - Sample comparison of old and new calibration constants for a pressure transducer.
All the pressure transducers used to monitor the jet condition measure gage pressure with
reference to the atmospheric pressure within the anechoic chamber. The pressure within the chamber
during test may not be equal to the atmospheric pressure outside, so a measurement of the absolute
pressure within the chamber is necessary. The atmospheric pressure within the anechoic chamber is
measured during the test by a Druck DPI 142 Resonant Sensor Barometer which is kept in the anechoic
chamber and records time series of atmospheric pressure within the chamber during testing. This
instrument is periodically sent out for recalibration.
Temperature is measured in the stilling chamber by a permanently installed thermocouple. This
thermocouple is periodically removed at calibrated against an Automatic Systems Laboratories model
F150 Precision Thermometer which includes a Platinum Resistance Thermometer (PRT). The calibration
60
is accomplished by mounting the thermocouple under test and the PRT in a an Automatic Systems
Laboratories model B140 Metal Block Calibrator. This unit has a set of interchangeable aluminum block
inserts each drilled for two probes, the PRT and the thermocouple under test. The different aluminum
block inserts have different diameter holes for the thermocouple under test so that a close fit can be
achieved. The PRT and the thermocouple under test are inserted into the interchangeable block which
fits most closely and then the block is inserted into the B140 calibrator unit. A temperature is selected
on the B140 input panel and the F150 thermometer is observed until the temperature becomes steady.
Once the temperature has stabilized the same data acquisition hardware and software used in actual
test is triggered and several seconds of data are recorded.
The output files are examined and a time history of the appropriate temperature channel is
averaged and the resulting temperature compared to the value presented by the F150 precision
thermometer. A new temperature is set and the process repeated. The average readings (in Volts) on
the thermocouple under tests are plotted against the values from the reference thermometer and a
best fit line is determined through the results by the method of least squares. The slope and intercept
of this line are determined and used as calibration constants. These constants are entered into the data
acquisition code to convert raw Volts into engineering units, in this case degrees Fahrenheit.
The calibration process is repeated periodically and the calibration constants checked to
determine if they have changed significantly from previous calibrations. Significant change would
indicate damage to the probe or data acquisition system. No significant change has been found during
the course of the measurements used in this dissertation.
3.4.2 Set Point Variation
One of the leading sources of uncertainty in jet noise measurements is usually the set-point
error. The jet is intended to be operated constantly at its set-point, but inevitably the control system
does not perfectly hold the set values. Plots of time traces of jet velocity are shown in Figure 3.12 for
61
the Md = 1.5 nozzle at the several set points. For the three conditions shown the total temperature set-
point was 300K and the npr set-points were 2.50, 3.671 and 5.0. The target velocity is shown in each
case by the solid black line. The mean velocities differ from the set-point velocities by less than 4 m/s
for all cases. The rms about the each time trace’s own mean are all less than 2 m/s indicating that the
flow conditions were stable and there were no large excursions. The rms of each trace from its set point
is less than 4 m/s. The overall rms of all traces against their set points 2.23 m/s, giving an uncertainty in
velocity of 4.5 m/s to a 95% confidence level. This is about 1% of the set-point velocities. The eighth-
power relationship for mixing noise allows one to estimate the effect an error in set point will have on
acoustic levels. It tells us that a 1% error in jet velocity will yield a 8% error in the acoustic Prms or a
difference of 0.7 dB.
Figure 3.12 - Variation in jet velocity for the Md = 1.5 nozzle
3.4.3 Repeatability of Acoustic Measurement
In order to eliminate all day-to-day variation it is usual to make comparisons between
measurements taken the same day as close to one another in time as possible. So the appropriate
measure of variation in acoustic measurement is to compare measurements taken back to back. This is
62
done in Figure 3.13 and Figure 3.14 for ψ = 35° and 150° respectively. Plotting the differences between
the ψ = 150° SPL spectra and the average of all spectra shows us the spread in the SPL values. Squaring,
averaging and taking the square root of these deviations shows that the rms in SPL is 0.3 dB. So the
uncertainty in acoustic spectrum taken same day is taken to be two rms or 0.6 dB to a 95% confidence
interval.
Figure 3.13 - Back-to-back acoustic measurements of Md = 1.5, Mj = 1.56, ψ = 35°.
Figure 3.14 - Back-to-back acoustic measurements of Md = 1.5, Mj = 1.56, ψ = 150°.
63
Figure 3.15 - variation from mean spectra for Md = 1.5, Mj = 1.56, ψ = 150°.
3.4.4 Comparison of Acoustic Spectra to Measurements at Other Facilities
Part of this research was funded by SERDP who simultaneously funded a project at Penn State
University and NASA Glenn to study the same kind of nozzles. Comparison among the three, different
sized nozzles measured in different facilities are shown in Figure 3.16. In order to make comparisons
between different scales the measured spectra from all three facilities was made lossless by ISO 9613,
scaled to 100 diameters and nondimensionalized, both in frequency and in amplitude.
Nondimensionalization in frequency is achieved by multiplication by Dj/Uj giving Sj a Strouhal number
based on fully expanded Mach number. The amplitude is nondimensionalized by dividing the SPL by the
frequency spacing (SPL/Hz) then multiplying by Uj/Dj giving amplitude in SPL/Stj. The comparison is very
good.
64
Figure 3.16 - Comparison of measured spectra with measurements of similar nozzles at other scales in other
facilities, Md = 1.5, Mj = 1.56, ψ = 150°, scaled to R/D = 100.
3.4.5 PIV Stokes Number Calculation
One important consideration in assessing the validity of PIV results is the degree to which the
seed particles accurately track the motion of the flow. The motion of these particles is usually analyzed
as a form creeping flow or Stokes flow which is achieved as , where D is the seed particle
diameter. The PIV measurements in this dissertation were all taken using olive oil seeders. The seed
particle size from these seeders was measured by Callender and published in his dissertation (Callender,
2004). He found that the droplet size from these seeders ranged from 0.4 to 1.2 μm and that the
median size was around 0.7 μm. For air near standard temperature and neglecting the order one
difference in density and taking the reference velocity to be on the order of 500 m/s we can find a
Reynolds number ReD = 24.
The Stoke’s number for a seed particle is
, where
, and
65
Where ρp is the particle density, Dp is the particle diameter, μ is the absolute viscosity of the air,
Kn is the Knudson number based on Dp, δ is the shear layer thickness and Uc is the centerline velocity in
the shear layer.
The shear layer thickness at its thinnest has an apparent thickness of 0.2 De or 1.5 mm. Using
the incompressible result that the visual thickness is about twice the vorticity thickness gives a vorticity
thickness, δ of 0.7 mm. Taking the centerline velocity in the shear layer to be about half the jet velocity
or 250 m/s and the seed diameter as 0.7 μm one can arrive at a Stoke’s number of 0.56. It would be
preferable to have a Stoke’s number below 0.25 so this is marginal and one must look further to see
where one may expect difficulty.
Assuming that the Stokes flow assumption is valid we can apply the Hadamard-Rybczynski drag
law and find a particle’s terminal velocity, Ut as:
Where g is the acceleration,
and the superscript i indicates the inner flow of oil and quantities
without this superscript apply to air. Applying this equation we find that for 1g acceleration the terminal
velocity of a 0.7 μm oil droplet in air with density and viscosity near the standard temperature values is
3 x 10-4 m/s. This is six orders of magnitude below the typical fluid velocities in the fluid of interest. This
is the velocity of the particle under a 1g acceleration. Even if the accelerations are 100g or 1000g the
terminal velocity will still be negligibly small when compared to the velocities of interest in the problem.
The one location where the accelerations may be very high is within the shocks themselves. Since no
attempt has been made to determine the velocity changes within the shocks, this is not a problem.
66
3.4.6 PIV Comparison to Pressure Probe Data and LES
It was originally planned to measure the centerline Mach number and static pressure with a
conical probe and from this determine velocities to compare with LES and later PIV. Unfortunately the
spatial extent of the cone probe is not small when compared with the features of interest in the jet and
the 0.75 inch difference between the tip port and the side ports created an apparent 0.75 inch
displacement of the data. In order to avoid this difficulty the pressure measured directly at the tip of
the probe was derived from LES and compared to the measured values. Since the probe creates a bow
shock in the supersonic flow, the value it measures is P02. The segment of bow shock directly in front of
the probe is considered to be a normal shock so the standard normal shock relations are used to convert
the total pressure P01 from in front of a bow shock to P02 behind the bow shock and this calculated P02 is
compared to the measured values in Figure 3.17. The axial velocity component, u, from LES is then
compared to PIV also in Figure 3.17. By this indirect comparison one may gauge something of the
accuracy of the PIV.
Figure 3.17 - Comparison PIV with LES and LES with pressure probe along the centerline of the jet. Md =
1.5. Mj = 1.56.
67
PIV and LES agree to within 5 m/s in regions where the slopes are low (the minima and maxima)
up to x/D = 4 or so The agreement becomes worse at greater axial positions. This correlates with a
reduction in PIV quality observed in the velocity contour plots. As the PIV suite was moved downstream
the features became less distinct. This is in part due to increasing unsteadiness of the shock diamonds
(See Chapter 4), but there also was an accumulation of oil on the lenses over the course of the
measurement series and earlier measurements, near the nozzle are of superior quality. There were also
regions of reduced quality at the edges of the PIV domains where they overlapped. These regions have
been omitted from Figure 3.17 and this is the reason for missing PIV data past x/D = 4 and x/D = 9.3.
The LES is compared to pressure measurements in the lower two traces in Figure 3.17. The
agreement between LES and pressure probe measurement is not as good. For x/D < 4 the agreement at
points of pressure minimum (velocity maximum) are good within P/Patm = 0.05 but the pressure maxima
(velocity minima) differ by as much as 0.15. This represents a Mach number difference of 1.5% or a
velocity difference of around 6 m/s. Assuming a worst case in which one would add the uncertainty
between PIV and Les to that between LES and pressure probe gives a very conservative estimate of the
uncertainty in PIV measurement of 11 m/s.
68
Chapter 4 – Baseline Nozzle Results
4.1 Double Diamonds
Since the early twentieth century it has been recognized that convergent-divergent nozzles
when operated off-design generate semi-periodic shock diamonds, as shocks and Prandtl-Meyer fans
alternate in the jet plume (Meyer, 1908). For smoothly-contoured C-D nozzles, designed for isentropic
expansion and parallel exit flow, matching the exit pressure to the ambient pressure produces a
supersonic jet which is shock free. Such a condition, with pressures matched at the exit is referred to as
the nozzle’s design condition.
In order to attain a shock free design condition C-D nozzles employed in most laboratory studies
treat the gas flowing through them gently. The nozzle throats are smooth with large-radius curves.
Isentropic expansion in the divergent section is achieved by designing the nozzle shape by the method of
characteristics or by more modern methods based on numerical simulation. The contours of these
nozzles approach cylindrical at the exit so that they produce parallel exit flows. For convenience these
nozzles will be referred to as traditional C-D nozzles. The smooth contours present a practical problem
for the designer of a high-performance jet engine exhaust nozzle. Since the aircraft must operate over a
range of atmospheric conditions and power levels, a variable-geometry nozzle is generally required. This
allows the throat area to be changed to attain the desired mass flows and the area ratio to be changed
to adapt to conditions and thrust requirements.
While it is possible to design a variable geometry nozzle with smooth contours, such a nozzle
would be complex and heavy. What is commonly done in high-performance jet aircraft exhausts is to
employ a variable geometry nozzle with flat plates in the convergent section and flat plates in the
divergent section with seals between so that the plates make a cross section that is polyhedral and
approximates a circular cross section. The plates are hinged between the convergent and divergent
69
sections making a relatively sharp corner at the throat. Such a nozzle trades a reduction in nozzle
efficiency for a reduction in weight and complexity.
The conic C-D nozzles employed in this study are simplified static models of these actual variable
geometry nozzles. Rather than build a laboratory model that moves, static nozzles have been produced
that approximate the real engine nozzles in different configurations corresponding to different
operating conditions. The laboratory model cross sections are circular rather than polyhedral so the
surfaces of the convergent and divergent sections are conic. There are no hinges at the throat, but the
sharp character of the throats is retained. These are the nozzles referred to as conical C-D nozzles.
Details of their construction are included in Chapter 3.
This type of nozzle geometry does not approach a cylinder at the exit, so unless the flow is
massively separated they can never produce parallel flow. Turning of the flow at the exit will be
necessary and this will produce shocks or Prandtl-Meyer waves in the jet even at the design condition
when there is no pressure mismatch. It will be shown that these nozzles are not shock free at or near
their design conditions. It will also be shown that these nozzles generate a second set of shock
diamonds superimposed on the first generating a double-diamond pattern. This second set of shock
diamonds has its origin at the sharp nozzle throat.
The presence or absence of shocks in the jet plume have a significant effect on the acoustic
emissions of the jet. Shocks introduce screech and broadband shock associated noise into the spectra
when present, so the absence of a shock free condition from this class of nozzles implies the presence of
shock associated noise even at the design condition. This will be confirmed below.
Mach number contours for a typical double diamond shock structure is shown in Figure 4.1. The
case is Md = 1.5, Mj = 1.56 and the flow variables have been averaged over time. This is a mildly
underexpanded case, so classical textbook theory would suggest that an expansion fan should be
anchored at the nozzle lip and run inward toward the axis. (See for example Liepmann and Roshko,
1957.) Since this nozzle is conic, the flow exits with a radially outward component of velocity and must
70
turn inward despite the underexpanded condition, so the wave running inward from the lip is a shock.
This can be seen by the drop in Mach number from the upstream side of the lip wave to the
downstream side.
Simulation by LES reveals what is happening inside the nozzle where it is impossible to make any
unobtrusive flow measurements. The LES reveals that the sharp throat produces an oblique shock inside
the nozzle which forms a Mach disk inside the nozzle. In this case it lies at x/De = 0.35 and the interface
between the oblique shocks and the Mach disk casts a slip line near the jet centerline with a diameter
w/De = 0.6. The onward-running oblique shock extends past the nozzle exit passes through the oblique
shock anchored at the nozzle lip and reflects from the shear layer outside the nozzle downstream from
the nozzle lip at T0/De = 0.1. The reflection of the throat shock is an expansion wave that then runs
parallel to the lip wave towards the centerline. As will be shown below, the slip line and the first
reflection of the throat shock will be visible in Shadowgraph and PIV confirming the inference by LES.
The flow simulated in Figure 4.1 differs from a typical textbook supersonic jet in two ways, both
due to the particular details of the nozzle. Firstly the conic expansion forces an inward turning of the
flow near the nozzle lip for all cases near the design condition. The flow leaves the nozzle with an
outward radial component of velocity and this must turn inward or expansion will continue without
limit. Secondly the sharp throat generates an oblique shock regardless of the condition outside the
nozzle. The result of these is that there are two overlapping sets of shock diamonds produced and, as
will be shown later, these double diamonds are present for the design condition as well as for
underexpanded and overexpanded conditions.
In Figure 4.2 shadowgraph and PIV measurements are compared for Md = 1.5 and Mj = 1.56.
Subfigure a) shows an instantaneous shadowgraph image of the jet. The turbulence near the nozzle
appears fine grained, but the scale of the turbulence increases in the downstream direction. The outer
edges of the jet are ragged with large scale structures and as these convect they produce Mach wave
71
radiation which can be seen propagating at a downstream angle to the main jet. The oblique throat
shocks can be seen emerging from the nozzle exit and reflecting from the shear layer at T0/De = 0.07.
This reflection makes a bright spot in the shadowgraph at the upper and lower shear layers and
a bright vertical line connecting these spots. This is due to the fact that shadowgraph is a technique
which integrates along a line of sight. The jet geometry is axisymmetric and so is the oblique throat
shock and its reflection. The bright spots at the top and bottom of the image are reflections viewed in
profile. Where the bright line crosses the jet centerline the camera is viewing the reflection through the
near and far edges of the jet. This reflection of the throat shock is outside the field of view of the PIV
images, but can be compared with the LES in Figure 4.1. The LES image, like the PIV is a section in an
axial planes, and does not line integrate. The reflection of the throat shock is clearly visible in Figure 4.1
but the vertical line is not present.
The first complete double diamond can be seen in Figure 4.2a, but as the turbulence is more
pronounced farther downstream the second cell is largely obscured. In order to reveal the relatively
stationary shock cell structures 100 shadowgraph images were averaged. This averages out the
turbulence and leaves the shock structures visible. This averaged shadowgraph image is shown in Figure
4.2b. In addition to the throat shock emerging from the nozzle and the first cell of the double diamond
the averaging brings out the reflection of the lip shock at L1/De = 1.1 and the reflection of the throat
shock at T1/De = 1.4, and the next set of reflections at L2/De = 2.4 and T2/De = 2.8. The shock structures
become less sharply images as they get farther from the nozzle. This is due to the fact that they are not
truly stationary. The shear layer is in motion as large scale structures pass along it. Each reflection of a
wave off the shear layer is reflecting off a moving entity so the reflected waves are moved by the
reflections. This effect is cumulative so as the number of reflections increases, the degree of motion of
the shocks and expansion waves increases, and the averaged images of these moving waves become
increasingly smeared.
72
Another feature revealed by the averaging of the shadowgraph images in Figure 4.2b is the slip
line cast from the Mach disk inside the nozzle. This appears as a dark horizontal feature running along
the centerline of the jet images. The width of the slip line, w, is less than 0.1De and so one may infer
that this is the diameter of the internal Mach disk. The presence of the slip line in the shadowgraph and
PIV to follow provides ample confirmation of the presence of the Mach disk predicted by the LES.
The bright vertical line associated with the throat wave reflection at T0 observed in the
instantaneous shadowgraph image is present in the averaged image as well. The averaging out of the
turbulence reveals similar, though less sharp vertical lines associated with the reflections at L1, T1, L2 and
T2 also. As previously discussed these are artifacts of the fact that shadowgraph is line integrating.
Comparing these features in the averaged shadowgraph in b) with the corresponding averaged PIV in d)
and the averaged LES in Figure 4.1 show that while the reflections are present, the vertical lines are not.
PIV in axial planes is shown in Figure 4.2c and d. A single instantaneous measurement from a
single image pair is shown in c, and an average of 500 such instantaneous measurements is shown in d.
While PIV has the benefit, relative to shadowgraph, of not being line integrating, it has a disadvantage in
regions near a solid surface like the nozzle itself. The laser used to illuminate the seed particles reflects
from the nozzle hardware and saturates the camera’s sensor in this region. For this reason the PIV
domain begins near x/De = 0.25. The plots shown are of the axial component of velocity and velocities
below 50 m/s have been omitted in order to mask out background noise.
The instantaneous measurement in c shows that the larger scale turbulence observed in the
instantaneous shadowgraph in is confined to the shear layer. In the shadowgraph one can see large
scale turbulence over the entire jet because of line integration. PIV shows a cut through an axial plane
and shows than the variation within the jet is small. There is large variation, however in the shear
layers. These are thin at the nozzle exit and thicken significantly in the downstream direction. Large
variation in velocity is apparent in the thickened shear layer as high-speed eddies engulf relatively still
73
air from the jet’s surroundings. Pockets of velocity below 50 m/s (shown in black) are drawn deep into
the shear layer.
The velocity differences across the shocks and expansion waves in the shock cells are small
enough to be comparable to the random variation in velocity (the sum of actual variation and
experimental uncertainty) so the shock cells are not very pronounced in the instantaneous velocity
plots. Averaging 500 measurements, suppresses this variation and the mean velocity plot in Figure 4.2d
clearly shows the double-diamond structure and the presence of the slip lines around the centerline.
The initial reflection of the throat shock occurs outside the measurement domain, but all the remaining
features previously observed are present.
As with the averaged shadowgraph, the first shocks are the sharpest in character. Later shocks
become somewhat smeared since they fluctuate in location due to accumulated variation from
additional reflections off the shear layer. The locations of the later waves should be understood to be
average locations since the waves are in motion.
The slip line, or more properly the wake of the internal Mach disk is evident throughout the
measurement domain. The width of this slip line, w, was measured for all three nozzles and over a
range of jet Mach numbers and it was found that it is chiefly a function of design Mach number.
Increased Md and increased area ratio lead to decreasing slip line width, and thus decreasing diameter
of the internal Mach disk. The slip line width w/De is 0.09, 0.06 and 0.045 for Md of 1.3, 1.5 and 1.65
respectively. There is also a very weak dependence on fully expanded jet Mach number, showing
reduced w with increased Mj. (See Figure 4.4). For the lowest pressure ratio for each nozzle, the cases
where the lip shocks form Mach disks, a second slip line is generated by these external Mach disks.
These external disks are larger in diameter than the internal ones and their slip lines surround the slip
lines from inside the nozzle. For the Md = 1.5 nozzle this second slip line is also faintly visible in the
shadowgraph in Figure 4.3.
74
4.2 Variation with Set-point
Figure 4.3 shows shadowgraph images for a range of NPRs including three overexpanded
conditions, the design condition and three underexpanded conditions. There are double-diamonds
apparent in all the shadowgraph images including the design condition (Mj = Md = 1.5). This indicates
that the conical C-D nozzles studied in this paper do not achieve a shock-free condition at the design
condition. In order to exclude the possibility that a shock-free condition went unobserved due to some
small error in construction shifting Md or some small instrumentation error causing an error in Mj a
shadowgraph movie was taken of the nozzle as the set-point was slowly varied through a range from Mj
= 1.22 through Mj = 1.71 (NPR = 2.0 up to NPR = 5.0), including the points around Mj = 1.5 where quasi 1-
D theory predicts perfect expansion. Careful observation of the movie reveals that there is no condition
in this range of Mj in which the jet is shock free.
For overexpanded conditions a decrease in Mj shortens the shock cells and also moves the two
diamond structures closer to one another (Li closer to Ti) until at the lowest condition the two sets of
waves appear to have coalesced by the first lip wave reflection. This may have something to do with the
lip shocks increasing in strength and forming external Mach disks. For Mj = 1.36 there is a Mach disk
associated with the first lip shocks with a diameter slightly larger than the internal Mach disk. By Mj =
1.22 the lip shock has formed a Mach disk three times the diameter of the internal Mach disk.
For underexpanded cases increased Mj causes the reflections grow closer to one another as the
shock cells grow longer. As the initial Prandtl-Meyer fan from the lip grows stronger it becomes
physically wider and comes to envelop the throat waves entirely.
One feature which is highly sensitive to Md but relatively insensitive to Mj is the position of the
initial throat wave reflection T0. (See Figure 4.5) For Md = 1.5 it is 0.06 or 0.07 De for all cases except for
Mj = 1.22 where T0 is slightly closer to the exit (0.04De). For the larger nozzle Md = 1.65 the position of
the initial throat reflection is farther from the nozzle at T0/De = 0.22, 0.29 and 0.32 for Mj of 1.43, 1.65
and 1.86 respectively. The smaller nozzle, with Md = 1.3 has the initial reflection of the throat wave
75
inside the nozzle. Oil deposition within the nozzle after running reveals the location of the reflection to
be at T0/De = -0.14.
Particle Image Velocimetry (PIV) was taken in streamwise planes through the axis for all three
nozzles. For each case pressure ratios were selected to represent overexpanded, design conditions and
underexpanded conditions. Figure 4.6 shows average axial velocity while Figure 4.7 shows cross-stream
velocity. These are nondimensionalized by Ud, the design exit velocity. The scale is from u/Ud = 0.7 to
1.3. Velocities below 0.7Ud are omitted in order to expand the scale over the velocity range of greatest
interest. It can be seen that the double diamond structure persists for two or three shock cells, then
coalesces into a single shock diamond structure.
Axial average velocity for single nozzle, Md = 1.5 is shown in Figure 4.8. The corresponding
cross-stream component of velocity are shown in Figure 4.9. Three values of Mj are shown representing
overexpanded, perfectly expanded, and underexpanded conditions. In many respects these plots show
us what we would expect. For the lower Mj where the exit pressure is below ambient, shocks are shed
from the trailing edge lip as the flow turns inward. At the lowest Mj the trailing edge shocks form a
Mach disk. When the trailing edge shocks reach the shear layer they reflect as Prandtl-Meyer waves as
the flow turns outward.
At pressure ratios above the design condition, where the exit pressure is above the ambient
pressure, a Prandtl-Meyer wave is emitted from the trailing edge lip as the flow turns outward. This
wave reflects at the centerline and upon reaching the shear layer reflects inward as a compression
which coalesces as a shock forming the next cell. For the higher Mj the shear layer is curved generating
the classical barrel shaped cells of the significantly underexpanded jet.
All of these features form the diamond shock-cell pattern expected of smoothly contoured
nozzles, designed in accordance with the method of characteristics. The nozzles under study in this
paper, with conic contraction, a sharp throat and a conic expansion section also include additional
features. There is a second shock emanating from inside the nozzle, passing through the lip shock or
76
Prandtl-Meyer fan and reflecting off the shear layer and setting up a second diamond pattern overlaid
on the cells from the nozzle lip.
4.3 Shock Cell Spacing
Axial locations (Li and Ti) of the reflections of both the lip waves and tip waves have been
extracted from the PIV measurements and examined. Figure 4.10 shows how the shock cell spacing is
determined. The location of each reflection from the shear layer is plotted. The solid symbols are the
lip waves and the open symbols are the throat waves. For this typical case only two throat reflections
are distinct from the lip reflections. Past the second diamond the smearing due to shock motion makes
it impossible to discern between lip and throat waves. Typically the shock cell spacing is not uniform.
The points lie on a curve concave downward indicating that the shock cells become shorter as the flow
develops. This is due to the thickening of the shear layers bringing the sonic lines closer together. As
the lateral length scale is compressed by this, the longitudinal scale must also shrink in order to preserve
the oblique shock and Prandtl-Meyer fan angles. Based on an examination of all the cases, five cells
were selected to average the characteristic shock cell length. Beyond the fifth cell the shrinking of the
cells becomes significant.
The shock cell spacing, Ls is shown in Figure 4.11. Also shown are the theoretical values using
the Prandtl-Pack relation .
, where (4.1)
as well as published data for a range of design Mach numbers from 1.0 to 2.0. Nearly all of the C-D
nozzles previously published have been of the smoothly varying type, though there has been an effort at
Penn State to study conic C-D nozzles concurrently with this work and some of their data is included.
The Prandtl-Pack relation is generally a good fit for convergent nozzles (Md = 1.0, depicted by small x’s.
But it generally over-predicts Ls for higher values of Md. This over-prediction becomes worse as Mj
increases. The general trend is that Ls increases with Mj, but for a given value of Mj the shock cell size
77
decreases with Md. The values of Ls extracted from PIV, from Shadowgraph, from centerline pressure
measurements and from LES all agree fairly well with one another and agree with other published
results for nozzles with design Mach numbers near 1.5. It can be seen from this that there is not any
significant difference in Ls introduced by the use of the more realistic conical C-D nozzles.
An improved correlation for Ls is proposed which accounts for the variation in Md.
, where , and . (4.2)
For Md = 1, n = 0 and the additional term vanishes, leaving the Prandtl-Pack relation (Eq. 4.1). The
equation may be re-ordered as
, or
. (4.3)
Where the right-hand side is a function only of the shock strength parameter,
. The
same data as in Figure 4.11 is collapsed by this relation in Figure 4.12.
4.4 Influence of Secondary Flow
Figure 4.13 shows shadowgraph images of nine secondary flow Mach numbers ranging from M2
= 0.0 to 0.8. The vertical lines aid in tracking features in the images. They are aligned with the features
in the first image (M2 = 0.0) and we can see how the features move relative to this condition in
subsequent images.
Features associated with the lip wave are marked with green lines. The first green line is at the
nozzle lip itself. The second green line, the dashed green line, is aligned with the point where lip wave
crosses the centerline. This crossing point remains fixed up to M2 = 0.4 after which it begins to move
upstream. The third green line tracks the first reflection of the lip wave from the shear layer which
78
likewise moves upstream past M2 = 0.4.with the lip wave are marked with green lines. The first green
line is at the nozzle lip itself. The second green line, the dashed green line, is aligned with the point
where lip wave crosses the centerline. This crossing point remains fixed up to M2 = 0.4 after which it
begins to move upstream. The third green line tracks the first reflection of the lip wave from the shear
layer which likewise moves upstream past M2 = 0.4.
Features associated with the wave from inside the nozzle are tracked by the red lines. The first
red line follows the first reflection of this wave from the shear layer. The second red line, the dashed
one, follows the point at which this reflected internal wave crosses the centerline. The third red line
follows the second reflection of this wave from the shear layer. These features also move upstream, but
they also become weaker as secondary flow Mach number increases. For M2 above 0.7 is becomes
difficult to make out the center crossing of this wave, but the reflection can be seen as high as M2 = 0.8.
4.5 Far-field Acoustics
Far-field acoustic spectra for the Md = 1.5 nozzle are shown in Figure 4.14 for three conditions.
Mj = 1.47, 1.50 and 1.56 representing mildly overexpanded, design condition, and underexpanded. All
three sets of spectra are remarkably similar. All three show unmistakable signatures of shock associated
noise. The narrow peak between St = 0.2 and 0.3 which radiates most strongly in the upstream direction
(ψ < 90°) is clearly a screech peak and is as prominent at the design condition as either off-design case.
All three sets also show the characteristic signature of broad-band shock-associated noise (BBSN). The
BBSN peak is much broader than the screech peak, is centered at St = 0.3 or 0.4 at ψ = 35°, and shifts to
higher Strouhal numbers, grows broader, and lower as it shifts to more aft observers. By ψ = 140° the
BBSN peak has shifted to St = 1.1, and is barely perceptible above the background mixing noise. At ψ =
150° the BBSN peak is negligible.
This similarity between the spectra of the design condition to those of off design conditions is
characteristic of the conical C-D nozzles used in this study. Typical smoothly varying C-D nozzles achieve
79
shock freedom at their design condition, and therefore do not produce screech or BBSN at or near
design condition. Operating a jet on-design can therefore offer significant reduction in noise for
smoothly varying nozzles. For the practical engine nozzles used on high-performance jet aircraft this
savings is not available even when the engine area ratio is closely matched to the operating condition.
Spectra for a far-field microphone at ψ = 35° are shown for all three nozzles as contour plots in
Figure 4.15. These plots were made by sweeping slowly through values of Mj so that any shock free
spectra could be identified. The horizontal black line through each plot is the design condition. For a
traditional C-D nozzle one would expect the screech and broadband shock associated noise to vanish, or
at least weaken as perfect expansion is achieved and the shock in the jet plume weaken and disappear.
There is no such behavior in any of the plots with respect to BBSN and only a diminution in screech
intensity and a mode shift in the screech peak as the jet switches from a toroidal to a helical mode. The
existence of BBSN near the design condition implies that the shocks are present and undiminished in
strength.
The peak frequency of the broadband shock associated noise is shown in Figure 4.16 for an
observer at ψ = 90°. These values are compared with published results for smoothly varying nozzles and
for the conical C-D nozzles tested by the group at Penn State. The frequencies are expressed in terms of
a Strouhal number based on Uj and Dj and these are plotted against Mj. There is good collapse for all
nozzles, whether smooth or conical, for all design Mach numbers.
There are also two theoretical curves due to Tam and Tanna *8+. Tam and Tanna’s equation is
based on a different derivation than Harper-Bourne and Fisher’s *9+ but the equation for the principal
BBSN peak is the same.
, (4.4)
where uc the convective velocity is taken to be 0.7 uj. Tam’s derivation depends on knowledge of
the shock cell spacing, Ls, for which he uses Prandtl-Pack’s equation above. The Tam-Prandtl-Pack line
80
on the plot uses Prandtl-Pack for this. Tam-Shadowgraph uses the shock cell spacing read from the
shadowgraph images in the present study. The Tam-Prandtl-Pack equation under-predicts the BBSN
frequency for nearly all cases, but correctly represents the trends. Substituting a measured value for Ls
improves the Tam and Tanna equation considerably, but it remains on the low side. The trend in
present measurements is for the BBSN frequency to rise with Md especially at lower values of Mj. There
are no values from the LES since no far-field acoustics have been extrapolated from the near-field
simulation domain.
Figure 4.17 shows a similar plot of screech frequency measurements, compared to published
data and to theoretical curves expanded to predict screech. Again the agreement among different
investigators is good, and again the trend is for increasing Screech frequency with increasing design
Mach number especially for lower values of Mj. Tam, Seiner and Yu [10] have proposed an explanation
of the relationship between screech and BBSN which holds that the upstream propagating component
of the screech feed-back loop is in fact the BBSN noise, and this the screech frequency will be the BBSN
frequency as propagated to ψ = 0°. Like with the BBSN frequency so the screech frequency is under-
predicted by Tam-Prandtl-Pack, but is better with Tam-Shadowgraph. Screech is predicted by LES and
the agreement with experiment is good.
The conic C-D nozzles under study agree with smoothly varying nozzles in the frequencies of screech and
BBSN, but the key difference acoustically is the presence of shock-associated noise near the design
condition for conical C-D nozzles where it is absent for smoothly varying nozzles. Plots of OASPL as a
function of βd (Figure 4.18) show that there is a broad region of diminished OASPL around the design
condition, but as we have shown above this is due to reduction in screech, but there is no reduction in
BBSN. Other published data co-plotted here show that for traditional C-D nozzles the reduction in
OASPL near the design condition is deeper than the present study and does not have the flat bottomed
curve shape of the present nozzles. Seiner and Norum (1979) tested a nozzle described as an “F15
nozzle” which seems likely to have been similar to the conical C-D nozzles studied here. Unfortunately
81
the OASPL curve is the only data published in their paper, and that data is reproduced here. There are
few points in the region near the design condition, but they do show less noise near the design
condition for the F15 nozzle than for a corresponding traditional C-D nozzle tested at the same time.
4.6 Near-field Acoustics
Contour plots for Md = 1.5 and Mj = 1.56 are presented in Figure 4.19. Triangles in each subplot
show the location of the corners of the shock cells where the shocks reflect from the shear layer.
Reflections of the throat shock are shown in red and reflections of the lip wave are shown in black.
Downstream where the data is smeared by motion of the shock cells the smeared reflections are
depicted as lip wave reflections. Subfigure a) shows the OASPL. It can be seen that the jet is making
noise across the entire length of the shock train. The maximum OASPL has an apparent source around
x/De = 10, but high levels of OASPL range from x/De = 2.5 to 13. SPL for selected frequencies are shown
in the remaining subfigures. Subfigure b) shows a Strouhal number of 0.166. This is in a frequency
range below which any shock associated noise is generated, so is taken to represent the mixing noise.
Mixing noise appears to be radiating from the later part of the shock train and extending beyond its end.
dB levels above 130 appear, ranging from x/De = 7.5 to 17.5. This apparent source region includes the
region of intense mixing at the end of the jet’s potential core. Subfigure c) at a Strouhal number of
0.266 is the screech frequency observed in the far-field. This plot shows the signature of screech in the
form of a lobed source distribution with lobes centered on the shock reflections. Subfigure d) at a
Strouhal number of 0.566 is based on the frequency of the BBSN peak observed in the far-field by an
observer at ψ = 90°. This distribution shows a single lobe centered around x/De = 10.5. This is the region
where the largest of the large scale structures encounter the latter shock cells. This figure shows two
directional lobes. The lobe emanating towards a direction of 80° or so is the BBSN noise itself. The
second lobe radiating in the downstream direction of 150° or so is the mixing noise which is also present
at this frequency.
82
Figure 4.20 shows the SPL measured along the innermost edge of the near-field region mapped
in Figure 4.21. These represent all seven set points for the Md = 1.5 nozzle. Subfigure a) is the OASPL.
The overall noise level is lowers for Mj = 1.22 and at downstream locations increases monotonically with
Mj. Except for Mj = 1.56 all the traces for Mj greater than 1.22 show a periodic oscillation in the first
seven to 13 diameters indicating that screech is dominating in this range. The regions of highest noise
levels grow longer as Mj increases since the jet, its potential core and its shock train all become longer.
In the high level region where most of the source locations are the peak levels are not monotonic with
Mj. Mj = 1.22 has the lowest levels, but the next lowest is Mj = 1.56 which is close to the design
condition of Md = 1.5.
The low frequencies are shown in Figure 4.20b. These are all at St = 1.66 which is below the
screech frequency for all cases. No shock associated noise occurs at this frequency so the noise sources
revealed are all due to mixing noise. Since mixing noise tends to peak near the end of the potential core
one can see the lengthening of the potential core in this plot. For Mj = 1.22 the noise levels are past the
peak values by x/De = six or seven. For Mj = 1.36 the high noise region extends to ten or so. Mj = 1.47
and 1.5 extend somewhat farther downstream and so on with the highest setting of Mj = 1.71 showing a
high noise region at this frequency extending past x/De = 20.
The frequency corresponding to each setting’s screech peak is plotted in Figure 4.20. Since
screech is an unsteady phenomenon and very sensitive to conditions near the nozzle the relative
amplitudes of the near-field curves are less meaningful than for other sources. Each trace was taken
instantaneously though, so the spatial distribution of near-field noise strength is reliable. The periodic
nature of screech shows up in this representation as a region of oscillation of the curve. For Mj = 1.22
there is no signature of screech apparent. For Mj = 1.36 the region of screech sources extends to x/De =
5. The length of the screech source region increases monotonically with Mj up to a value of 1.64 for
which the source region extends to x/De = 12. The highest setting, Mj = 1.71 does not show as clear a
signature of screech.
83
BBSN source location can be inferred from Figure 4.20d. Each trace in this plot is taken at the
frequency associated with the BBSN peak as observed by a far-field microphone at ψ = 90°. For Mj = 1.22
the peak value occurs at x/De = 5 and the position of the peak increases with Mj up to x/De = 13 for the
highest setting of Mj = 1.71.
4.7 Baseline Summary
Conical C-D nozzles operate differently from traditional C-D nozzles in two important ways.
They form shocks at their throats which set up a system of shock diamonds independent of the shock
diamonds produced at the nozzle exit. These two systems of shocks are superimposed on one another
producing a double-diamond pattern. Conical C-D nozzles have expansion sections which continue to
expand all the way to the nozzle exit. This implies that there is a radially outward component of velocity
at the exit. Traditional C-D nozzles, by contrast have parallel flow approaching the exit. Since the jet
cannot expand without limit the flow must eventually turn into itself to achieve parallel flow. Because
of this there will never be a shock free condition at or near the design condition of the nozzle. Since the
nozzle is never shock-free there will never be an absence of shock-associated noise near the design
condition.
Aside from the presence of shock-associated noise near the design condition the acoustics of
conical C-D nozzles are like traditional C-D nozzles. They make BBSN and Screech at the same
frequencies since they have shock cells the same size as traditional C-D nozzles operated off their design
points.
The Prandtl-Pack equation is generally used to model the behavior of shock associated noise,
providing the shock-cell spacing. The Prandtl-Pack equation expresses the shock-cell spacing, Ls,
nondimensionalized by the fully expanded jet diameter, Dj, as a function only of the jet Mach number,
Mj. Examination of a large number of investigator’s data shows that shock cell spacing is also a weaker
function of the nozzle’s design Mach number, Md. An improved correlation is proposed for Ls/Dj as a
84
function of Md as well as Mj. This relation reduces to the Prandtl-Pack relation for the case where Md =
1.0. Both Conical C-D nozzles and traditional C-D nozzles obey this correlation.
85
Figure 4.1 - Mach number contours inside the nozzle by LES (figure from Munday, Gutmark, Liu and
Kailasanath, 2009).
a)
b)
c)
d)
Figure 4.2 - Flow field representations by shadowgraph, PIV for Md = 1.5 and Mj = 1.56. a) Instantaneous
shadowgraph. b) Average of 100 shadowgraph images. c) Instantaneous PIV. d) Average of 500 PIV image
pairs.
86
Mj = 1.22, NPR = 2.5
Mj = 1.36, NPR = 3.0
Mj = 1.47, NPR = 3.5
Mj = 1.50, NPR = 3.671
Mj = 1.56, NPR = 4.0
Mj = 1.64, NPR = 4.5
Mj = 1.71, NPR = 5.0
Figure 4.3 – Conical C-D nozzle (Md = 1.5) shadowgraph. One hundred images averaged to suppress
turbulence and emphasize stationary features.
87
Figure 4.4 - Width of the slip line, w, at x/De = 0.125. The diameter of the slip line indicates the size of the
internal Mach disk which shed it. It is dominantly a function of the design Mach number of the nozzle, and
weakly a function of the nozzle pressure ratio.
Figure 4.5 - Axial position of first throat reflection, T0. The reflections for Md = 1.30 are inside the nozzle.
The reflections for Md = 1.50 are taken from shadowgraph. For Md = 1.65 they are taken from PIV.
88
Figure 4.7 – Mean v/Ud, for different nozzles, perfect expansion. a) Mj = Md = 1.3. b) Mj = Md = 1.5. c) Mj =
Md = 1.65.
x/De
v/Ud
y/De
Mj = Md = 1.65
Mj = Md = 1.5
Mj = Md = 1.3
Figure 4.6 – Mean u/Ud for different nozzles, perfect expansion. a) Mj = Md = 1.3. b) Mj = Md = 1.5. c) Mj = Md
= 1.65.
Mj = Md = 1.3
x/De
u/Ud
y/De
Mj = Md = 1.5
Mj = Md = 1.65
89
Figure 4.9 – Mean v/Ud for the same nozzle with different conditions. Md = 1.5. a) Mj = 1.22, overexpanded.
b) Mj = 1.50, perfectly expanded. c) Mj = 1.71, underexpanded.
x/De
v/Ud
y/De Mj = 1.5
Mj = 1.22
Mj = 1.71
Figure 4.8 – Mean u/Ud for the same nozzle with different conditions. Md = 1.5. a) Mj = 1.22, overexpanded.
b) Mj = 1.50, perfectly expanded. c) Mj = 1.71, underexpanded.
x/De
u/Ud
y/De Mj = 1.5
Mj = 1.22
Mj = 1.71
90
Figure 4.10 -- Shock reflection locations for Mj = Md = 1.5.
Figure 4.11 -- Shock Cell size, Ls as a function of Mj.
91
Figure 4.12 - Shock cell spacing collapsed for all valued of Md.
92
M2 = 0.0
M2 = 0.1
M2 = 0.2
M2 = 0.3
M2 = 0.4
M2 = 0.5
M2 = 0.6
Figure 4.13 – Shadowgraph. One hundred images averaged to suppress turbulence and emphasize shock
cells. Mj = Md = 1.56, T0/Ta = 1.22. Solid lines descend from reflections at the shear layer in M2 = 0.0. Dashed
lines descend from waves crossing the centerline in M2 = 0.0. Green lines pertain to the wave from the lip.
Red lines pertain to the wave from inside.
M2 = 0.7
M2 = 0.8
93
Figure 4.16 -- Peak BBSN frequencies for an observer ψ = 90º.
Figure 4.15 – Far-field SPL at ψ = 35°. a) Md = 1.3. b) Md = 1.5. c) Md = 1.65.
Mj
Frequency [Hz] Frequency [Hz] Frequency [Hz]
SPL
Figure 4.14 – Far-field spectra for Md = 1.50. a) Mj = 1.47, overexpanded. b) Mj = 1.50, perfectly expanded.
c) Mj = 1.56, underexpanded.
Md = 1.50 , Mj = 1.50 Md = 1.50 , Mj = 1.47 Md = 1.50 , Mj = 1.56
94
Figure 4.17 -- Strouhal number of screech peak.
Figure 4.18 -- Variation in OASPL with βd = ±(|Mj2-Md
2|)
0.5.
95
a)
b)
c)
d)
Figure 4.19 -- Near-field contour maps of OASPL and 50 Hz bands for a slightly underexpanded case, Md =
1.50, Mj = 1.56. Levels are in dB. (a) Over All Sound Pressure level. (b) Mixing noise, St = 0.166. (c) Screech,
St = 0.266. (d) BBSN, St = 0.566.
BBSN, St = 0.566
Shock reflections
Screech, St = 0.266
Mixing, St = 0.166
OASPL
96
a)
b)
c)
d)
Figure 4.20 -- Near-field OASPL and 50 Hz band SPL in dB along a line beginning in the exit plane of the
nozzle at r/De = 0.85 and sloping outward with an angle of 10º from the axis. (a) OASPL. (b) Low frequency
screech, f = 1000Hz. (c) Screech peak frequency.
0 5 10 15 20 25125
130
135
140
145
150
155
160
Over All Sound Pressure
X/Deq
oaspl [d
B]
Mj = 1.22
Mj = 1.36
Mj = 1.47
Mj = 1.50
Mj = 1.56
Mj = 1.64
Mj = 1.71
0 5 10 15 20 25105
110
115
120
125
130
135
140
145
Mixing noise
X/Deq
spl [d
B]
Mj = 1.22
Mj = 1.36
Mj = 1.47
Mj = 1.50
Mj = 1.56
Mj = 1.64
Mj = 1.71
0 5 10 15 20 25105
110
115
120
125
130
135
140
145
Screech
X/Deq
spl [d
B]
Mj = 1.22
Mj = 1.36
Mj = 1.47
Mj = 1.50
Mj = 1.56
Mj = 1.64
Mj = 1.71
0 5 10 15 20 25105
110
115
120
125
130
135
140
145
BBSN noise
X/Deq
spl [d
B]
Mj = 1.22
Mj = 1.36
Mj = 1.47
Mj = 1.50
Mj = 1.56
Mj = 1.64
Mj = 1.71
97
Figure 4.21 – Near-field pressure contours for the Md = 1.50 nozzle. Column 1 is a 50 Hz band centered at
each condition’s screech frequency. Column 2 is a 50 Hz band centered at the BBSN peak frequency as it is
observed at ψ = 90°.
Screech tone BBSN peak (90°)
98
Chapter 5 – Chevron Nozzle Results
5.1 Gross Flow-field Changes
In subsonic jets chevrons have come to be well enough understood that they have passed
beyond the stage of exploration and test and have been installed on commercial engines for sale to
airlines where they are doing their jobs carrying passengers for hire. In this chapter chevrons applied to
supersonic jets will be studied. In particular chevrons applied to high-performance military aircraft
nozzles will be examined.
The flow features from the Md = 1.5 nozzle are first examined in Figure 5.1. The nozzle with and
without chevrons is shown. The jet Mach number, Mj = 1.56, making this a slightly underexpanded case.
The jet in this case is cold. The images were created by shadowgraph which is a line integrating
technique so structures in the near and far shear layers are seen as well as those from inside the jet.
The baseline case shows that there is little turbulence right at the nozzle exit. The bright line just past
the nozzle exit is the reflection of the throat shock from the shear layer and both the throat and lip
shocks can be seen through the first shock cell. As the intensity of the turbulent structures in the shear
layer strengthen they obscure the shock cell structures inside the jet beyond the first cell. (See Chapter
4).
Comparing this with the chevron image in Figure 5.1b one can see that there is considerably
stronger turbulence right at the nozzle exit. Even the initial shock cell is obscured. The increased
spreading of the jet is clearly evident. This is due to forced bulk interchange between the high-speed
flow in the jet with the lower speed flow outside the jet bringing about much greater mixing. The
chevrons introduce diagonal lines near the nozzle exit which can best be seen near the jet centerline. In
order to better see the shock structures it will be necessary to render the shear layer invisible.
99
Averaging one hundred images like those in Figure 5.1 causes the turbulence in the shear layer
to be averaged out revealing the more stationary structures in the flow. This makes it easier to examine
the shock cells since they are nearly stationary. Averaged images are shown in Figure 5.2 for the Md =
1.5 nozzle for a range of operating conditions.
For the design condition, Mj = 1.50, three complete shock cells are apparent from the baseline
nozzle. The first cell is very sharp. The second cell, which begins as the waves reflect from the shear
layer, is less sharp. This is because the reflections occur at a shear layer which is not stationary.
Turbulent structures convecting through the shear layer cause the sonic line to move about. As waves
reflect from the sonic line they acquire some unsteadiness at the point of reflection. Since the second
cell is fluctuating with a small amplitude the averaging operation causes the image to be smeared. The
third cell is still less sharp because the second reflection imparts additional unsteadiness to the onward
running wave. The unsteady influence of multiple reflections is cumulative. Each cell fluctuates more
than the one before and so the averaged image of each cell is more smeared than the one before.
The chevron image for Mj = 1.5 shows that this progressive smearing of later shock cells is stronger with
chevrons. The first and second cells are visible on the chevron image, but the third is indiscernible. The
overexpanded cases (Mj = 1.22, 1.36 and 1.47) show less difference between the baseline and chevron
cases in this respect. The most overexpanded chevron case, Mj = 1.22 looks no less clear than the
corresponding baseline image. The underexpanded cases do show a difference in clarity between the
chevron and baseline images.
All chevron images with Mj > 1.22 reveal a pair of roughly axial lines trailing from somewhere in
the middle of each chevron edge. Each pair of lines from neighboring chevrons converge with one
another at some point downstream. These are the signatures of the vortices shed from each chevron
edge. For the highest jet Mach number the vortices shed very close to the chevron root and merge with
their counter-rotating neighbors very shortly after. The lines begin to merge at a point barely
100
downstream of the chevron tips. For lower jet Mach number the point at which the vortices shed
moves closer to the tip of the chevron. The pair of lines start farther apart and merge farther
downstream. For Mj = 1.36 the point at which the vortices shed is two thirds of the way to the chevron
tip and merger does not occur until the end of the first shock cell. For Mj = 1.22 no such vortex lines
appear in the image. This indicates that the chevrons are having little if any effect for this low jet Mach
number.
For all cases of Mj > 1.22 the chevron images exhibit a large number of diagonal lines which are
very sharp near the nozzle. They become more pronounced as the jet Mach number raises and for the
highest value, Mj = 1.71, they completely obscure the lines associated with the shock cells. Detailed
Particle Image Velocimetry measurements in a plane containing the jet axis (shown in the next section)
will not reveal any corresponding linear features so one may conclude that these additional lines are
stationary features in the shear layer. The absence of these lines for Mj = 1.22 is another indication that
the chevrons do little for this operating condition.
Nozzles with conical convergent and divergent sections and sharp throats have previously been
shown to produce shock cells when operated on-design as well as off-design (Chapter 4). The
shadowgraph images in Figure 5.2 reveal that the introduction of chevrons does not change this. Shock
cells are apparent for the design condition as well as over and underexpanded conditions.
The introduction of chevrons produces substantial mixing by bulk interchange of fluid between
the jet and its surroundings. The gross increase in spreading shown in Figure 5.1b shows that the outer
extent of the mixing zone is greatly expanded. The corresponding Mj = 1.56 chevron image in Figure 5.2
has two bright lines diverging from the upper edge of the jet and matching set diverging from the lower
edge. The inward running line traces the shear layer deflected inward by the presence of the chevron.
The outward running line traces the shear layer that emerges from between the chevrons. Since
shadowgraph integrates along a line of sight these two are superimposed in one image. Comparing the
101
position of these lines with near-nozzle PIV shown in Figure 5.3 confirms that the two lines do in fact
mark the positions of the shear layer downstream of a chevron tip (Figure 5.3b) and emerging from
between two chevrons (Figure 5.3c). In this case the inward line on the shadowgraph corresponds to
the edge of the high-velocity region in the plane containing the chevron tips and the outward line
corresponds to the edge of the high-velocity region in the plane between the chevrons.
5.2 Effective Penetration of Chevrons
Lines marking the differences between the chevron tip and chevron valley planes are present in
all the images with Mj > 1.22. In all cases the angle of the inward line is the same for all jet Mach
numbers. The angle of the outward running line changes with jet Mach number turning farther outward
as jet Mach number increases. Increasing jet Mach number takes the jet in the direction from
underexpansion toward overexpansion and turns outward the shear layer from the baseline case as can
be seen in the series of baseline images in Figure 5.2. So as the jet Mach number rises, the undisturbed
angle of the flow near the nozzle lip turns increasingly outward. Placing fixed chevrons in the path of
this flow will then be a greater intrusion into the undisturbed flow the greater the jet Mach number. For
the case of Mj = 1.22 it appears that the chevrons have negligible effect. This is because the effective
penetration is zero. As the jet Mach number increases, and the flow attempts to turn farther outward
past the fixed chevrons which do not change their angle. The angle between this undisturbed flow angle
and the angle of the chevrons is one aspect of chevron penetration and from the fact that the angle
increases with increasing Mj one may conclude that effective penetration increases as Mj does. This has
a strong acoustic influence as will be shown in a later section.
5.3 Shock-cell Structures and Shear Layer Changes
In order to escape the line-integrating limitation of shadowgraph PIV was taken very near the
nozzle in two planes through the axis of the jet. The first plane includes the tips of opposite chevrons
102
and reveals the behavior of the fluid which is forced inward by the chevrons. The second plane lies in
the center of the valley between chevrons and similarly reveals the behavior of the outward flowing
fluid. These planes are compared with corresponding PIV for the baseline case in Figure 5.3. Since the
baseline case is axisymmetric one plane is sufficient. The chevron plots begin farther downstream that
the baseline plot because of the necessity to avoid laser reflections from the chevrons themselves. The
baseline plot measurement domain begins close to the nozzle exit, while the chevron nozzle
measurement domain begins slightly downstream of the chevron tips.
The difference in the shock structure between tip and valley planes is minimal however. The lip
shock is made steeper by the presence of chevrons. It forms a Mach disk at x/De = 0.4 while the
corresponding Mach disk in the baseline plot lies between x/De = 0.5 and 0.6. Even when far from the
axis however there is no difference between the lip shock in the tip and valley planes. (Shock strengths
will be examined below.)
In the baseline nozzle the throat shock reflects from the shear layer at an axial location that the
chevrons occupy in the chevron nozzle. While the throat shock will reflect from a shear layer in opposite
sense as a Prandtl-Meyer wave, the throat shock should reflect from the surface of the chevrons in the
same sense as a shock wave. No shock wave is discernable, however at the axial location where the
measurement domain begins. The two reflected waves have coalesced into an expansion which reaches
the centerline at x/De = 0.8 and the position of this crossing is not changed by the presence of the
chevrons.
The shear layer in the chevron valley plane is shifted radially outward when compared to the
baseline plane. This is required to make up for the forcing inward of the flow by the chevrons. The edge
of the shear layer in the chevron tip plane is more complicated. There is a strong shear layer which
slopes inward downstream of the chevron tip, but there is some accelerated flow at larger radius. This
represents flow accelerated by the neighboring high-speed flow from between the chevrons. Since the
103
chevrons will produce a low pressure region behind them some higher speed flow shifts
circumferentially in the direction from the valley plane toward the tip plane to make up this pressure
deficit. This causes the band of accelerated flow outside the main shear layer and will eventually lead to
a coalescence as the get returns to a roughly axisymmetric condition farther downstream.
Figure 5.4 shows cross-stream velocity profiles from PIV for the Md = 1.5, Mj = 1.47 case with
chevrons. A cross-stream cut through the jet in a plane at x/De = 2 shows that strong velocity
components in the outward radial direction exist between the chevrons. The regions of outward radial
velocity expand outward as they move downstream. These outward flowing regions are what produce
the outer lines visible in the averaged shadowgraph. Since shadowgraph is a line-integrating technique
both chevron trough and adjacent chevron valley features are visible in the same images.
Cross-stream Stereo PIV was taken in a limited number of planes behind this nozzle and for a
limited number of operating conditions. (More planes were taken behind the Md = 1.56 nozzle and
these will be examined below) All three components of velocity are shown for Mj = 1.47 and x/De = 2.0
in Figure 5.4. The streamwise velocity is shown by the color map while the cross-stream velocities are
shown by arrows. The black circle indicates the exit diameter of the nozzle, and the missing data regions
were spoiled by laser light reflected from the hardware contaminating the PIV images.
The application of chevrons produces a large convolution of the shear layer. Chevrons force
negative radial velocity behind the lobes and induce positive radial velocity between the lobes. This
convolution persists several diameters downstream of the exit as can be seen in Figure 5.4. The
potential core of the jet is reduced in diameter, and the sonic surface is also convoluted and made
radially smaller. The radially smaller supersonic region reduces the shock cell spacing which in turn
shifts the peak frequencies.
Shock cell size is often found by examining the pressure or velocity along the centerline of the
jet. The presence of the central slip line from this type of nozzle makes the centerline a special case
104
containing subsonic regions after the Mach disks and substantial accelerations not caused directly by
expansion waves. Instead of determining shock cell spacing from centerline data, features associated
with the shear layer will be used. At the end of every shock cell a shock wave or a Prandtl-Meyer wave
reflects from the shear layer. These reflections are easily identifiable and are features present in
smoothly varying C-D nozzles as well as the conical C-D nozzles under study here. The shock cell size will
therefore be determined by finding the axial distance between these reflections.
The positions of these reflections are plotted in Figure 5.5. These positions are extracted from
the shadowgraph images. For the baseline cases where a double-diamond is shown, the reflection from
the upstream diamond is used since this is related to the wave emanating from the nozzle lip. It can be
seen that the effect of chevrons is to reduce the shock cell size. This is likely due to the increased
spreading of the shear layer, which reduces the diameter of the supersonic region. This decreases the
lateral length scale, and since the cell size is governed by the oblique shock and Prandtl-Meyer angles it
also reduces the length of the shock cells. The cells with chevrons are on average 5% shorter than the
baseline cases. For the highest Mj cases it was impossible to determine which reflection was the one of
interest in the chevron images, so Mj of 1.64 and 1.71 have been omitted from Figure 5.5.
Shadowgraph images of the chevron nozzle show numerous diagonal features near the nozzle
exit which are not present for the baseline nozzle. These features in addition to those present in the
baseline case are weakest at low Mj but become more pronounced as Mj increases until by Mj = 1.64
they obscure the expansion fan initiating the shock train. The PIV in Figure 5.3 shows that for Mj = 1.56
there are no corresponding high-gradient features in the cross-sections measured. This implies that
these lines are not from shocks within the core of the jet. They must be features within the shear layer
which show in the shadowgraph because of the line integrating nature of the measurement technique.
Shadowgraph of the Md = 1.56 nozzle with and without chevrons is shown in Figure 5.6. The jet
is operating at its design condition with a secondary flow Mach number of 0.1. These images are an
105
average of 100 instantaneous shadowgraph images. This averaging suppresses the turbulence in order
to better show the stationary features of the flow.
This set of chevrons differs in detail from the chevrons applied to the Md = 1.5 nozzle, but the
major features in the shadowgraph are the same. For the baseline case one can see the features
expected for this class of nozzle. There is a shock shed from the sharp throat, which forms a Mach disk
inside the nozzle. The slip line from this Mach disk exits the nozzle near the centerline. One can also
see the onward, reflected shock as it emerges from the nozzle exit and reflects from the shear layer at
around x/De = 0.2. From here it reflects as an expansion fan running radially inwards until it meets the
slip line near the jet axis at around x/De = 0.9. This reflection occurs around the circumference of the jet
making a bright line in the shadowgraph which appears as a vertical line in the image.
These nozzles have conical convergent sections, so the velocity at the exit has an outward radial
component even when the nozzle is operated at the design condition with the pressure matched at the
exit. As a result the flow must turn into itself in order to become a parallel flow. This generates a lip
wave even at the design condition. The inward running shock wave from the nozzle lip reaches the slip
line near the jet axis at around x/De = 0.55. This lip shock then crosses the centerline and continues
outward reaching the jet shear layer at around x/De = 1.0. There are two systems of shocks with their
origins at the nozzle throat and the nozzle lip. Each of these shocks starts a train of shock cells or shock
diamonds in the jet. These are superimposed upon one another producing the double-diamond system
previously observed in unheated single-flow jets by Munday, Gutmark, Liu and Kailasanath [12].
In the chevron image, Figure 5.6b, if one looks between the chevrons near the top and bottom
of the nozzle, the internal shock can still be seen. The chevrons are 0.225De long so the shock reflects
from the chevron inner surface and from the shear layer between the chevrons. Looking between the
chevrons nearer the centerline of the image one can still see the bright lines indicating the reflection
from the near side of the jet. In this case the reflection is not circular since it is a reflection off of a shear
106
layer which is not of constant radius. The shear layer and the sonic surface within it expands between
the chevrons carrying the point of shock reflection outward with it.
A shock reflecting from a hard surface like the inside surface of a chevron will reflect as a shock.
A shock reflecting from a shear layer like the one between chevron tips will reflect as an expansion fan.
These adjacent pressure waves will tend to cancel one another as they run onward. The resultant wave
runs radially inward until it meets the slip line near the jet centerline at around x/De = 0.9. PIV shown in
Figure 5.7 reveals that the resulting wave is a shock.
The chevron image becomes somewhat difficult to interpret past the chevron tips. There are a
large number of diagonal lines superimposed on the streamwise lines generated by the chevron bulk
mixing. The double-diamond features appear to remain, but these additional features obscure things
somewhat. In order to have a better view of the flow features, PIV was performed in the near-nozzle
region. Reflection of the laser sheet from the nozzle itself spoils the PIV process and may damage the
camera so the camera was adjusted to keep the nozzle lip or the chevron tips just outside the field of
view. For the baseline nozzle PIV was taken in a single plane containing the jet axis. For the chevrons,
two axial planes were used; one passing through the chevron tips and one passing through the valleys
between the chevrons. Contour plots of axial velocity are shown in Figure 5.7. The contour interval for
all three images is 10 m/s and selected contours have been labeled with the velocity in m/s. This
depiction gives a good qualitative picture of the flow and particularly brings out the high-gradient
features.
The baseline plot, Figure 5.7a shows velocities within 0.01De from the nozzle exit. It shows the
slip line with a width of 0.04De along the centerline, giving an estimate of the Mach disk diameter. The
throat shock enters the image at 0.013De with a shock angle of 38° with respect to the jet axis.
Projecting this upstream to a Mach disk radius of 0.02De gives an estimate of the Mach disk axial
location of x/De = -0.42. This shock reflects from the shear layer at around 0.18 De creating an expansion
107
fan which runs inward until is reflects off of the slip line at x/De = 0.82. The outward running wave
reflected is again a shock so the reflection was due to the shear layer created by the perimeter of the
upstream Mach disks.
The lip generates an inward running shock which forms a Mach disk at x/De = 0.55, forming an
outward running shock with reflects from the shear layer at x/De = 1.0. The inward running wave from
this point is an expansion fan which runs beyond the measurement domain.
The shock strengths can be evaluated by determining the shock angles, the component of
velocity normal to the shocks and the ratio of normal velocities before and after the shocks. The ratio of
normal velocities is related to the ratio of densities by continuity:
un1/un2 = ρ2/ρ1
and from this one can find the normal Mach number and the shock strength P2/P1 from standard shock
tables or equations. This calculation has been performed on the shocks at two radial locations, r/De =
0.1 and 0.4. The points where the shocks reach these radii are labeled by letters on Figure 5.7a. The
locations, angles and shock strengths are tabulated below. Locations “a” and “f” are associated with the
throat wave. The remaining locations are associated with the lip wave.
The most striking difference between the baseline and the chevron cases is the position of the
shear layer. For the baseline case, the jet remains generally cylindrical and the radius of the shear layer
remains roughly r/De = 0.5. For chevron nozzle we see very large shifts in the shear layer position. For
x/De = 1.0 we see r/De = 0.45 for the plane passing through the chevron tips and r/De = 0.6 for the plane
passing through the valleys between the chevrons.
Velocity profiles at x/De = 0.5 are shown in Figure 5.8 for the baseline nozzle and in two planes
for the chevron nozzle. There is a low velocity region near the axis for all three cases, then a higher
velocity outside the slip line, then one can see the lip shock reducing the velocity again. The shear layer
location varies at this location between the different nozzles. For the baseline the shear layer is
108
centered on r/De = 0.51. In the plane containing the chevron tips the shear layer is centered at r/De =
0.46 and in the plane of the valleys at r/De = 0.55. In part (b) of the same figure the corresponding
turbulent kinetic energy (TKE) profiles are plotted. The peaks locations correspond with the shear layer
locations. At this radial location it is clear that the chevrons are producing more TKE than the baseline in
both planes.
Cross-section views of the mean axial velocity at x/De = 1.0, 2.0 and 4.0 are shown in Figure 5.9.
These give a qualitative picture of the development of the chevron shear layer. Between x/De = 1.0 and
2.0 the convolution of the shear layer due to the chevrons becomes less severe. By x/De = 4.0 the jet as
evolved into an axisymmetric state.
These changes in the shear layer geometry are what is commonly seen in subsonic jets, and one
would expect this effect to generate more high-frequency mixing noise near the nozzle, reduce the
lower frequency mixing noise near the end of the potential core and shorten the potential core. The
principal interest in this study is the shock-associated noise, and how the mechanisms of shock
associated noise are modified by chevrons. Effort is concentrated on the changes to the shock
structure.
Centerline mean axial velocity is plotted in Figure 5.10a. The centerline lies within the slip line in
a region which is subsonic over parts of its length, but examination of Figure 5.7 reveals that normal
shocks cross the centerline where the oblique shocks reach the slip line. Figure 5.10a shows that the
reflection of the lip shock is shifted upstream from x/De of 0.55 to 0.50. Despite interacting with the lip
shock which moves, the position of the throat shock reflection at x/De = 0.89 remains fixed in position
with or without the chevrons. Figure 5.10b shows the mean axial velocity at r/De = 0.1 which is outside
the Mach disks and slip lines for all cases. This plot shows a closely spaced pair of shocks near where the
lip shock forms a Mach disk. We see the inward running shock immediately followed by the outward
running reflected shock. Both of these are shifted upstream by the chevrons. These are followed by an
109
acceleration due to the expansion fan which reflects as a shock which crosses at x/De = 0.95. The third
plot in this figure, (c) is at r/De = 0.4 which is inside the shear layer, but close to it. For the baseline case
one can see two closely spaced shocks at x/De = 0.062 and 0.131. These are the outward running throat
shock and the inward running lip shock respectively. The outward running lip wave appears at x/De 0.92
and 0.83 for the baseline and chevron nozzles respectively. Note that there is no difference in the
position of the shock between the tip and valley planes of the jet with chevrons.
The strength of the lip shock at location “c” where r/De = 0.1 on the inward running lip shock are
shown in Table 5.1 For the three lower values of M2 of 0.0, 0.1 and 0.3 we see a pattern in which the
shock in the plane with the chevron tips is stronger than the baseline shock, which is stronger than the
shock in the plane of the chevron valleys. For M2 = 0.8 the situation is different. The strength in the
chevron valley plane is stronger than the baseline case. For M2 = 0.8 the data for the chevron tip plane
is unavailable due to failure of the seeders while taking data. The position of point “c” is the same for
chevron tip and valley, to within experimental uncertainty, and this point moves upstream when the
chevrons are applied relative to the baseline location for M2 = 0.0, 0.1 and 0.3. For M2 = 0.8 the location
of point “c” is farther downstream with chevrons than it is with the baseline nozzle.
Since point “a” is not within the measurement domain for the chevron nozzle the only location
where one can see the effect of chevrons on the throat wave is location “f”. This is at r/De = 0.1, after
the initial outward running throat shock has reflected as an inward running expansion, the then
reflected again outward as a shock. The shock strengths for this location are shown in Table 5.2. For M2
= 0.0, 0.1, and 0.3 the location of point “f” changes little with either changes in M2 or with the addition
of chevrons. The shock strengths also change little for these three conditions, but the trend is for
chevrons to weaken the shock at this location. The most striking change in location “f” is it’s complete
absence for M2 = 0.8. The shock is so weakened for this condition that it is immeasurable with or
without chevrons.
110
5.4 Far-field Acoustics
Chevrons have been shown to reduce shock associated noise. It has long been understood that
breaking up the helical mode by breaking symmetry will reduce or eliminate screech, so it is unsurprising
that chevrons eliminate screech. The goal of this paper was to look into the mechanisms of reduction of
broadband shock associated noise (BBSN) by chevrons by examining the effect of chevrons on the shock
structure within the jet. It has been shown that chevrons do reduce shock strength in places, but also
that they increase shock strength in others. Within the near-nozzle region it was shown that chevrons
increase turbulence, though it would not be surprising to learn that they reduce turbulence farther
downstream. Further work is warranted in looking at the turbulence farther downstream, and in
looking at the length scales of the turbulence throughout the jet.
Far-field acoustic measurements were taken of the Md = 1.5 nozzle with and without chevrons.
The results are summarized in Figure 5.11. Three inlet angles are shown. ψ = 35°, in the forward
(upstream) quadrant best shows the shock associated noise, both screech and Broad-Band Shock-
associated Noise (BBSN) propagate most strongly into the forward quadrant. The spectra for the
different values of Mj have been shifted vertically for greater clarity, but corresponding spectra with and
without chevrons remain on the same scale. The addition of chevrons has no discernable effect on Mj =
1.22. Presumably the flow parallel to the chevron surfaces as it contracts for this most strongly
overexpanded case, and the effective penetration is negligible.
For all other cases the influence of the chevrons is quite strong. As one would expect, the
chevrons break the axial symmetry of the nozzle, suppressing or even eliminating the screech tone.
Screech frequencies and amplitudes observed at ψ = 35° are shown in Table 5.3. The reductions in peak
amplitude range from 17.5 to 26.4 dB which represent a substantial reduction, but it must be
recognized that screech is not common in full-scale heated jets so this substantial reduction is of mostly
academic interest, and is fully expected for any symmetry breaking flow control technique.
111
Fortunately, the influence of chevrons gives more than screech reduction. For most cases the
BBSN peak as observed at ψ = 35° is also reduced and shifted to higher frequency. The influence at Mj =
1.22 is again negligible. At Mj = 1.36 the BBSN is slightly elevated with chevrons, but for all remaining
cases the amplitude of BBSN as observed from the forward quadrant is the same or is reduced.
The frequency of BBSN changes with the observation angle due to Doppler shift, so we would
not expect the near-field fluctuations generating BBSN to occur at the frequencies observed in the
forward quadrant. A near-field microphone somewhere along the jet will see some sources moving
towards it causing a Doppler shift to higher frequencies, and some sources moving away from it causing
a shift to lower frequencies. So there is no single frequency we can tie to the generation of BBSN. The
best we can do is try to look at an unshifted frequency by taking the far-field measurement at ψ = 90° as
our guide in looking for BBSN sources. The spectra from this angle are shown in Figure 5.11b.
The far-field spectra from a side angle show that chevrons generally reduce the amplitude of the
BBSN peak and shift it to higher frequencies as in the forward angle measurement. The side angle
measurement also reveals in the chevron data the presence of the second lower amplitude peak at
approximately twice the frequency of the primary BBSN peak. This is a harmonic effect and the small
increase in noise at these frequencies is due to BBSN. A second peak is not visible in the baseline nozzle
case. Presumably this is because it is masked by mixing noise. The chevrons are reducing the mixing
noise and revealing the presence of this second harmonic of the BBSN. The frequencies and amplitudes
of the BBSN peaks as observed from ψ = 90° are also shown in Table 5.3.
For Mj = 1.22 the effect of the chevrons is negligible. For Mj = 1.36, there is a small increase in
the BBSN peak of less than 2 dB. For the remaining cases there is a reduction in peak BBSN from 2.3 to
9.1 dB. The reduction in BBSN noise increases as the degree of overexpansion increases. This is due to
the increased effective penetration of the chevrons as the local velocity vectors point more in the radial
112
direction while the angle of the chevrons remains fixed. The shift in frequency between the baseline
BBSN peak and the chevron BBSN peak also increases with Mj.
Both components of shock-associated noise dominate in the forward direction, while mixing
noise tends to propagate most strongly into the aft quadrant. Far-field measurements from ψ = 150°
are shown in Figure 5.11c. At this angle the signature of the shock associated noise is not apparent. This
angle is therefore useful in examining the effect of chevrons on mixing noise.
As with all other components of noise, the effect of chevrons for Mj = 1.22 is negligible. For Mj =
1.36 and 1.47, both overexpanded cases, there is a low frequency reduction of noise and no change in
amplitudes at higher frequencies. The frequency at which reduction ceases is lower for Mj = 1.36 than
for 1.47. It appears that this is unrelated to the overexpanded condition since the trend continues with
the region of nose reduction extending to higher and higher frequencies as Mj increases. For Mj = 1.64
and 1.71 there is reduction across the entire measured range. The peak mixing noise is also included in
Table 5.3. The reduction in peak noise as measured from ψ = 150° ranged from 3.2 to 5.0 dB except for
Mj = 1.22 where the change is negligible.
Looking again at Figure 5.11a&b, measured spectra at ψ = 35° and 90°, we further note that for
frequencies below the screech tone and Mj higher than 1.22 we see either reduction or no change. This
is another indication of reduction in mixing noise since shock noise is confined to frequencies at or
above the screech tone.
Far-field OASPL is shown in Figure 5.12. These show that when all noise sources are integrated
together the chevrons can increase this overall noise for overexpanded conditions in the forward
quadrant at angles of 50° and 70°. Their overall effect is negligible for Mj = 1.22 at all angles and for 1.50
except for the aft-most angles. For all underexpanded cases, however, there is OASPL benefit at all
angles.
113
5.5 Near-field Acoustics
Near-field measurements were taken beginning with one microphone positioned in the exit
plane of the baseline nozzle at r/De = 0.85 and an additional 31 microphones arrayed along a line angled
10° from the nozzle axis in order to clear the shear layer as the jet spreads. These microphones are
evenly spaced to an axial distance of x/De = 11.4. These microphones were then traversed outward
along a line perpendicular to their length sweeping out an area of near-field measurement.
The spectra from all 32 microphones in their initial positions is shown in Figure 5.13. These are
the spectra just outside the shear layer. The left side shows the baseline nozzle without chevrons. The
most prominent feature in these plots is the screech tone. For Mj = 1.36 we see the screech tone
originates from a region from the nozzle exit extending axially to x/De = 6.5 if we take the 135 dB line as
its limit. As Mj increases, the region emitting screech extends farther downstream to at least x/De = 11.4
which is the limit of our present measurements.
Examining Mj = 1.36 and taking the 120dB contour as our guide we can see that a much more
broad-band source of noise extends from x/De = 2 to 8.5 with a sharp reduction in both axial directions
from this region. As we move to higher values of Mj we see the same sharp change near x/De = 2, but
the levels remain high to the downstream limit of measurement. We suspect that the region of broad-
band noise grows longer with increasing Mj, but further measurement will be necessary to confirm or
deny this hypothesis. We suspect that the downstream limit of this broadband source is the end of the
shock train.
The right side of Figure 5.13 shows similar spectra for the nozzle with chevrons. For the
overexpanded cases there is a faint screech tone visible, but the dominant feature is a much broader
peak which increases in frequency in the downstream direction. If we look at the 125 dB contour it
looks like a finger curved to the right. The frequency associated with the BBSN peak measured at 90° in
114
the far-field corresponds roughly to the tip of the finger and the tip moves downstream with increasing
Mj.
This finger-like feature is present in the overexpanded and perfectly expanded cases, but
disappears for the underexpanded cases for which there is a trend of generally increasing noise across
the spectrum with increasing Mj. All frequencies are loudest near the nozzle exit with a high intensity
lobe extending to x/De = 2 or 3 then lower levels evenly distributed farther downstream. This is an
indication that the chevrons themselves are creating noise. This is not unexpected. In subsonic cases
we attempt to balance high frequency noise production by the chevrons near the nozzle exit, against
lower frequency noise reduction farther downstream. In this case, however we are seeing low
frequency noise generated near the nozzle as well, particularly at high Mj.
Spatial maps of the distribution of near-field sound are shown in Figure 5.14 through Figure
5.18. Frequencies were selected based on the far-field spectral features listed in Table 5.3.
Examining the maps for 1000Hz in Figure 5.14, a frequency below that at which shock-
associated noise occurs, we can see the low frequency mixing noise characteristics. For Mj = 1.22, as in
everything else we have examined, there is no discernable difference with and without chevrons. For Mj
= 1.36 we see the reduction of a region of noise production from x/De = 5 to 10. For Mj = 1.47 we see a
similar reduction, but farther downstream, from x/De = 6 to the limits of our measurement. This trend
of noise reduction moving farther downstream continues until we reach Mj = 1.56 where we begin to
see the chevron case producing an increase in noise from x/De = 1.75 to 4. This lobe of noise generated
by the chevrons does not shift appreciably as Mj increases, but the amplitude of the generated noise
increases.
Examining the plots corresponding to the screech frequency in Figure 5.15 we see that for the
baseline nozzle the pattern is a periodic source distribution along the axis. Introduction of chevrons
removes these periodic lobes, and reduces noise overall at this frequency for all Mj below 1.50. For this
115
value and above we see an overall reduction except in the region from x/De = 1.75 to 4. In this narrow
range we again see noise produced by the chevrons and their vigorous mixing.
Figure 5.16 shows the frequencies associates with the BBSN peak measured at side angles in the
far-field. We see in these that the baseline nozzle is producing a large lobe of noise generated from x/De
= 5.0 for Mj = 1.22 and shifting to 10 or 11 by Mj = 1.71. For all Mj above 1.22 we see this lobe being
reduced in intensity and moving downstream when chevrons are added. Since BBSN tends to be
greatest near the end of the potential core, this suggests that the core length is increased by chevrons.
Again we see that chevrons are producing noise in the near-nozzle region from x/De = 1.5 to 3.
We cannot tie the high-frequency plots of 30,000Hz in Figure 5.17 to any specific generation
mechanism. We take 30,000Hz to represent the upper frequencies, which are the only part of the
spectrum to show any far-field increase due to chevrons. These increases are modest compared to the
reductions we see in other parts of the spectrum and only occur in overexpanded or perfectly expanded
conditions. For all conditions above Mj = 1.22 we see an increase in sound at this frequency in the near-
nozzle region. For the Mj = 1.36 the increase occurs over a substantial axial range, but for all higher
cases the sound production is confined to the region near the nozzle. Interestingly, the increase in the
near nozzle region at these upper frequencies gets stronger with increasing Mj but in the far field this
strong increase is counterbalanced by reductions farther downstream so that for all Mj = 1.56 or above
there is no far-field increase at this frequency.
Finally, looking at the OASPL maps in Figure 5.18 we see that for Mj = 1.22 there is not any clear
trend when chevrons are added. For the baseline nozzle without chevrons we see increasing overall
noise as Mj increases, with the noisy region becoming wider and moving downstream. In the
downstream region adding Chevrons reduces OASPL beyond x/De of 4. From x/De of 1.75 to 4, however
we see OASPL increases for all Mj of 1.50 and above.
116
Shadowgraph showed large increase in bulk mixing due to chevrons. This mixing causes the
shear layer to thicken, which reduces the diameter of the supersonic region. This in turn shortens the
shock cells. Sorter shock cells drive the shock-associated noise components to higher frequencies. The
BBSN frequency observed in the near field has a dependence on the axial position. It increases as we
move downstream. This suggests a reduction of shock cell spacing in the streamwise direction. Such a
shortening of the cell size is consistent with a thickening shear layer reducing the supersonic diameter as
the jet moves downstream.
Experience with chevrons in subsonic jets leads us to expect that they will create high frequency
noise near the nozzle exit, and that they will reduce the lower frequency noise farther downstream. We
also expect the penetration of the chevrons and the shear velocity across them to be the important
factors driving the degree of both of these effects. For the supersonic case we have examined, with
shock cells present at all conditions we see these same trends of lowered mixing noise away from the
nozzle and noise production near the nozzle. In this case, however we see noise generation near the
nozzle to extend to quite low frequencies.
We see substantial suppression of screech by the application of chevrons. This is hardly
surprising since screech generally depends on axial symmetry and the chevrons eliminate this. Further,
since screech is not a problem for full-scale heated jets this finding is of little practical help.
The most significant observations in this test campaign are the large reductions in broad-band
shock-associated noise in this class of nozzles. For underexpanded cases we observed reductions on the
order of 5-10 dBs. That is quite substantial.
We found that these reductions increased as Mj was increased and the degree of
underexpansion was also increased. Increase in Mj will produce an increase in the jet velocity and thus
the shear velocity across the chevrons. Greater underexpansion will increase the radial component of
velocity at the nozzle exit near the shear layer. Since the chevrons remain fixed, this increase in
117
outward direction of velocity will increase the angle between the chevron and the flow, thus increasing
the effective penetration of the chevron. This may allow substantially lower physical penetration angles
to have a pronounced effect on the nozzle when it is operated underexpanded.
5.6 Chevron Summary
Chevrons applied to supersonic jets behave in many ways as chevrons applied to subsonic jets.
They introduce streamwise vorticity and produce a jet with a lobes cross-section. They enhance bulk
mixing. They cause increased spreading of the jet. They reduce TKE and low frequency mixing noise
where it is greatest near the end of the potential core of the jet, but they introduce new TKE near the
nozzle exit and this produces new high-frequency noise in this region.
One important difference between subsonic and supersonic jets with regard to chevrons is that
the angle of flow changes with increasing jet Mach number as the jet moves from an overexpanded to
an underexpanded condition. This changes the angle of flow with respect to the fixed chevrons, so the
effective penetration of chevrons is a function of jet Mach number.
The increase of mixing due to chevrons causes the shear layer to thicken, and the diameter of
the potential core to be reduced. This also reduces the sonic radius at which the shocks reflect. This
reduces the diameter of the shock cells. Since the length of the shock cells is determined by the shock
angles and the locations at which reflection occurs, reduction of shock cell diameter also causes
reduction of shock cell length. Reduction of shock cell length causes an increase in peak frequencies of
BBSN and screech.
While the shear layer does become lobed or corrugated, the shock structure does not. The
shock cells shift and shorten, but the shocks are not corrugated and remain conical.
Shock cells originating at the nozzle exit are initially shifted upstream by chevrons, but the cells
originating at the nozzle throat are unchanged by chevrons.
118
Chevrons kill screech as tabs do. They also reduce the amplitude of broad-band shock-
associated noise and shift the peak frequency higher.
119
Table 5.1 – Shock properties, location “c”, Lip wave, inward running, r/De = 0.1
Nozzle M2 x/De angle [°] P2/P1
Baseline 0.0 0.51 -39 1.63
ChevTip 0.0 0.48 -44 1.71
ChevVal 0.0 0.48 -44 1.56
Baseline 0.1 0.50 -39 1.64
ChevTip 0.1 0.48 -44 1.70
ChevVal 0.1 0.48 -44 1.56
Baseline 0.3 0.49 -40 1.67
ChevTip 0.3 0.47 -45 1.70
ChevVal 0.3 0.47 -45 1.58
Baseline 0.8 0.43 -44 1.66
ChevVal 0.8 0.44 -47 1.70
Table 5.2 – Shock properties, location “f”, Throat wave, second outward wave, r/De = 0.1
Nozzle M2 x/De angle [°] P2/P1
Baseline 0.0 0.96 42 1.20
ChevTip 0.0 0.93 43 1.18
ChevVal 0.0 0.93 43 1.17
Baseline 0.1 0.96 42 1.22
ChevTip 0.1 0.94 42 1.19
ChevVal 0.1 0.94 42 1.20
Baseline 0.3 0.94 41 1.19
ChevTip 0.3 0.95 43 1.17
ChevVal 0.3 0.95 43 1.18
Baseline 0.8 -- -- --
ChevVal 0.8 -- -- --
120
Table 5.3 – Spectral features from Far-field observation
Mj Screech ψ=35°
BBSN (1) ψ=90°
BBSN (2) ψ=90°
Mixing ψ=150°
[Hz] [dB] [Hz] [dB] [Hz] [dB] [dB]
Baseline
1.22 6150 96.5 105.2
1.36 2000 117.0 3900 102.5 112.7
1.47 1750 111.9 3500 105.4 114.4
1.50 1650 110.1 3250 106.8 115.9
1.56 1600 106.0 3400 107.5 115.1
1.64 1600 114.3 3150 110.8 118.0
1.71 1500 119.3 2900 112.8 119.3
Chevron
1.22 6450 95.4 12100 90.6 104.7
1.36 2050 97.4 4900 104.3 9550 96.7 108.4
1.47 1800 94.3 4500 103.0 9550 97.2 110.5
1.50 1750 92.6 4400 101.1 9450 97.3 110.9
1.56 1600 88.2 4150 98.8 8200 99.1 111.9
1.64 7450 102.0 113.5
1.71 1400 92.9 3500 103.7 7100 103.8 115.0
Figure 5.1 – Instantaneous shadowgraph images, Md = 1.5, Mj = 1.56. a) baseline. b) chevron.
(
a)
d
)
121
Figure 5.2 – Averaged shadowgraph images of nozzle with and without chevrons (100 images averaged). The
camera is in a plane passing through the two chevron tips.
Mj=1.22
Mj=1.36
Mj=1.47
Mj=1.56
Mj=1.64
Mj=1.71
Mj=1.50
122
Figure 5.3 - PIV images for Md = 1.5, Mj = 1.56. Left image is the baseline nozzle. Middle image is the
chevron nozzle in a plane through the chevron tips. Right image is the chevron nozzle in a plane through the
valleys between chevrons.
Figure 5.4 – PIV of velocity modification due to chevrons, Md = 1.5, Mj = 1.47, x/De = 2. Color map is axial
velocity. Arrows show cross-stream velocity. The black circle has a diameter equal to the nozzle exit. The
missing data regions are due to hardware reflections contaminating the PIV images of the seeded flow.
123
Figure 5.6 – Shadowgraph, 100 images averaged, Md = 1.56, Mj = 1.56, T0 = 367 K, M2 = 0.1. (a) Baseline
nozzle. (b) Chevron nozzle.
b)
a)
Figure 5.5 – Shock reflection axial position with and without chevrons.
Mj = 1.22
Mj = 1.36
Mj = 1.47
Mj = 1.50
Mj = 1.56
x
/De
124
Figure 5.7 – Mean axial velocity from PIV of jet in axial planes. For all three cases: Mj = 1.56, T0 = 367 K, M2
= 0.1, T0 = 300K. Contour interval is 10 m/s. Selected contours have been labeled. a) Baseline nozzle. b)
Chevron nozzle, plane through chevron tips. c) Chevron nozzle, plane through chevron valleys. The letters
in (a) are the locations where shock strengths are determined
a)
b)
c)
u [m/s]
125
Figure 5.10 – Mean axial velocity along lines of constant radius. a) r/De = 0.0. b) r/De = 0.1. c) r/De = 0.4.
c) b) a)
Figure 5.9 – Mean axial velocity at an axial position. The contour interval is 20 m/s. Selected contours are
labeled in n/s. (a) x/De = 1.0. (b) x/De = 2.0. (c) x/De = 4.0.
4
50
4
50
2
0
0
4
50 4
50
2
0 4
50
a
)
b
)
c
)
Figure 5.8 – Axial velocity and Turbulent Kinetic Energy at x/De = 0.5, Mj = 1.56, T0 = 367 K, M2 = 0.1, T0 =
300K. a) Mean Axial Velocity. b) Turbulent Kinetic Energy.
b
)
a
)
126
Figure 5.12 – Far-field OASPL a Md = 1.50 nozzle with and without chevrons at a distance of 47 exit
diameters.
Figure 5.11 – Far-field acoustic measurements of a Md = 1.50 nozzle with and without chevrons at a distance
of 47 exit diameters from the nozzle exit. a) ψ, of 35°. b) ψ, of 90°. c) ψ, of 150°.
(
a)
(
b)
(
c)
127
Figure 5.13 – SPL Spectra in dB along a line just outside the jet, with and without chevrons.
Mj=1.22
Mj=1.36
Mj=1.47
Mj=1.56
Mj=1.64
Mj=1.71
Baseline Chevron
Mj=1.50
128
Figure 5.14 – Maps of near-field SPL at 1000Hz representing low-frequency mixing noise.
Mj=1.22
Mj=1.36
Mj=1.47
Mj=1.56
Mj=1.64
Mj=1.71
Mj=1.50
Baseline Chevron
129
Figure 5.15 – Maps of near-field SPL at the screech frequency for each condition.
Mj=1.36
Mj=1.47
Mj=1.56
Mj=1.64
Mj=1.71
Mj=1.50
Baseline Chevron
130
Figure 5.16 – Maps of near-field SPL at the peak BBSN frequency for each condition.
Mj=1.22
Mj=1.36
Mj=1.47
Mj=1.56
Mj=1.64
Mj=1.71
Mj=1.50
Baseline Chevron
131
Figure 5.17 – Maps of near-field SPL at the 30,000Hz for each condition.
Mj=1.22
Mj=1.36
Mj=1.47
Mj=1.56
Mj=1.64
Mj=1.71
Mj=1.50
Baseline Chevron
132
Figure 5.18 – Maps of near-field OASPL for each condition.
Mj=1.22
Mj=1.36
Mj=1.47
Mj=1.56
Mj=1.64
Mj=1.71
Mj=1.50
Baseline Chevron
133
Chapter 6 – Fluidic Chevron Results
6.1 Flow-field Changes Due to Fluidic Chevrons
Conventional chevrons modify the shear layer around a jet by introducing streamwise vorticity.
Each edge of the chevron sheds a vortex and the direction of rotation of the trailing vortex is opposite
for opposite sides of the chevron, thus each chevron produces a counter-rotating vortex pair. The
effects of these vortex pairs was examined in the last chapter.
In this chapter an attempt is made to introduce similar vortex pairs without chevrons. Removing
the chevrons means removing the small exit area blockage the chevrons make, and removing additional
nozzle surface and the drag associated with the flow passing over this surface. Blockage and scrubbing
drag are present in chevrons throughout the flight while the acoustic benefit desired mostly an issue in
the airport, airfield or carrier deck environment.
Fluidic chevrons aim to produce the counter-rotating vortex pairs characteristic of chevrons by
blowing air into the shear layer. The air supplied is not free. It must come from the engine somewhere
and so it will introduce losses to the total engine cycle, but unlike chevrons, fluidics be turned on for
noise sensitive portions of the flight, and turned off when noise reduction is not needed. This should
reduce the system cost for the overall mission profile.
Two fluidic arrangements were examined. For convenience they may be called the 36-20 and
60-0 configurations. The 36-20 configuration is pictured in Figure 3.5. It consists of six pairs of tubes.
Each tube is angled at 36° from the jet axis and 20° towards its partner in the pair. This configuration is
based on a configuration found successful in subsonic jets by Callender, Gutmark and Martens (2007).
The 60-0 configuration pictured in Figure 3.6 consists of 12 tubes located in the same location as the
chevron tips and angled 60° from the jet axis and 0° with respect to either neighboring tube. The tubes
in the 60-0 configuration are evenly spaced as the 12 chevrons were. This configuration is based on one
134
which was found to be successful for subsonic jets by Alklislar, Krothapalli, Butler (2007). Both the 36-20
and the 60-0 configurations were tested on the Md = 1.5 nozzle and results will be compared with both
the baseline and chevron Md = 1.5 cases.
Figure 6.1 shows shadowgraph of the 60-0 configuration compared with the baseline and
chevrons for Md = 1.5 and Mj = 1.56. Instantaneous shadowgraph images of each case are shown along
with averages of 100 instantaneous images. These averaged images emphasize the stationary features
in the flow and deemphasize the turbulence.
The instantaneous images clearly show that the application of fluidic injection is causing
increased spreading of the jet. The baseline image in Figure 6.1a shows a baseline jet with an outer limit
of the turbulence region that does not increase significantly across the width of the image. The 60-0
blowing case in Figure 6.1b. The outer limit of the jet is clearly expanding from the beginning and fills
most of the image height by the downstream end of the image. This level of jet expansion is
comparable to that shown for the chevron case in Figure 6.1c which also shows a jet that expands to
nearly fill the height of the image frame by the downstream end. The level of influence for a given
chevron geometry is a function only of the jet condition. For the fluidic case the level of influence is also
a function of the microjet pressure, Mach number or mass flow rate. These three are dependent on one
another. The case shown had a mass flow of 1.4% of the main jet mass flow which was the highest level
attainable with the supply piping used. Less mass flow (and velocity, Mach and momentum flux) would
presumably influence the shear layer less. In the limiting case of zero mass flow it would not influence
the shear layer negligibly. Greater mass flow (and velocity, Mach and momentum flux) could have a still
larger effect on the jet spreading.
Averaged shadowgraph images are shown in Figure 6.1d-f. The averaging hides unsteady
phenomena like turbulence and emphasizes the stationary features of the flow. The averaged 60-0
blowing image in Figure 6.1e is strikingly different from the averaged baseline image (Figure 6.1d) and
135
the averaged chevron image (Figure 6.1f). The baseline and chevron images are much sharper. In both
the baseline and chevron images individual shock and expansion waves are clearly evident, but the 60-0
blowing image is much more blurry. This initially caused concern that the optics might have been in
motion during the test, but careful observation reveals that the entire image is not blurred.
A feature of these military nozzles which has been presented previously (Chapter 4) is that they
produce shocks at the throat of the nozzle. For many such nozzles including this one, these throat
shocks form a Mach disk inside the nozzle which then trails a slip line in its wake. For this nozzle the
onward-running shock from the internal Mach disk emerges from the nozzle and reflects from the shear
layer outside the nozzle. Both the slip line from the internal Mach disk and the reflection of the
extended throat shock have been noted in previous chapters. In Figure 6.1d the slip lines appear as a
pair of horizontal lines passing out of the nozzle exit. The reflection of the throat shock can be seen at
the top and bottom of the jet as this shock reflects from the shear layer. Since shadowgraph is a
technique that integrates along the line of sight, this initial throat wave reflection can also be seen as a
bright vertical line which appears to connect the points of reflection at the top and bottom of the jet.
This bright vertical line is also visible near the jet centerline.
If one examines the averaged fluidic injection image Figure 6.1e in the region nearest the nozzle,
upstream of the injection tube exits, the image is quite clear. One can plainly see the slip line shed by
the Mach disk inside the nozzle and the bright vertical line where the throat shock reflects. The
sharpness of the features visible upstream of the injection tubes reveals that the optics were in fact
stationary so it must be the “stationary” features in the flow which are moving. They are not wholly
stationary, but are oscillating about a mean position leaving a blurred image in the shadowgraph.
The presence of shock diamonds can certainly be discerned in Figure 6.1e, but the fact that they
are not clear indicates that they are moving. This is in contrast to the chevron case where the shock
structures of the first shock cells remained stationary when the shear layer was disturbed. One may
136
conclude from this that the shear layer in the region of even the first reflections is made much less
steady by fluidic injection. Despite the smearing induced by the unsteady nature of the features shock
cells can be discerned in the averaged fluidic image.
In the chapter on chevrons (Chapter 5) it was noted that chevrons produce numerous diagonal
lines on the averaged shadowgraph which do not appear in detailed PIV cross sections. These can be
seen in Figure 6.1f and depict features on the near and far surfaces of the shear layer. Though they are
less clear in the averaged shadowgraph of the 60-0 blowing in Figure 6.1e they do appear indicating the
presence of similar features on the near and far surfaces of the shear layer as influenced by fluidics.
Shadowgraphs were also taken of the microjets operating with the main jet turned off. Figure
6.2a shows an instantaneous view in which the microjets can be seen coming together along the axis of
the main jet and inducing a turbulent jet passing along the main jet axis. Sound waves can clearly be
seen emanating from these microjets propagating in a direction upstream from them. The averaged
shadowgraph in Figure 6.2b shows that there are shock cells in each microjet. The microjets come from
tubes with a nominally cylindrical inner surface. They are operated at a pressure ratio well above 2.0
producing a strongly underexpanded condition so the presence of shock cells is unsurprising. This
motivates concern over the amount of noise the fluidic injection system generated independent of the
main jet. This question will be addressed in the next section.
6.2 Far-field Acoustics
The question of the noise produced by the fluidic injectors themselves is addressed in Figure 6.3.
The far-field acoustic spectrum produced by the 60-0 injectors at their maximum flow rate of 54 g/s
fluidic injection air. The three subfigures show spectra for observers at three propagation directions, ψ
= 35°, 90° and 150°. These are compared with spectra of the main jet with and without the microjets
turned on and with the background spectrum for the anechoic chamber. The 60-0 configuration is
137
shown because the microjet noise from this configuration was louder than that for the 36-20
configuration.
Over most of the range of frequencies the difference between the main jet spectra and the
noise from the fluidic injectors alone is more than 20 dB making the noise from the injectors negligible.
At the higher frequencies, above 30 kHz, there are a series of peaks in the injector spectra which radiate
strongly in the upstream and side-angle directions, but only weakly towards the ψ = 150° microphone.
At ψ = 35° one of these peaks reaches a level above that of the main jet. These are screech tones
generated by the microjets. They radiate as strongly at ψ = 90° as at ψ = 35° because the microjets have
varying orientations. The ψ = 90° microphone faces the microjet on the near side of the main jet at a
polar angle of 30° because the microjet itself is turned 60° to the main flow. Because of symmetry on
the horizontal plane, each microphone sees sound radiated at six polar angles with respect to the twelve
microjets. This spreads the peak radiation angle from the microjets.
If there were no interaction between the microjets and the main jet one would see a peak in the
main jet with microjet spectrum at 45 kHz due to the microjet screech. The level of the microjet
spectrum is above the level due to the main jet at this frequency so the peak would be visible in the
combined spectrum. The microjets and main jet do interact, and this interaction eliminates the narrow
peaks generated by the microjets. We are chiefly interested in the influence on the microjets on the
main jet, but since the main jet is so much larger than the microjet, the influence on the microjet will be
immense. With the main jet off, each microjet is axially symmetric and can support a helical oscillation
mode which supports the screech. When the main jet is turned on, however there is imposed a
substantial difference in the upstream and downstream sides of each microjet (upstream and
downstream with respect to the main jet flow). Symmetry is broken, and neither a helical nor a toroidal
mode can be supported so the screech from the microjets is eliminated.
138
With the screech tones removed by the main jet/microjet interaction the remaining microjet
spectra are each almost 20 dB below the spectra of the main jet alone and that of the main jet with
microjets even at the highest frequencies. The self noise from the microjets will be considered
negligible for the 60-0 configuration, and since the 36-20 configuration produced noise at a lower level it
will be considered negligible as well. The back ground noise, being more than 40 dB below the spectra
of interest, are considered negligible and ignored.
The fluidic injector tubes on an actual engine installation would be carefully integrated into the
nozzle so that they would present no additional drag on the outside of the aircraft. The experimental
apparatus used in the fluidic injection portion of this investigation, the Md = 1.5 nozzle, has no forward
flight simulation, and no forced flow over the outside of the nozzle. For simplicity’s sake in initial testing
of blowing arrangements the tubes injecting air into the shear layer lie outside the nozzle and may
influence the flow even when no air is supplied to the microjets. The flow entrained by the main jet
must pass over or through the supply plenum and injection tubes and this will influence the acoustic
behavior of the jet as can be seen in Figure 6.4.
Far-field acoustic measurements were taken of the main jet alone, the main jet with the 36-20
injection arrangement attached and with the 60-0 injection arrangement attached, but with no air
supplied to the microjets. Three observer angles are shown, ψ = 35°, 90° and 150° representing
forward, side-line and aft observers.
An aft observer at ψ = 150° observes little difference among the spectra. The 36-20 spectrum is
slightly lower than the others below St = 40. Above this value the 36-20 spectrum exhibits a step change
in slope turning up and raising above the other two spectra. Experience has shown that this change in
slope and spectral rise at high frequencies is a behavior associated with the difference between data
taken with grid caps on the microphones and the associated microphone corrections applied as was the
standard practice in the earlier part of this investigation. Later measurements were taken without grid
139
caps or grid cap corrections and the change in procedure occurred between the period when the 36-20
injection was tested and the period when the 60-1 injection was tested. In light of this explanation of
the change, the differences in the spectra observed at ψ = 150° are considered insignificant. This is the
direction in which mixing noise propagates most strongly and a direction in which shock-associated
noise tends to be unobservable so one may infer that the mixing noise is unchanged by the presence of
the injection hardware.
The spectra for a forward observer at ψ = 35°, a direction in which shock-associated noise is
known to propagate strongly, shows significant differences due to the presence of the injection
hardware. For both the 36-20 and the 60-0 configurations the presence of the injection hardware
causes a substantial drop in the SPL levels across the entire spectral range. This is due to suppression of
screech. The main jet entrains flow which flows over the outside of the nozzle and this flow passes over
the injection hardware. This breaks the axial symmetry within the shear layer which kills screech. Since
screech supplies a naturally occurring periodic forcing it produces a broad-band amplification as
discussed in Chapter 2. Killing screech removes this broadband amplification bringing the entire
spectrum down.
A side-line observer at ψ = 90° shows similar changes as for the forward observer. The screech
observed at 90° is completely suppressed for both the 36-20 and the 60-0 configurations. The
broadband changes are stronger for the 60-0 configuration and much weaker for 36-20. One must
conclude from this that a significant portion of the reduction found for these blowing arrangements will
be due to the influence of the injection hardware and one must be cautious against attributing all of the
benefit to the microjets interaction with the shear layer.
Far-field results for the 36-20 configuration are shown in Figure 6.6. Comparing the ψ = 35° plot
to Figure 6.4 shows that the noise reduction is dominated by the mere presence of the external injection
tubes. Adding mass flow makes very small changes, comparable in size to the uncertainty in the
140
measurement. This is particularly disappointing at ψ = 90° where even the reduction due to the
presence of the tubes is small. Since ψ = 90° dominates any fly-by measurement one can expect no
significant benefit in the community noise measure.
Scaling this data to full scale and considering some points of interest to carrier deck crewmen
show this configuration to have a net detrimental effect. The noise levels have been estimated with and
without fluidic injection at two locations where launch crew must work near the aircraft during launch.
Both locations are 8m from the aircraft centerline, this being 60% of an FA-18E’s span. One is at ψ = 90°
and one is at ψ = 35°. For both cases the engine diameter is scaled up by a factor of eight and the
observer distance is scaled to 8m for the first crewman and 14m for the second. A-weighting is applied
and the resulting weighted spectra are integrated to arrive at a single number to describe the perceived
noise. The crewman at 90° will see a -0.1 dB(A) change in sound level. The crewman at 35° sees a -4
dB(A) change which is quite significant, but is due to the presence external hardware.
Several limitations in this estimation must be noted. First 8m and 14m are not truly within the
geometric far field of the jet. Secondly no accounting is made for reflected sound from the deck or from
the blast deflector behind the aircraft. Twin jet interactions are not accounted for as would need to be
done for a twin-engined aircraft like the F/A 18. Finally both the sound levels with and without flow
control are reduced by the fact that we the experiments were run cold. Cold jets have lower sound
speed, and thus lower jet velocities and the eighth power law tells one that this will lead to a significant
reduction in sound level. This reduction will reduce both the baseline case and the fluidic injection case.
These limitations all influence both cases equally though, so one may infer from the difference that this
configuration does not produce any useful noise reduction.
The 60-0 configuration, on the other hand, does produce some useful noise reduction. The
lossless spectra are shown in Figure 6.7. The forward propagating sound spectra at ψ = 35° show
attenuation of screech, and BBSN reduction beyond what is produced by the mere presence of the
141
external hardware. There is significant reduction in ψ = 90° which is encouraging for the community
noise issue. The BBSN peak is reduced and shifted to higher frequency, which is the same behavior one
sees with chevrons. At ψ = 150° there is noise reduction below St = 40. For all angles a turn up in the
spectrum above St = 40 is seen. This is due to noise generated by the breakdown of the streamwise
vortices produced by the injection.
Considering our two carrier launch crew locations again the spectra are scaled and weighted as
described above. These give a -4 dB(A) change for the forward crewman at ψ = 35°. For a crewman at ψ
= 90° there is a 1 dB(A) reduction in perceived noise. (The limitations noted above on the scaling
technique apply equally here.)
The reduction near ψ = 90° suggests benefit in the community noise problem since for any fly-by
condition, the dominating part of the radiated noise will occur when the aircraft flying by is closest to
the observer. For the overwhelming majority of trajectories this occurs when the observer is near ψ =
90°.
6.3 Comparison with Chevrons
For comparison, spectra from fairly aggressive chevrons are shown in Figure 6.10. It can be seen
that these high-penetration chevrons have much greater noise reduction at all angles. Screech, BBSN
and mixing noise are all reduced. Only at high frequencies is there no noise reduction. Chapter 5
showed that high frequency noise is generated by the chevrons near the nozzle exit and this partially
offsets noise reduction in other locations. For a crewman 8m from the engine at ψ = 90°, chevrons will
reduce perceived noise by 1.7 dB(A). A crewman farther forward at ψ = 35° will experience an even
greater reduction of 2.2 dB(A). This powerful noise reduction is offset by a performance penalty in the
form of increased losses in the nozzle. One significant disadvantage of chevrons is that this performance
penalty must be carried throughout the entire flight, not just in the noise sensitive portions at the take-
off and landing.
142
6.4 Community Noise Extrapolation
Projection of the 60-0 data to the airport environment is shown in Figure 6.8. This figure shows
contours of peak dB(A) in the region around an airport. The plot is based on a trajectory in which the
aircraft accelerates to 90 m/s at 1200m down the runway. It then continues to accelerate as it climbs at
10° until it reaches 190 m/s. From this point it continues to climb at 190 m/s until 180 seconds at which
point it is well away from the airport and the noise levels are past their peak values for any observer
within the plot. For any location within the plotted region the noise experienced is computed at 0.5
second intervals. From this dB(A) history the peak value is extracted and used to make the contour plot.
The noise footprint for any given dB(A) level is defined as the number of square kilometers contained
within that level’s contour. Noise footprint values for baseline and 60-0 fluidics are shown in Table 6.1.
Fluidics make a substantial reduction in the noise footprint. Reductions of 20 to 30% are seen in the
number of square kilometers exposed to different limit sound levels.
OASPL for full-scale nozzle at a distance of eight meters are shown in Figure 6.9a. At all observer
angles greater than 35° the reduction by the 36-20 configuration is minor and is attributable to screech
suppression, but for all angles the 60-0 configuration produced substantial reductions. On an OASPL
basis there is a reduction of at least 1 dB at all angles. The reduction is greatest in the forward direction
and is less in the aft quadrant. Chevrons show a similar trend with best reduction forward and less
reduction aft, however the reductions are greater than the fluidics at all angles except 35°. The
reduction due to chevrons is greater than 2.5 dBOASPL at all angles. Figure 6.9b shows a similar plot for
dB(A). The trends are identical, though the differences are uniformly smaller. It should be remembered
that the chevron case shown is a fairly aggressive one, and the blowing mass-flow is only 1.4%. The
amount of blowing air used was limited by the supply piping, and a higher blowing fraction may well
produce stronger effects.
143
Our collaborator’s LES study, which fall outside the scope of this dissertation, examines the
same geometry as the 60-0 configuration studied here. Two mass flows are presented 1.2% which is
close to the 1.4% used in the experiments, but also a higher mass flow of 2.4%. The near-field spectra
predicted by LES show that increasing the mass flow increases the magnitude of the spectral changes to
a level comparable to the chevron results This suggests that increasing mass flow in the experiment
would lead to stronger noise reductions, and stronger high-frequency penalties. LES predicts that the
changes in flow and near-field acoustics imposed by 2.4% mass flow will be similar to those imposed by
chevrons. The mechanism of this is the reduction in growth of large scale coherent structures in the
shear layer. As mass flow increases, the scale of structures near the end of the shock train are reduced,
and since BBSN and screech are both products of the interaction of these structures and the shocks,
reducing the scale of the structures reduces sound production.
Fluidic injection is a promising noise reduction technique for shock containing flows. The 60-0
configuration tested herein showed reductions in far-field noise of as much as 4 dB on an OASPL bases.
The same configuration also reduced the community noise footprint by 20-30%. LES shows that that
increasing mass flow further will bring even stronger results equal to chevrons.
Injection with 36° pitch and 20° yaw produced small benefit beyond what was produced by the
hardware without any mass flow.
Mechanism of noise reduction is the same a chevrons: streamwise vortices enhance mixing and
inhibit growth of large scale structures. It appears that vortex breakdown induces thickens shear layer,
but is also a source of high-frequency noise
6.5 Fluidic Chevron Summary
Fluidic injection influences the supersonic jet in many ways like microjets have been shown to
influence subsonic jets, and like chevrons influence supersonic jets. They produce a lobed or corrugated
cross-section. They enhance bulk mixing. They increase jet spreading, though this blowing arrangement
144
did not increase it as much as this chevron arrangement did. They reduce low frequency noise and
increase high frequency noise, though again the effects were not as strong as the chevron arrangement
tested.
Microjets reduce the amplitude of broad-band shock-associated noise and shift the peak
frequencies higher. The tubes mounted externally in this arrangement break the symmetry of the
entrained flow over the outside of the nozzle and reduce screech even when there is no injection air
flowing. Turning on the injection air further reduces screech.
This particular blowing arrangement produces smaller effects than this chevron arrangement,
but LES simulations performed by our collaborators at the Naval Research Lab of this arrangement and
an identical arrangement with higher mass flow suggest that doubling the mass flow will bring the
effects of the blowing into line with the chevron result.
Table 6.1 Noise footprint values with and without fluidic injection in the 60-0 configuration with a mass
fraction of 1.4%.
145
a)
b)
Figure 6.2 - Shadowgraph of fluidic injection with the main jet off. a) instantaneous image. b) average of 100
images.
Figure 6.3 – As measured spectra with and without fluidic injection compared with the spectra for the
injection tubes operating without the main jet and the background spectra for the room. The fluidic injection
case shown is the 60-0 configuration with a mass fraction of 1.4%.
Md = 1.5. Mj = 1.56.
Figure 6.1 – Shadowgraph images of Md = 1.5 nozzle alone, with fluidics and with chevrons, Mj = 1.56. The
camera is in a plane passing through the two fluidic nozzles or two chevron tips. (a) (b) and (c) are single
images. (d) (e) and (f) are each averages of 100 images. (a) and (d) are baseline. (b) and (e) are with fluidics
in the 60-0 configuration with a mass fraction of 1.4%, (c) and (f) are with chevrons.
a) b) c)
d) e) f)
146
Figure 6.6 –Spectra with and without fluidic injection. The fluidic injection case shown is the 36-20
configuration supplied with 40 psig of air. Md = 1.5. Mj = 1.56.
Figure 6.5 – Baseline far-field spectra compared spectra similar nozzles at NASA, Glenn and Penn State
University. Md = 1.5. Mj = 1.56.
Figure 6.4 – Baseline far-field spectra compared spectra with the fluidic hardware mounted, but turned off.
Md = 1.5. Mj = 1.56.
147
Figure 6.9 – OASPL and dB(A) plots for the jet scale up by a factor of 8 and taken at an observer distance of
8m. Md = 1.5. Mj = 1.56.
Figure 6.8 – Community noise footprint plots with and without fluidic injection in the 60-0 configuration with
a mass fraction of 1.4%. Md = 1.5. Mj = 1.56.
Figure 6.7 – Spectra with and without fluidic injection. The fluidic injection case shown is the 60-0
configuration with a mass fraction of 1.4%. Md = 1.5. Mj = 1.56.
Md = 1.5. Mj = 1.56.
148
Figure 6.10 – Spectra with and without chevrons. Md = 1.5. Mj = 1.56.
149
Chapter 7 – Contribution Summary
This dissertation makes contributions in advancing the state of knowledge of supersonic jets and
jet noise in five general areas. 1) It expands the state of knowledge about the operation of practical
convergent-divergent nozzles like those used on high-performance military aircraft and how they differ
from the traditional nozzles with smooth contours and nearly isentropic flow. 2) It expands the state of
knowledge of the behavior of supersonic jets with chevrons applied and how supersonic jets are
different from subsonic jets with chevrons. 3) It similarly expands the state of knowledge with respect
to microjets or fluidic chevrons. 4) It provided high-quality reference data to two CFD groups to aid
them in validating their codes and combining simulations with experiments in jointly illuminating the
physics behind the behavior of all of these jet configurations. 5) An improved correlation is proposed for
calculating shock sell spacing which accounts for variation due to the design Mach number.
7.1 Practical Supersonic Engine Nozzles
There has been almost no work on practical nozzles published in the open literature. One paper
(Seiner & Norum, 1979) makes mention of “an F15 nozzle” but no details are given and the only results
presented are a plot of OASPL as a function of β. (This data has been reproduced in Figure 4.18.) It was
shown that the F15 nozzle made more noise at low β than a similarly sized traditional nozzle at the same
condition, but no explanation was offered.
There has, of course, been some research done by engine companies including GE, who
provided design guidance for our model development. After the baseline results included in this
dissertation were published in conference proceedings some of the GE data was published in Long and
Martens, 2009 and Martens and Spyropoulos, 2010. Some of the far-field data from the 2009 paper was
available to the author confidentially before it was published, but this was presented in 1/3rd octave
150
bands which obscured the spectral features used to identify source features and the absolute
magnitudes were not available.
Concurrent with this research program another group at Penn State University has been carrying
out a parallel project on geometrically similar nozzles at much smaller scale with screech suppressed
artificially, collaborating with NASA Glenn on a larger-scale model. Samples of data from both facilities
are included in Figure 3.16. The focus of this parallel project was on extrapolation of far-field from near-
field and not on the peculiarities of this class of nozzle.
The key original findings of this dissertation research with respect to the behavior of jets from
conical C-D nozzles follow.
That the jets form shocks at their throats which produce a set of shock diamonds which are
independent of and superimposed upon the set of shock diamonds cast from the nozzle exit. These two
sets of diamonds together have been called a double-diamond pattern which is characteristic of conical
C-D nozzles. Conical C-D nozzles have expansion sections which expand all the way to the nozzle exit, so
the flow approaching the exit is expanding and it has a radially outward component of velocity at the
exit. Beyond the exit this expansion cannot continue indefinitely so the flow must eventually turn in
upon itself and form a shock. This is true even for the design condition where there is perfect expansion
and a perfect pressure match at the exit. Because of this expanding flow and because of the shock
system cast from the nozzle throat there will never be a shock-free condition near the design point for
this class of nozzles. This is the explanation of the increased noise near the design condition observed
by Seiner & Norum. Further, observation of the spectra at and near the design condition shows that the
characteristics of shock-associated noise are present. Both screech and Broad-Band Shock-Associated
noise features are present in these spectra.
151
Away from the design condition, Conical C-D nozzles in many respects produce jets similar to
those from traditional C-D nozzles. The shock cell spacing is the same as for traditional nozzles. The
screech and broad-band shock-associated noise peaks are the same.
7.2 Chevron Nozzles
Much work has previously been done on chevrons applied to subsonic jets. A small amount of
work has been done on chevrons applied to separate flow exhaust systems with centerbodies like those
used on commercial aircraft engines by Rask, Gutmark and Martens (2006, 2007). These jets were at
low supersonic conditions convergent nozzles and with a maximum Mach number of 1.18. Shortening
of the shock cells was observed and an increase in broad-band shock-associated noise.
The GE tests by Long and Martens, 2009 and Martens and Spyropoulos, 2010 included chevrons,
but the results were published after those in this dissertation and only in 1.3rd octave bands and with
magnitudes obscured.
This work includes the first complete set of measurements presented of a conical C-D nozzle or
any nozzle without a centerbody that includes flow measurements, narrow-band far-field spectra and
near-field source mapping.
In several ways chevrons applied to supersonic jets behave like chevrons applied to subsonic
jets. They introduce streamwise vortices. They create a lobed or corrugated jet cross section. They
enhance bulk mixing and increase spreading. They reduce TKE near the end of the jet’s potential core
and introduce increased TKE near the nozzle exit. They reduce low frequency noise from near the end
of the potential core, but increase noise from the first few diameters from the nozzle, especially at high
frequencies.
One difference between subsonic jets and supersonic jets is that when you change the jet
velocity or jet Mach number a subsonic jet will not change the direction of flow at the nozzle. The flow
will go faster or slower, but will continue to flow in the same direction. Supersonic jets, on the other
152
hand, will change the flow direction as they move from overexpanded to underexpanded the flow near
the nozzle lip will change from flowing inward to flowing outward. With chevrons installed this direction
change is significant because the angle of the flow changes relative to the chevrons. As the jet Mach
number raises the angle between the undisturbed flow and the chevrons increases, thus increasing
effective chevron penetration. Since most chevron effects are strongly dependant on the degree of
penetration this will have a significant influence on the effectiveness of the chevrons. Chevron
effectiveness both good and bad will rise with effective penetration and thus with jet Mach number.
Chevrons cause a corrugation of the shear layer, but they do not similarly corrugate the shock
structure. The position of the shocks is axisymmetric even when chevrons are applied. The thickening
of the shear layer reduces the radius of the potential core, and the sonic radius as well and this shortens
the shock cells, and the lip shock is shifted upstream while the throat shocks are not.
Chevrons reduce broad-band shock-associated noise and because of the shortened shock cells
shift the peak frequency of BBSN higher. Chevrons reduce screech as tabs have previously been show to
(Tanna, 1977) and the mechanism is the same. They break the symmetry necessary for the toroidal or
helical modes that support screech.
7.3 Fluidic Chevron Nozzles
Fluidic injection has previously been studied with respect to mildly supersonic flow from
separate flow nozzles with centerbodies (Henderson and Norum, 2007, 2008) and at higher Mach
number on convergent (Krothapalli, Greska and Arakeri, 2002, Greska, Krothapalli, Arakeri, 2003) and
Greska, Krothapalli, Burnside and Horne, 2004) and traditional C-D nozzles (Greska, Krothapalli and
Arakeri, 2003) but with very high injection pressures in excess of 250 psi. This work is the first study on
supersonic jets from axisymmetric C-D nozzles with moderate injection pressures.
Fluidic injection on supersonic jets behaves in many ways like supersonic jets with chevrons and
like subsonic jets with fluidic injections. They produce a corrugated or lobed shear layer, they enhance
153
mixing and increase spreading. They reduce low frequency noise and increase high frequency noise.
They reduce broad-band shock-associated noise and shift its peak frequency higher. The external tubes
used to supply the fluidics reduce screech even when turned off. Applying blowing increases screech
further.
The particular fluidic arrangement employed at the maximum microjet mass flow used
produced less mixing, less BBSN reduction and less mixing noise reduction than the chevron geometry
employed in this study, however this blowing configuration was simulated by our collaborators at the
Naval Research Lab and also a case was simulated in which the mass flow was doubled. Comparison of
the two simulation cases suggests that increased mass flow would bring the influence of the blowing
into line with the chevrons.
7.4 CFD Validation
This dissertation work was structured as two separate projects with two separate collaborations
funded by two separate entities. In both projects there was a numerical group employing LES to
simulate the same cases as were run in the laboratory. Highly detailed data was taken on flow field as
well as acoustics and shared among the collaborators. This data was used to validate two different LES
approaches for the two different projects. The validations were published as Liu, Kailasanath,
Ramamurti, Munday, Gutmark, Lohner (2009) and Burak, Eriksson, Munday, Gutmark, Prisell (2010).
7.5 Improved Correlation for Shock Sell Spacing
The Prandtl-Pack relation provides an equation for predicting the shock cell spacing in a shock-
containing jet. It has been incorporated into the leading predictive theories for broad-band shock-
associated noise by Harper-Bourne and Fisher and by Tam. The Prandtl-Pack relation does not account
for the design Mach number, Md, of the nozzle employed, but examination of Figure 4.11 reveals that
there is in fact a strong dependence on Md. This dissertation includes a new correlation (Eq. 4.3) which
154
accurately accounts for variation in Md and reduces to the Prandtl-Pack relation for the special case in
which Md = 1. Use of this new equation will improve the accuracy of the predictive equations for BBSN
and screech and the codes built on them.
155
Chapter 8 – Recommendations for Future Work
8.1 Two-Point Correlation Studies in the Shear Layer
The shock-associated contributions to noise from supersonic jets arises from interactions
between the large-scale structures in the shear layer and the shocks in the shock cells. This study has
closely examined the shock cells and how these are influenced by the introduction of chevrons and
fluidic injection. Further study should concentrate on the behavior of the large-scale structures and how
these are influenced by chevrons and fluidics. Two-point correlation measurements by a pair of Laser
Doppler Anemometers is one approach, which would require borrowing a second LDA from another lab.
Another possibility is the use of time resolved PIV. At the time of this writing a high-speed PIV system
has recently been purchased by a lab in the UC medical school with whom we have shared equipment in
the past. This system will provide high temporal resolution, but only over a limited area. The shape of
this area can be configured into a long and narrow region, so perhaps a shear layer study with this
device might elucidate the size of the large scale structures in the shear layers studied in this effort.
8.2 Screech Removal
The presence of screech in the baseline cases studied here has been a persistent complicating
factor in this study. Full-scale engines in service do not screech, and the reason they do not is an open
question at present. One theory with some experimental support is that the difference is not scale, but
it temperature. The Md = 1.56 nozzle studied here was operated with a total temperature of 367K, but
real engines operate at temperatures as high as 800K. At present a smaller test rig is under construction
which will allow tests at temperatures representative of actual engine tests. If these tests remove
screech from the scale nozzles like the ones under study here, then it will be possible to better assess
the influence of chevrons and fluidics on BBSN without the interference of screech and the broad-band
amplification it brings.
156
For cold tests, or warm ones, further tests could benefit from an altered baseline nozzle with
small tabs inserted to kill the screech. This will, unfortunately, change the baseline jet, and require our
computational partners to duplicate the tabs in their simulations. The benefit, on the other hand, is to
allow similar examination of flow control’s effectiveness on BBSN and mixing noise without the
amplification due to screech.
8.3 Chevrons on Different Nozzles.
The nozzles built to study cold flow without a concentric secondary jet (Md = 1.3, 1.5 and 1.65)
were designed to all have the same throat diameter. Replacement nozzles can made with different
throat areas, but with exit areas and outer contours matching the Md = 1.5 nozzle. These simple
turnings would be far less expensive to make than different sized chevron caps. Since the position of
the first throat reflection (T1) varies between the nozzles making these nozzles all sized to De = 1.868”
would allow study of the interaction between chevrons and throat reflections inside the nozzle and
beyond the chevron tips.
8.4 Increased Mass Flow for Fluidics
The LES simulations done by our partners at NRL suggest that doubling mass flow to the 60-1
fluidic configuration will bring the noise reduction into line with that due to chevrons. The limitation
this far in supplying air to the fluidics is not the fluidic injectors themselves, but the supply piping.
Feeding the fluidic injectors from the main jet’s seeder port would be one way to increase the mass
flow. Feeding from the 4” line would require more hardware, but would certainly supply ample air to
increase the effectiveness of the fluidics.
157
8.5 Near-field Mapping of the Blowing Configuration
Near-field acoustical mapping has been performed on the baseline configuration and on the
chevron configuration for both the Md = 1.5 and 1.56 configurations. The source locations inferred from
these maps have been valuable in assessing the changes in the jet plume and the consequent changes in
the positions and strengths of the different source mechanisms. No similar near-field mapping has been
undertaken for either blowing configuration applied to the Md = 1.5 nozzle. Near-field maps should be
taken at the same locations as were performed for the chevron and baseline cases so that direct
comparisons can be made and inferences drawn about the changes in the different source mechanisms
under the influence of the 60-0 blowing configuration. If time is available mapping could also be
performed on the 36-20 configuration, but since the 60-0 configuration has a much larger influence
priority should be placed there.
8.6 Cross-stream PIV of the Blowing Configuration
Cross-stream PIV of the quality presented by Alklislar Krothapalli and Butler (2007) is within our
capabilities. Performing this measurement on the blowing 60-0 blowing configuration and maybe also
the 36-20 configuration. This may then be compared to the chevron cross-stream PIV or the cross-
stream PIV might be retaken so as to match the blowing cases and the data compared in a manner
similar to Alkislar’s. His paper draws conclusions from a single chevron and a single blowing case.
Comparing to a different chevron case and a different blowing configuration may or may not replicate
his results and would expand understanding of the behavioral differences between chevrons and
blowing. The aim would be to generate a paper of the depth and quality necessary to appear in Journal
of Fluid Mechanics.
158
8.7 Centerline Static Pressure Measurements
Total pressure measurements were performed using a five-hole conical probe with sampled
total pressure behind the probe’s own bow shock and a static pressure some 0.75” behind the point at
which the total pressure was measured. Simultaneous knowledge of the total and static pressures
behind a probe shock is sufficient to calculate Mach number and static pressure before the probe shock.
Careful examination of the resulting data showed that the displacement between the measurement
locations for total and static pressure introduced a problem. Particularly when a shock in the jet crossed
the probe between the two measurement locations. The remedy to this is to take the total and pressure
measurements at separate times and to use a static probe that is small compared to the features in the
flow. I have designed a suitable super-sonic probe scaled down from one used by NASA by Norum. The
solid models are complete and engineering drawings should be made and the probe used to measure
the static pressures. Calculation of Mach number and total pressure will make for better comparisons to
LES and provide a measured comparison to the PIV.
159
Bibliography
Aberg, M., Szasz, R. Z., Fuchs, L., Gutmark, E. (2007) “Numerical study of fluidic injection for noise
reduction,” AIAA-2007-11.
Ahuja, K. K., and Brown, W. H. (1989) "Shear Flow Control by Mechanical Tabs," AIAA-1989-0994.
Ahuja, K. K., Manes, J. P., Massey, K. C., and Calloway, A. B. (1990) "An Evaluation of Various
Concepts of Reducing Supersonic Jet Noise," AIAA-1990-3982.
Alkislar, M. B., Krothapalli, A. and Butler, G. W. (2007) “The effect of streamwise vortices on the
Aeroacoustics of a Mach 0.9 jet,” JFM 578:139-169.
Alklislar, M. B., Krothapalli, A., Lourenco, L. M., Butler, G. W. (2005) “The effect of streamwise
vorticity on the aeroacoustics of Mach 0.9 axisymmetric jet,” AIAA-2005-3045.
Alkislar, M. B (2008) “Aeroacoustics of Mach 0.9 jet with chevron-microjet combination,” AIAA-2008-
3041.
Alkislar, M., (2009) “Flow Characteristics of a Jet Controlled with Chevron–Microjet Combination for
Noise Reduction ,” 47th AIAA Aerospace Sciences Meeting including The New Horizons Forum and
Aerospace Exposition, Orlando, Florida, Jan. 5-8, 2009 AIAA-2009-851.
Anderson, John, D., (1990) Modern Compressible Flow, Boston (McGraw Hill).
Arakeri, V. H., Krothapalli, A., Siddavaram, V., Alklislar, M. B., and Louranco, L. M. (2003) “On the use
of microjets to suppress turbulence in a Mach 0.9 axisymmetric jet,” JFM 490:75-98.
Bechert, D. and Pfizenmaier, E. (1975) “On the amplification of broad band jet noise by a pure tone
excitation,” Journal of Sound and Vibration, Vol. 43, pp. 581-587.
Bradbury, L. J. S., Khadem, A. H. (1975) “The distortion of a jet by tabs,” JFM 70:801-813.
Bridges, J., Brown, C. (2004) “Parametric Testing of Chevrons on Single Flow Hot Jets,” AIAA-2004-
2824
Bridges, J. & Wernet, M.P. (2002) “Turbulence Measurements of Separate Flow Nozzles with Mixing
Enhancement Features” AIAA-2002-2484.
Bridges, J., Wernet, M., and Brown, C. (2003) Control of Jet Noise Through Mixing Enhancement,
NASA/TM 2003-212335.
Brown, G. L. and Roshko, A. (1974) “On density effects and large structure in turbulent mixing layers,”
Journal of Fluid Mechanics, Vol. 64, pp. 775-816.
Burak, M, Eriksson, L., Munday, D., Gutmark, E., Prisell, E. (2010) “Experimental and Numerical
Investigation of a Supersonic C-D Nozzle,”, AIAA Journal (submitted).
160
Callender, B. (2004) An Investigation of Innovative Technologies for the Reduction of Jet Noise from
Medium and High Bypass Turbofan Engines. Dissertation, University of Cincinnati.
Callender, B., Gutmark, E., Martens, S., (2004) “ Far-Field Acoustic Investigation into Chevron Nozzle
Mechanisms and Trends,” AIAAJ 43:87-95.
Callender, B., Gutmark, E., Martens, S., (2008) “Near-Field Investigation of Chevron Nozzle
Mechanisms,” AIAAJ, 46:36-45.
Callender, B., Gutmark, E., Martens, S., (2007) “A Comprehensive Study of Fluidic Injection Technology
for Jet Noise Reduction,” 13th AIAA/CEAS Aeroacoustics Conference (28th AIAA Aeroacoustics
Conference) , Rome, Italy, May 21-23, 2007, AIAA-2007-3608.
Camussi, R., Guj, G., Tomassi, F., Sisto, R. (2008) “Effect of air injection on the far field pressure
radiated from a jet at subsonic Mach numbers,” International J of Aero. 7:69-81.
Castelain, T., Sunyach, M., Juve, D., Bera, J.-C. (2006) “Effect on microjets on a high-subsonic jet.
Parametric study of far-field noise reduction,” AIAA=2006-2705.
Castelain, T., Sunyach, M., Juve, D., Bera, J.-C. (2008) “Jet-noise reduction by impinging microjets: an
acoustic investigation testing microjet parameters,” AIAAJ 46:1081-1087.
Chauvet, Deck and Jacquin (2007) “Numerical Study of Mixing Enhancement in a Supersonic Round
Jet,” AIAAJ, 45:1675-1687.
Cooper, M., and Webster, R. (1951). “The use of an uncalibrated cone for determination of flow angles
and Mach numbers at supersonic speeds,” NACA-TN-2190.
Crow, S. C. and Champagne, F. H. (1971) “Orderly structure in jet turbulence,” Journal of Fluid
Mechanics, Vol. 48, pp. 547-591.
Ffowcs-Williams, J. E., and Maidanik, G. (1965) “The MachWave Field Radiated by Supersonic Shear
Flows.” J. Fluid Mech., 21, 641–657.
Gliebe, P. R., Brausch, J. F., Majjigi, R. K., Lee, R. (1995) “Jet Noise Supression,” in Aeroacoustics of
Flight Vehicles, H. H. Hubbard, ed., Woodbury, CT (Acoustical Society of America) v. 2. pp. 207-270.
Greska, B., Krothapali (2005) “The near-field effects of microjet injection,” AIAA-2005-3046.
Greska, B., Krothapalli, A., Arakeri, V. (2003) “A further investigation into the effects of microjets on
high-speed jet noise,” AIAA-2003-3228.
Greska, B., Krothapalli, A., Burnside, N., Horne, W. D. (2004) “High-speed jet noise reduction using
microjets on a jet engine,” AIAA-2004-2969.
Gunston, Bill (1995) The Development of Jet and Turbine Aero Engines, Sparkford, Somerset, UK,
Patrick Stevens Limited
Gutmark, E. J., Schadow, K. C., and Yu, K. H., (1995) “Mixing Enhancement in Supersonic Free Shear
Flows,” Annual Reviews of Fluid Mechanics, Vol. 27, pp. 375-417.
161
Harper-Bourne, M. and Fisher, M. J., (1974) “The Noise From Shock Waves in Supersonic Jets” in Noise
Mechanisms, AGARD-CP-131 pp. 11-1 to 11-13.
Harrison, S., Gutmark, E., Martens, S. (2007) “Jet noise reduction by fluidic ingection on a separate flow
exhaust system., AIAA-2007-439.
Henderson, B. (2010) “Fifty years of fluidic injection for jet noise reduction,” International Journal of
Aeroacoustics, Vol. 9, pp. 91-122.
Henderson, B., Kinzie, K., Whitmire, J., Abeysinghe, A. (2005) “The Impact of Fluidic chevrons on jet
noise,” AIAA-2005-2888.
Henderson, B., Kinzie, K., Whitmire, J., Abeysinghe, A. (2006) “Aeroacoustic improvements of fluidic
chevron nozzles,” AIAA-2006-2706.
Henderson, B., Norum, T. (2007) “Impact of fluidic chevrons on supersonic jet noise,” AIAA-2007-3595.
Henderson, B., Norum, T. (2008) “Impact of azimuthally controlled fluidic chevrons on jet noise,” AIAA-
2008-3062.
Jubelin, B. (1980) “New Experimental Studies on Jet Noise Amplification,” AIAA 6th Aeroacoustics
Conference, Hartford, CT, 4-6 June 1980, AIAA-1980-0961.
Kinzie, K., Henderson, B., Whitmire, J., Abeysinghe, A. (2004) “Fluidic checrons for jet noise
reduction,” ACTIVE04, Williamsberg, Virginia, Sept 20-24, 2004.
Krothapalli, A., Greska, B., Arakeri, V. (2002) “High speed noise reduction using microjets,” AIAA-
2002-2450.
Laurendeau, E., Bonnet, J. P., Delville, J. (2006) “Impact od fluidic chevrons on the turbulence structure
of a subsonic jet,” AIAA-2006-3510.
Lepicovski, J., Ahuja, K. K., Brown, W. H. and Burrin, R. H., (1987) “Coherent Large-Scale Structures in
High Reynolds Number Supersonic Jets,” AIAA Journal, Vol. 25, pp. 1419-1425.
Liepmann and Roshko, Elements of gasdynamics, New York (John Wiley & Sons) 1957.
Lighthill (1952) “On Sound Generated Aerodynamically: I. General Theory.” Proc. Roy. Soc. London
Ser. A, 211, 564–581.
Lighthill (1954) “On Sound Generated Aerodynamically: II. Turbulence as a Source of Sound.” Proc.
Roy. Soc. London Ser. A, 222,1–32.
Lilley, G.M. (1974) “On the Noise from Jets. Noise Mechanisms,” AGARD-CP-131, pp. 13.1–13.12.
Long, D., Martens, S. (2009) “Simultaneous Noise and Performance Measurements for High Speed Jet
Noise Reduction Technologies,” GT2009-59073, Proceedings of ASME Turbo Expo 2009: Power for
Land, Sea and Air, Orlando, Florida, Jun 8-12, 2009.
162
Martens, S., Haber, L. (2008) “Jet noise reduction for high speed exhaust systems,”, Proc. Of ASME
Turbo Expo 2008: Power for Land, Sea, and Air, Berlin, Germany, Jun 9-13, 2008, GT2008-50455
Martens, S., Spyropoulos, J. T. (2010) “Practical Jet Noise Reduction for Tactical Aircraft,” Proceedings
of ASME Turbo Expo 2010: Power for Land, Sea and Air, Glasgow, Scotland, Jun 14-18, 2010 GT2010-
23699.
Meyer, T. (1908). Ueber zweidimensionale Bewegungsvorgaenge in einem Gas, das mit
Ueberschallgeschwindigkeit stroemt. Dissertation, Goettingen.
Michalke, A. (1965) “Spatially Growing Disturbances in and Inviscid shear Layer,” Journal of Fluid
Mechanics, Vol. 23 pp 521-544.
Liu, J., Kailasanath, K., Ramamurti, R., Munday, D., Gutmark, E., Lohner, R. (2009) “Large-Eddy
Simulations of a Supersonic Jet and Its Near-Field Acoustic Properties,” AIAA Journal, Vol. 47, 2009, pp.
1849-1864.
Munday, D., Gutmark, E., Liu J. and Kailasanath, K. (2008) “Flow and Acoustic Radiation from Realistic
Tactical Jet C-D Nozzles,” 14th AIAA/CEAS Aeroacoustics Conference, Vancouver, British Columbia, 5-
7 May 2008, AIAA-2008-2838.
Munday, D., Gutmark, E., Liu J. and Kailasanath, K. (2009) “Flow structure of Supersonic Jets from
Conical C-D Nozzles,” AIAA-2009-4005.
Munday, D., Heeb, N., Gutmark, E., Burak M., Eriksson, L and Prisell, E. (2009) “Supersonic Jet Noise
from a Conical C-D Nozzle with Forward Flight Effects,” 47th AIAA Aerospace Sciences Meeting,
Orlando, Florida, 5-8 Jan 2009, AIAA-2009-0287.
Norum, T. D. (1983) “Screech Suppression in Supersonic Jets.”, AIAA Journal, Vol. 21, pp. 235-240.
Norum, T, D. and Seiner, J, M. (1982) “Measurements of Mean Static Pressure and Far-Field Acoustics
of Shock-Containing Supersonic Jets,” NASA TM-84521.
Norum, T. D. and Shearin, J. G. (1986) “Shock Noise from Supersonic Jets in simulated Flight to Mach
0.4,” AIAA 10th Aeroacoustics Conference, Seattle, Washington, 9-11 July 1986, AIAA-1986-1945.
Opalski, A. B., Wernet, M. P., Bridges, J. (2005) “Chevron Nozzle Performance Characterization Using
Stereoscopic DPIV,” AIAA-2005-444
Pack (1950) “A note on Prandtl’s formula for the wavelength of a supersonic gas jet,” in Quarterly
Journal of Mechanics and Applied Mathematics, Vol. 3, pp. 173-181.
Pao, S. P. & Salas, M. D., (1981) “A Numerical Study of Two-Dimensional Shock Vortex Interaction,”
AIAA 14th Fluid and Plasma Dynamics Conference, 23-25 June 1981, Palo Alto, California, AIAA-81-
1205.
Pao & Seiner (1983) “Shock-associated noise in supersonic jets,” AIAA Journal, Vol. 21 pp. 687-693.
163
Papamoschou and Hubbard (1993) “Visual observations of supersonic transverse jets,” Experiments in
Fluids, 44, 468-471.
Powell, A. (1953) “The Noise of Choked Jets,” Journal of the Acoustical Society of America, Vol. 25.
Rask, O., Gutmark, E., Martens, S. (2006) ”Broadband Shock Associated Noise Suppression by
Chevrons,” AIAA 2006-0009.
Rask, O., Gutmark, E., Martens, S. (2007) “Shock Cell Modification due to Chevrons,” AIAA-2007-
0831.
Rask, O., Harrison, S., Munday, D., Harris, C., Mihaescu, M., Gutmark, E. (2007) “Jet aircraft propulsion
noise reduction research at University of Cincinnati,” AIAA-2007-5631.
Saiyed, N., Mikkelsen, K.L., and Bridges, J., 2000, "Acoustics and Thrust of Separate-Flow Exhaust
Nozzles With Mixing Devices for High-Bypass-Ratio Engines," NASA TM 2000-209948.
Samimy, M, Zaman, K. B. M. Q., Reeder, M. F. (1993) Effect of tabs on the flow and noise field of an
axisymmetric jet,” AIAAJ 31:609-619.
Seiner, J. M. and Yu, J. C. (1984) “Acoustic Near-Field Properties Associated With Broadband Shock
Noise,” AIAA Journal, Vol. 22, pp. 1207-1215.
Seiner, J. M., and Norum, T. D., (1979) “Experiments of Shock Associated Noise on Supersonic Jets,”
12th AIAA Fluid and Plasma Dynamics Conference, 23-24 July 1979, Williamsburg, VA, AIAA-79-1526.
Smith, M. T. J (1989) Aircraft Noise, Cambridge, England (Cambridge University Press).
Tam, C. K. W. (1995) “Jet Noise Generated by Large Scale Coherent Motion,” in Aeroacoustics of Flight
Vehicles, H. H. Hubbard, ed., Woodbury, CT (Acoustical Society of America) v. 1. pp. 311-390.
Tam (1998) “Jet noise since 1952,” Theoretical and Computational Fluid Dynamics 10:393-405.
Tam, C. K. W. and Chen, K. C. (1979) “A statistical model of turbulence in two-dimensional mixing
layers,” Journal of Fluid Mechanics, Vol. 92, pp. 303-326.
Tam, C.K.W., Golebiowski, M., and Seiner, J.M. (1996) “On the Two Components of Turbulent Mixing
Noise from Supersonic Jets.” AIAA-1996-1716.
Tam, C. K. W., Seiner, J. M. and Yu, J. C. (1986) “Proposed Relationship between Broadband Shock
Associated Noise and Screech Tones,” Journal of Sound and Vibration, Vol. 110, pp. 309-321.
Tam, C. K. W. and Tanna, H. K. (1982) “Shock Associated Noise of Supersonic Jets from Convergent-
Divergent Nozzles,” Journal of Sound and Vibration, Vol. 81, pp. 337-358.
Tanna, H. K., (1977) "An Experimental Study of Jet Noise, Part II Shock Associated Noise," Journal of
Sound and Vibration, 50:429-444.
164
Yu, J. C. and Seiner, J. M., (1983) “Nearfield Observations of Tones Generated from Supersonic Jet
Flows,” AIAA 8th Aeroacoustics Conference, 11-13 April 1983, Atlanta Georgia, AIAA-83-0706
Tam, C. K. W., Viswanathan, K. Ahija, K. K. and Panda, J. (2008) The Sources of Jet Noise -
experimental evidence - JFM vol. 615, pp 253-292. 2008
Yule, A. J. (1978) “Large Scale Structure in the Mixing Layer of a Round Jet,” Journal of Fluid
Mechanics, Vol. 89 pp. 413-432.
Zaman, K. B. M. Q. (2007) “Subsonic jet noise reduction by microjets with various injection port
geometries,” AIAA-2007-3643.
Zaman, K. B. M. Q. and Hussain, A. K. M. F. (1984) Natural Large-Scale Structures in the Axisymetric
Mixing Layer,” Journal of Fluid Mechanics, Vol. 138 pp. 325-351.
