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NASA/TM{1999{209336
Aeroacoustic Data for a High ReynoldsNumber Axisymmetric Subsonic Jet
Michael K. Ponton
Langley Research Center, Hampton, Virginia
Lawrence S. Ukeiley
Langley Research Center, Hampton, Virginia
Sang W. Lee
The George Washington University Joint Institute for Advancement of Flight Sciences
Langley Research Center, Hampton, Virginia
May 1999
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NASA/TM{1999{209336
Aeroacoustic Data for a High ReynoldsNumber Axisymmetric Subsonic Jet
Michael K. Ponton
Langley Research Center, Hampton, Virginia
Lawrence S. Ukeiley
Langley Research Center, Hampton, Virginia
Sang W. Lee
The George Washington University Joint Institute for Advancement of Flight Sciences
Langley Research Center, Hampton, Virginia
National Aeronautics andSpace Administration
Langley Research CenterHampton, Virginia 23681{2199
May 1999
Acknowledgment
Lawrence Ukeiley would like to acknowledge National Research Council wherehe has a NASA LaRC Research Associateship.
Available from:
NASA Center for AeroSpace Information (CASI) National Technical Information Service (NTIS)
7121 Standard Drive 5285 Port Royal Road
Hanover, MD 21076{1320 Spring�eld, VA 22161{2171
(301) 621{0390 (703) 605{6000
Summary
The near �eld uctuating pressure and
aerodynamic mean ow characteristics of a
cold subsonic jet issuing from a contoured
convergent nozzle are presented. The data
are presented for nozzle exit Mach num-
bers of 0.30, 0.60, and 0.85 at a constant
jet stagnation temperature of 104�F. The
uctuating pressure measurements were
acquired via linear and semi-circular mi-
crophone arrays and the presented results
include plots of narrowband spectra, con-
tour maps, streamwise/azimuthal spatial
correlations for zero time delay, and cross-
spectra of the azimuthal correlations. A
pitot probe was used to characterize the
mean ow velocity by assuming the sub-
sonic ow to be pressure-balanced with the
ambient �eld into which it exhausts. Pre-
sented are mean ow pro�les and the mo-
mentum thickness of the free shear layer
as a function of streamwise position.
Introduction
The noise due to the engine exhausts
of current subsonic commercial transports
continues to be a major environmental
concern to airport communities. This
noise is created by the turbulent mixing
of the exhausted jet plume with the ambi-
ent thus creating pressure uctuations in
the hydrodynamic near �eld and acoustic
far �eld regions of the jet ow. Wlezien
et al. (1998) state that this acoustic emis-
sion has limited aircraft operation to desig-
nated hours in many airports and that lo-
cal noise standards for acceptable acoustic
levels (more restrictive than current FAA
guidelines) may be imposed upon enter-
ing aircraft. They assert that noise abate-
ment may be facilitated by the incorpora-
tion of control methods designed to alter
the turbulent noise sources residing in the
free shear layer of the jet plume.
Seiner (1998) proposes that control
schemes may be based upon a low-
dimensional model of the turbulent ow
�eld. He posits that these dynamical
models can be generated by applying the
Proper Orthogonal Decomposition (POD)
(Holmes, Lumley & Berkooz, 1996) tech-
nique to the correlations of turbulent two-
point statistics. Seiner (1998) asserts
that upon completion of such a model,
Lighthill's (1952) acoustic analogy ap-
proach to understanding aerodynamically
generated sound may be used to determine
which low order turbulent spatial struc-
tures are responsible for noise generation
thus providing the base state for the design
of control methodologies. Ukeiley, Seiner,
and Ponton (1999) provide insight into the
spatial structure of the turbulent veloc-
ity properties of a subsonic jet by applica-
tion of the POD. However, further work is
necessary to establish the relationship be-
tween these turbulent velocity structures
and the turbulent pressure structures re-
sponsible for far �eld noise generation.
Michalke and Fuchs (1975) provide in-
sight into the azimuthal structure of the
turbulent pressure and velocity �elds in a
subsonic jet (Mach 0.2) shear layer while
Arndt, Long, and Glauser (1997) use the
POD technique to de�ne the structure of
the near �eld pressure uctuations sur-
rounding a Mach 0.07 jet. The purpose
of this paper is to continue characterizing
the near uctuating pressure �eld thus en-
abling additional insights into the nature
of acoustic noise sources at higher subsonic
Mach numbers. To facilitate meaningful
comparisons with research data acquired
in other facilities, the aerodynamic char-
acteristics of the plume's ow �eld are also
presented.
1
Symbols
D nozzle exit diameter, 2 in.
fc center frequency of the emitted
broadband jet noise
Mae local jet Mach number at the
nozzle exit based upon the
nozzle pressure ratio
OASPL Overall SPL in dB
re 20� 10�6 N/m2
pa test cell ambient pressure
pt local jet total pressure from
the pitot probe
r radial coordinate perpendicular
to x; referenced from the jet
centerline
SPL Sound Pressure Level in dB
re 20� 10�6 N/m2
x axial coordinate parallel to the
jet centerline; referenced from
the nozzle exit plane
U local jet velocity
Ue nozzle exit velocity
� compressible momentum
thickness
Experimental Details
The experiments were conducted in the
Small Anechoic Jet Facility (SAJF) lo-
cated at the NASA Langley Research Cen-
ter. Model hardware and instrumenta-
tion are available within the SAJF for re-
search directed at measuring the uid dy-
namic and acoustic characteristics associ-
ated with internal and external air ows.
The interior walls of the SAJF are ane-
choically treated with acoustic wedges that
absorb in excess of 99% of the incident
sound for frequencies above 100 Hz. The
internal dimensions of the SAJF (within
the wedge tips) are 10.5 ft by 10 ft by 12
ft along the x-direction. Research mod-
els are connected to an air delivery system
capable of supplying 2.5 lbm/s of contin-
uous dry air. A 275 kW resistance heater
is used to create a constant cold stagna-
tion temperature of 104�F thereby estab-
lishing an operating temperature indepen-
dent of variations in supply temperatures.
An electronically controlled valve main-
tains the nozzle pressure ratio to within
0.5% of the desired set point and pressure
transducers used by the ow control sys-
tem receive frequent in-situ calibration.
The subsonic nozzle consists of a con-
toured transition section connecting a 6
inch settling chamber to a 2 inch inside
diameter convergent nozzle. Metallic hon-
eycomb is installed in the settling chamber
to diminish large scale propagating distur-
bances. The nozzle is designed for parallel
exit ow. A 2 ft diameter circular duct
treated with �ne mesh screen is positioned
concentric to the nozzle assembly thus fa-
cilitating co- ow aspiration.
The linear and semi-circular arrays (Fig-
ure 1) incorporated seven 1/4 inch phase-
matched microphone systems. The sepa-
ration distance between each microphone
on the linear array was 1 D (i.e., 2 inches)
and the array was positioned parallel to
the jet centerline. On the semi-circular ar-
ray, a constant azimuthal separation of 30�
was used with each sensor positioned at
r/D = 2. The plane of this array was per-
pendicular to the jet centerline. For data
acquisition, both arrays were traversed in
2
the x-direction while only the linear array
was traversed in the r-direction. Data were
acquired using the semi-circular array at
x/D = 0, 1, 2, 3, 4, 5, 6, 7 and 8. For
the linear array, data were acquired at r/D
= 3, 4, 6, 8, 10, 12, 14, 16 and 18 and
the array was traversed axially whereby
the upstream microphone varied in posi-
tion from x/D = 0, 4, 7 to 13. For the
linear array data, each microphone signal
was digitized at 50 kHz and bandpass �l-
tered between 160 Hz and 20 kHz. For the
semi-circular array data, the signals were
digitized at 30 kHz and bandpass �ltered
between 160 Hz and 12.5 kHz. For all mi-
crophone data, 128 independent blocks of
1024 usable data points were recorded.
Aerodynamic Results
Presented in �gures 2 and 3 are the ra-
dial distributions for the axial mean veloc-
ity pro�les and the computed compressible
momentum thickness, respectively. The
data were reduced using pitot probe mea-
surements of total pressure by assuming
a statically pressure balanced jet. Addi-
tionally, the stagnation temperature was
assumed to be a constant 104�F for all
calculations even at large radial positions.
Because the ambient temperature within
the SAJF elevated quickly when the ex-
periment was conducted, the di�erence be-
tween the test cell ambient and the jet
stagnation temperatures introduce negligi-
ble errors in velocity and momentum thick-
ness computations. Isentropic ideal gas
ow is assumed and the ratio of speci�c
heats at constant pressure to constant vol-
ume was taken to be 1.40. The local speed
of sound was calculated using the local
jet static temperature as determined from
the stagnation temperature and the Mach
number based upon the local pressure ra-
tio, pt/pa. For momentum thickness cal-
culations, the local static density was de-
termined via isentropic equations relating
total to static density.
Acoustic Results
Presented in �gures 5 through 63 are
the narrowband spectra for the data ac-
quired using the linear microphone array.
To facilitate comparisons, the amplitude
range plotted is constant. Because the
spectral processes of primary interest are
dominant at low frequencies, a logarithmic
frequency scale is employed. A reduced
data set is presented for Mae = 0.3 due
to the presence of strong re ections from
the near �eld array supports that convo-
lute the amplitude distribution at large ra-
dial distances. Table 1 contains a descrip-
tion of the data presented within these �g-
ures. Each spectrum was computed using
128 averages of Fast Fourier Transformed
(FFT) spectral images. Each FFT image
was computed from 1024 temporal data
points.
Figures 64 and 65 contain the near �eld
pressure contour maps of OASPL as well
as SPL in select frequency bands, fc, for
Mae = 0.6 and 0.85. The data were re-
duced by digitally �ltering the FFT gener-
ated spectra in select 488.3 Hz bands. The
lowest fc value plotted corresponds to the
approximate peak frequency of the emit-
ted jet noise as indicated from the micro-
phone data acquired at x/D = 19 and r/D
= 8. This position was used to determine
the peak frequency because the end of the
potential core is located at approximately
x/D = 5 and jet noise is primarily emitted
from this location at a polar angle of about
30� with respect to the jet centerline. The
additional fc values plotted correspond to
3
Fig Mae r/D x/D Fig Mae r/D x/D
4 0.30 3 0-5 34 0.60 18 0-5
5 0.30 3 8-11 35 0.60 18 8-11
6 0.30 4 0-5 36 0.60 18 12-17
7 0.30 4 8-11 37 0.85 3 0-5
8 0.30 6 0-5 38 0.85 3 8-11
9 0.30 6 8-11 39 0.85 3 12-17
10 0.60 3 0-5 40 0.85 4 0-5
11 0.60 3 8-11 41 0.85 4 8-11
12 0.60 3 12-17 42 0.85 4 12-17
13 0.60 4 0-5 43 0.85 6 0-5
14 0.60 4 8-11 44 0.85 6 8-11
15 0.60 4 12-17 45 0.85 6 12-17
16 0.60 6 0-5 46 0.85 8 0-5
17 0.60 6 8-11 47 0.85 8 8-11
18 0.60 6 12-17 48 0.85 8 12-17
19 0.60 8 0-5 49 0.85 10 0-5
20 0.60 8 8-11 50 0.85 10 8-11
21 0.60 8 12-17 51 0.85 10 12-17
22 0.60 10 0-5 52 0.85 12 0-5
23 0.60 10 8-11 53 0.85 12 8-11
24 0.60 10 12-17 54 0.85 12 12-17
25 0.60 12 0-5 55 0.85 14 0-5
26 0.60 12 8-11 56 0.85 14 8-11
27 0.60 12 12-17 57 0.85 14 12-17
28 0.60 14 0-5 58 0.85 16 0-5
29 0.60 14 8-11 59 0.85 16 8-11
30 0.60 14 12-17 60 0.85 16 12-17
31 0.60 16 0-5 61 0.85 18 0-5
32 0.60 16 8-11 62 0.85 18 8-11
33 0.60 16 12-17 63 0.85 18 12-17
Table 1: List of Figures for Narrowband
Autospectra
the second, fourth, and sixth harmonics of
the peak jet noise frequency.
Presented in �gures 66 through 74 are
the cross-correlation coe�cients of the lin-
ear array data for zero time delay; thus,
these plots indicate the level of axial spa-
tial correlation. Each microphone on the
array was processed as the reference mi-
crophone and correlated with the remain-
ing six microphone signals. The legend be-
side each plot indicates the symbols used
to designate the reference microphone. Ta-
ble 2 contains a description of the data pre-
sented within these �gures.
Figures 75 and 76 present the cross-
correlation coe�cients of the semi-circular
array data for Mae = 0.6 and 0.85, respec-
tively, where the microphone positioned
at 0� was processed as the reference mi-
crophone. Also included are the correla-
tions for data digitally �ltered about the
Fig Mae r/D x/D Fig Mae r/D x/D
66 0.30 3-4 0-13 71 0.85 3-16 0-6
67 0.60 3-16 0-6 72 0.85 3-16 4-10
68 0.60 3-16 4-10 73 0.85 3-16 7-13
69 0.60 3-16 7-13 74 0.85 3-16 13-19
70 0.60 3-16 13-19
Table 2: List of Figures for Zero Time Lag
Pressure Correlations
peak jet noise frequency. These data in-
dicate the level of azimuthal spatial corre-
lation. For the digitally un�ltered data,
�gures 77 through 79 contain the cross-
spectra of the azimuthal cross-correlations
for Mae = 0.3, 0.6, and 0.85. These �gures
provide insight into the spatial structure
of the azimuthal pressure �eld at r/D=2.
The cross-correlation levels are consistent
with the limited measurements presented
by Pao and Maestrello (1976).
Concluding Remarks
Near �eld pressure and mean ow data,
acquired at the NASA Langley Research
Center, are presented for a contoured con-
vergent nozzle. Velocity pro�les and mo-
mentum thickness distributions are given
as well as spectra, contour maps, cross-
correlations, and cross-spectra of the uc-
tuating pressure �eld. The data are pre-
sented for nozzle exit Mach numbers of
0.30, 0.60, and 0.85 at a constant jet stag-
nation temperature of 104�F. These mea-
surements should prove useful in further-
ing the understanding of the spatial char-
acteristics of the hydrodynamic pressure
�eld and the structure of noise generating
mechanisms. Such an understanding will
ultimately lead to the development of con-
trol methodologies that minimize acous-
tic emissions thereby reducing the envi-
ronmental impact caused by subsonic com-
mercial transports.
4
References
[1] Arndt, R. E. A., Long, D. F., &
Glauser, M. N. (1997). \The Proper
Orthogonal Decomposition of Pressure
Fluctuations Surrounding a Turbulent
Jet." Journal of Fluid Mechanics 340,
1-33.
[2] Holmes, P., Lumley, J. L., &
Berkooz, G. (1996). \Turbulence, Co-
herent Structures, Synamical Systems
and Symmetry." Cambridge, Great
Britain: Cambridge University Press.
[3] Lighthill, M. J. (1952). \On Sound
Generated Aerodynamically." Proceed-
ings of the Royal Society 211(1106),
564-587.
[4] Michalke, A., & Fuchs, H. V. (1975).
\On Turbulence and Noise of an Ax-
isymmetric Shear Flow." Journal of
Fluid Mechanics 70, 179-205.
[5] Pao, S.P. and Maestrello, L. (1976).
\Evidence of the Beam Pattern Concept
of Subsonic Jet Noise Emission." NASA
TN D-8104.
[6] Seiner, J. M. (1998). A New National
Approach to Jet Noise Reduction." The-
oretical and Computational Fluid Dy-
namics 10, 373-383.
[7] Ukeiley, L. S., Seiner, J. M., & Pon-
ton, M. K. (1999, July). \Azimuthal
Structure of an Axisymmetric Jet Mix-
ing Layer." Paper presented at the 3rd
ASME/JSME Joint Fluids Engineering
Conference, San Francisco, CA.
[8] Wlezien, R. W., Horner, G. C., Mc-
Gowan, A. R., Padula, S. L., Scott,
M. A., Silcox, R. J., & Simpson, J.
O. (1998, April). \The Aircraft Mor-
phing Program." AIAA Paper 98-1927
presented at the 39th Structures, Struc-
tural Dynamics, and Materials Confer-
ence and Exhibit, Long Beach, CA.
5
Figure 1: Near Field Microphone Arrays
6
Mae=0.30
-2 -1 0 1 2r/D
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
U/U
e
x/D=10x/D=9x/D=8x/D=7x/D=6x/D=4x/D=1
Mae=0.60
-2 -1 0 1 2r/D
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
U/U
e
x/D=10x/D=9x/D=8x/D=7x/D=6x/D=4x/D=1
Mae=0.85
-2 -1 0 1 2r/D
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
U/U
e
x/D=10x/D=9x/D=8x/D=7x/D=6x/D=4x/D=1
Figure 2: Mean Streamwise Velocity Pro�les
7
0 2 4 6 8 10x/D
0
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
0.11
0.12
0.13
0.14
0.15
Θ
Mach 0.3Mach 0.6Mach 0.85
/D
Figure 3: Momentum Thickness
8
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=3.0, x/D=0.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=3.0, x/D=1.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=3.0, x/D=2.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=3.0, x/D=3.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=3.0, x/D=4.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=3.0, x/D=5.0
Figure 4: Near Field Pressure Spectra, Mae=0.30, r/D=3.0
9
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=3.0, x/D=6.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=3.0, x/D=7.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=3.0, x/D=8.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=3.0, x/D=9.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=3.0, x/D=10.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=3.0, x/D=11.0
Figure 5: Near Field Pressure Spectra, Mae=0.30, r/D=3.0
10
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=4.0, x/D=0.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=4.0, x/D=1.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=4.0, x/D=2.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=4.0, x/D=3.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=4.0, x/D=4.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=4.0, x/D=5.0
Figure 6: Near Field Pressure Spectra, Mae=0.30, r/D=4.0
11
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=4.0, x/D=6.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=4.0, x/D=7.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=4.0, x/D=8.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=4.0, x/D=9.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=4.0, x/D=10.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=4.0, x/D=11.0
Figure 7: Near Field Pressure Spectra, Mae=0.30, r/D=4.0
12
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=6.0, x/D=0.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=6.0, x/D=1.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=6.0, x/D=2.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=6.0, x/D=3.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=6.0, x/D=4.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=6.0, x/D=5.0
Figure 8: Near Field Pressure Spectra, Mae=0.30, r/D=6.0
13
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=6.0, x/D=6.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=6.0, x/D=7.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=6.0, x/D=8.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=6.0, x/D=9.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=6.0, x/D=10.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=6.0, x/D=11.0
Figure 9: Near Field Pressure Spectra, Mae=0.30, r/D=6.0
14
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=3.0, x/D=0.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=3.0, x/D=1.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=3.0, x/D=2.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=3.0, x/D=3.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=3.0, x/D=4.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=3.0, x/D=5.0
Figure 10: Near Field Pressure Spectra, Mae=0.60, r/D=3.0
15
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=3.0, x/D=7.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=3.0, x/D=6.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=3.0, x/D=8.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=3.0, x/D=9.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=3.0, x/D=10.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=3.0, x/D=11.0
Figure 11: Near Field Pressure Spectra, Mae=0.60, r/D=3.0
16
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=3.0, x/D=12.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=3.0, x/D=13.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=3.0, x/D=14.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=3.0, x/D=15.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=3.0, x/D=16.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=3.0, x/D=17.0
Figure 12: Near Field Pressure Spectra, Mae=0.60, r/D=3.0
17
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=4.0, x/D=0.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=4.0, x/D=1.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=4.0, x/D=2.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=4.0, x/D=3.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=4.0, x/D=4.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=4.0, x/D=5.0
Figure 13: Near Field Pressure Spectra, Mae=0.60, r/D=4.0
18
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=4.0, x/D=6.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=4.0, x/D=7.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=4.0, x/D=8.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=4.0, x/D=9.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=4.0, x/D=10.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=4.0, x/D=11.0
Figure 14: Near Field Pressure Spectra, Mae=0.60, r/D=4.0
19
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=4.0, x/D=12.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=4.0, x/D=13.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=4.0, x/D=14.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=4.0, x/D=15.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=4.0, x/D=16.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=4.0, x/D=17.0
Figure 15: Near Field Pressure Spectra, Mae=0.60, r/D=4.0
20
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=6.0, x/D=0.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=6.0, x/D=1.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=6.0, x/D=2.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=6.0, x/D=3.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=6.0, x/D=4.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=6.0, x/D=5.0
Figure 16: Near Field Pressure Spectra, Mae=0.60, r/D=6.0
21
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=6.0, x/D=6.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=6.0, x/D=7.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=6.0, x/D=8.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=6.0, x/D=9.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=6.0, x/D=10.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=6.0, x/D=11.0
Figure 17: Near Field Pressure Spectra, Mae=0.60, r/D=6.0
22
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=6.0, x/D=12.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=6.0, x/D=13.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=6.0, x/D=14.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=6.0, x/D=15.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=6.0, x/D=16.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=6.0, x/D=17.0
Figure 18: Near Field Pressure Spectra, Mae=0.60, r/D=6.0
23
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=8.0, x/D=0.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=8.0, x/D=1.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=8.0, x/D=2.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=8.0, x/D=3.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=8.0, x/D=4.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=8.0, x/D=5.0
Figure 19: Near Field Pressure Spectra, Mae=0.60, r/D=8.0
24
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=8.0, x/D=6.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=8.0, x/D=7.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=8.0, x/D=8.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=8.0, x/D=9.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=8.0, x/D=10.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=8.0, x/D=11.0
Figure 20: Near Field Pressure Spectra, Mae=0.60, r/D=8.0
25
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=8.0, x/D=12.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=8.0, x/D=13.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=8.0, x/D=14.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=8.0, x/D=15.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=8.0, x/D=16.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=8.0, x/D=17.0
Figure 21: Near Field Pressure Spectra, Mae=0.60, r/D=8.0
26
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=10.0, x/D=0.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=10.0, x/D=1.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=10.0, x/D=2.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=10.0, x/D=3.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=10.0, x/D=4.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=10.0, x/D=5.0
Figure 22: Near Field Pressure Spectra, Mae=0.60, r/D=10.0
27
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=10.0, x/D=6.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=10.0, x/D=7.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=10.0, x/D=8.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=10.0, x/D=9.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=10.0, x/D=10.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=10.0, x/D=11.0
Figure 23: Near Field Pressure Spectra, Mae=0.60, r/D=10.0
28
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=10.0, x/D=12.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=10.0, x/D=13.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=10.0, x/D=14.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=10.0, x/D=15.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=10.0, x/D=16.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=10.0, x/D=17.0
Figure 24: Near Field Pressure Spectra, Mae=0.60, r/D=10.0
29
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=12.0, x/D=0.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=12.0, x/D=1.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=12.0, x/D=2.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=12.0, x/D=3.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=12.0, x/D=4.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=12.0, x/D=5.0
Figure 25: Near Field Pressure Spectra, Mae=0.60, r/D=12.0
30
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=12.0, x/D=6.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=12.0, x/D=7.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=12.0, x/D=8.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=12.0, x/D=9.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=12.0, x/D=10.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=12.0, x/D=11.0
Figure 26: Near Field Pressure Spectra, Mae=0.60, r/D=12.0
31
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=12.0, x/D=12.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=12.0, x/D=13.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=12.0, x/D=14.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=12.0, x/D=15.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=12.0, x/D=16.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=12.0, x/D=17.0
Figure 27: Near Field Pressure Spectra, Mae=0.60, r/D=12.0
32
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=14.0, x/D=0.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=14.0, x/D=1.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=14.0, x/D=2.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=14.0, x/D=3.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=14.0, x/D=4.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=14.0, x/D=5.0
Figure 28: Near Field Pressure Spectra, Mae=0.60, r/D=14.0
33
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=14.0, x/D=6.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=14.0, x/D=7.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=14.0, x/D=8.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=14.0, x/D=9.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=14.0, x/D=10.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=14.0, x/D=11.0
Figure 29: Near Field Pressure Spectra, Mae=0.60, r/D=14.0
34
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=14.0, x/D=12.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=14.0, x/D=13.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=14.0, x/D=14.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=14.0, x/D=15.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=14.0, x/D=16.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=14.0, x/D=17.0
Figure 30: Near Field Pressure Spectra, Mae=0.60, r/D=14.0
35
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=16.0, x/D=0.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=16.0, x/D=1.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=16.0, x/D=2.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=16.0, x/D=3.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=16.0, x/D=4.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=16.0, x/D=5.0
Figure 31: Near Field Pressure Spectra, Mae=0.60, r/D=16.0
36
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=16.0, x/D=6.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=16.0, x/D=7.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=16.0, x/D=8.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=16.0, x/D=9.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=16.0, x/D=10.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=16.0, x/D=11.0
Figure 32: Near Field Pressure Spectra, Mae=0.60, r/D=16.0
37
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=16.0, x/D=12.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=16.0, x/D=13.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=16.0, x/D=14.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=16.0, x/D=15.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=16.0, x/D=16.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=16.0, x/D=17.0
Figure 33: Near Field Pressure Spectra, Mae=0.60, r/D=16.0
38
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=18.0, x/D=0.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=18.0, x/D=1.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=18.0, x/D=2.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=18.0, x/D=3.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=18.0, x/D=4.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=18.0, x/D=5.0
Figure 34: Near Field Pressure Spectra, Mae=0.60, r/D=18.0
39
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=18.0, x/D=6.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=18.0, x/D=7.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=18.0, x/D=8.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=18.0, x/D=9.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=18.0, x/D=10.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=18.0, x/D=11.0
Figure 35: Near Field Pressure Spectra, Mae=0.60, r/D=18.0
40
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=18.0, x/D=12.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=18.0, x/D=13.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=18.0, x/D=14.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=18.0, x/D=15.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=18.0, x/D=16.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=18.0, x/D=17.0
Figure 36: Near Field Pressure Spectra, Mae=0.60, r/D=18.0
41
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=3.0, x/D=0.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=3.0, x/D=1.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=3.0, x/D=2.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=3.0, x/D=3.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=3.0, x/D=4.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=3.0, x/D=5.0
Figure 37: Near Field Pressure Spectra, Mae=0.85, r/D=3.0
42
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=3.0, x/D=6.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=3.0, x/D=7.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=3.0, x/D=8.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=3.0, x/D=9.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=3.0, x/D=10.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=3.0, x/D=11.0
Figure 38: Near Field Pressure Spectra, Mae=0.85, r/D=3.0
43
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=3.0, x/D=12.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=3.0, x/D=13.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=3.0, x/D=14.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=3.0, x/D=15.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=3.0, x/D=16.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=3.0, x/D=17.0
Figure 39: Near Field Pressure Spectra, Mae=0.85, r/D=3.0
44
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=4.0, x/D=0.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=4.0, x/D=1.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=4.0, x/D=2.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=4.0, x/D=3.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=4.0, x/D=4.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=4.0, x/D=5.0
Figure 40: Near Field Pressure Spectra, Mae=0.85, r/D=4.0
45
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=4.0, x/D=6.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=4.0, x/D=7.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=4.0, x/D=8.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=4.0, x/D=9.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=4.0, x/D=10.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=4.0, x/D=11.0
Figure 41: Near Field Pressure Spectra, Mae=0.85, r/D=4.0
46
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=4.0, x/D=12.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=4.0, x/D=13.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=4.0, x/D=14.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=4.0, x/D=15.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=4.0, x/D=16.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=4.0, x/D=17.0
Figure 42: Near Field Pressure Spectra, Mae=0.85, r/D=4.0
47
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=6.0, x/D=0.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=6.0, x/D=1.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=6.0, x/D=2.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=6.0, x/D=3.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=6.0, x/D=4.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=6.0, x/D=5.0
Figure 43: Near Field Pressure Spectra, Mae=0.85, r/D=6.0
48
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=6.0, x/D=6.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=6.0, x/D=7.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=6.0, x/D=8.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=6.0, x/D=9.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=6.0, x/D=10.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=6.0, x/D=11.0
Figure 44: Near Field Pressure Spectra, Mae=0.85, r/D=6.0
49
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=6.0, x/D=12.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=6.0, x/D=13.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=6.0, x/D=14.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=6.0, x/D=15.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=6.0, x/D=16.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=6.0, x/D=17.0
Figure 45: Near Field Pressure Spectra, Mae=0.85, r/D=6.0
50
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=8.0, x/D=0.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=8.0, x/D=1.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=8.0, x/D=2.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=8.0, x/D=3.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=8.0, x/D=4.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=8.0, x/D=5.0
Figure 46: Near Field Pressure Spectra, Mae=0.85, r/D=8.0
51
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=8.0, x/D=6.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=8.0, x/D=7.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=8.0, x/D=8.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=8.0, x/D=9.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=8.0, x/D=10.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=8.0, x/D=11.0
Figure 47: Near Field Pressure Spectra, Mae=0.85, r/D=8.0
52
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=8.0, x/D=12.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=8.0, x/D=13.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=8.0, x/D=14.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=8.0, x/D=15.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=8.0, x/D=16.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=8.0, x/D=17.0
Figure 48: Near Field Pressure Spectra, Mae=0.85, r/D=8.0
53
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=10.0, x/D=0.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=10.0, x/D=1.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=10.0, x/D=2.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=10.0, x/D=3.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=10.0, x/D=4.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=10.0, x/D=5.0
Figure 49: Near Field Pressure Spectra, Mae=0.85, r/D=10.0
54
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=10.0, x/D=6.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=10.0, x/D=7.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=10.0, x/D=8.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=10.0, x/D=9.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=10.0, x/D=10.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=10.0, x/D=11.0
Figure 50: Near Field Pressure Spectra, Mae=0.85, r/D=10.0
55
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=10.0, x/D=12.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=10.0, x/D=13.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=10.0, x/D=14.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=10.0, x/D=15.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=10.0, x/D=16.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=10.0, x/D=17.0
Figure 51: Near Field Pressure Spectra, Mae=0.85, r/D=10.0
56
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=12.0, x/D=0.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=12.0, x/D=1.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=12.0, x/D=2.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=12.0, x/D=3.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=12.0, x/D=4.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=12.0, x/D=5.0
Figure 52: Near Field Pressure Spectra, Mae=0.85, r/D=12.0
57
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=12.0, x/D=6.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=12.0, x/D=7.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=12.0, x/D=8.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=12.0, x/D=9.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=12.0, x/D=10.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=12.0, x/D=11.0
Figure 53: Near Field Pressure Spectra, Mae=0.85, r/D=12.0
58
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=12.0, x/D=12.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=12.0, x/D=13.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=12.0, x/D=14.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=12.0, x/D=15.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=12.0, x/D=16.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=12.0, x/D=17.0
Figure 54: Near Field Pressure Spectra, Mae=0.85, r/D=12.0
59
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=14.0, x/D=0.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=14.0, x/D=1.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=14.0, x/D=2.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=14.0, x/D=3.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=14.0, x/D=4.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=14.0, x/D=5.0
Figure 55: Near Field Pressure Spectra, Mae=0.85, r/D=14.0
60
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=14.0, x/D=6.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=14.0, x/D=7.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=14.0, x/D=8.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=14.0, x/D=9.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=14.0, x/D=10.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=14.0, x/D=11.0
Figure 56: Near Field Pressure Spectra, Mae=0.85, r/D=14.0
61
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=14.0, x/D=12.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=14.0, x/D=13.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=14.0, x/D=14.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=14.0, x/D=15.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=14.0, x/D=16.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=14.0, x/D=17.0
Figure 57: Near Field Pressure Spectra, Mae=0.85, r/D=14.0
62
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=16.0, x/D=0.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=16.0, x/D=1.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=16.0, x/D=2.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=16.0, x/D=3.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=16.0, x/D=4.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=16.0, x/D=5.0
Figure 58: Near Field Pressure Spectra, Mae=0.85, r/D=16.0
63
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=16.0, x/D=6.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=16.0, x/D=7.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=16.0, x/D=8.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=16.0, x/D=9.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=16.0, x/D=10.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=16.0, x/D=11.0
Figure 59: Near Field Pressure Spectra, Mae=0.85, r/D=16.0
64
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=16.0, x/D=12.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=16.0, x/D=13.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=16.0, x/D=14.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=16.0, x/D=15.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=16.0, x/D=16.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=16.0, x/D=17.0
Figure 60: Near Field Pressure Spectra, Mae=0.85, r/D=16.0
65
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=18.0, x/D=0.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=18.0, x/D=1.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=18.0, x/D=2.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=18.0, x/D=3.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=18.0, x/D=4.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=18.0, x/D=5.0
Figure 61: Near Field Pressure Spectra, Mae=0.85, r/D=18.0
66
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=18.0, x/D=6.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=18.0, x/D=7.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=18.0, x/D=8.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=18.0, x/D=9.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=18.0, x/D=10.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=18.0, x/D=11.0
Figure 62: Near Field Pressure Spectra, Mae=0.85, r/D=18.0
67
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=18.0, x/D=12.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=18.0, x/D=13.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=18.0, x/D=14.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=18.0, x/D=15.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=18.0, x/D=16.0
102 103 104
Frequency, Hz
60
70
80
90
100
110
120
130
SP
Lin
48
.8H
zB
and
,dB
r/D=18.0, x/D=17.0
Figure 63: Near Field Pressure Spectra, Mae=0.85, r/D=18.0
68
Overall fc = 732 Hz
0 5 10 15x/D
2
4
6
8
10
12
14
16
18
20r/
D
108
110
110
110
112
112
114
114
114
116
116
118
118
120
120
122
122
124
126126
128 130132
0 5 10 15x/D
2
4
6
8
10
12
14
16
18
20
r/D
87
87
89
89
89
91
91
91
93
93
93
95
95
95
97
97
99
99
101 101103
103
105
105107109111
fc = 1465 Hz fc = 2930 Hz
0 5 10 15x/D
2
4
6
8
10
12
14
16
18
20
r/D
85
8687
88
88
89
89
90
90
91
91
91
92
92
92
93
93
94
94
95
95
96
96
96
97
97
98
98
99
99100
100101
102101103103
104
0 5 10 15x/D
2
4
6
8
10
12
14
16
18
20
r/D
8485
85
86
86
87
87
87
88
88
89
89
90
90
91
91
92
92
92
9393
9494
95
95
9696
96
9798
99
fc = 4395 Hz
0 5 10 15x/D
2
4
6
8
10
12
14
16
18
20
r/D
83
84
84
85
85
85
86
86
87
8787
88
88
88
88
89
8989
90
90
8991
91
91
92 92
93
93
94 9495
95
Figure 64: Contours of Acoustic Near Field for Mae=0.60, Overall and Bandpassed at
Center Frequency Denoted
69
Overall fc = 1123 Hz
0 5 10 15x/D
2
4
6
8
10
12
14
16
18
20r/
D
108
108
110
110
110
112
112
112
114
114
114
116
116
118
118
120120
122
122
124124
126
128128
130 132
0 5 10 15x/D
2
4
6
8
10
12
14
16
18
20
r/D
95
96
96
97
97
98
98
98
99
99
99
99
100
100
101
101
102
102
102
103
103
104
104
105
105
105
106
106
107
107
108
108
109
109
110
110
111
111
112
112
113
113
114114115
116116117 117118 119
fc = 2246 Hz fc = 4492 Hz
0 5 10 15x/D
2
4
6
8
10
12
14
16
18
20
r/D
94
95
96
96
97
97
97
98
98
98
99
99
100
100
101
101
102
102
103
103
103
104
104
105
105
106
106
107
107
108108
109
109
110111
112
0 5 10 15x/D
2
4
6
8
10
12
14
16
18
20
r/D
93
94
94
95
95
96
96
96
97
97
97
98
98
98
99
99
100
100
101
101
101
102
102
102
103
103
104
104
105
106 107108
fc = 6738 Hz
0 5 10 15x/D
2
4
6
8
10
12
14
16
18
20
r/D
92
93
93
94
94
94
95
95
95
96
96
96
96
97
97
97
97
98
98
98
99
99
99
100
100
101
101
102
102
103
103104105
Figure 65: Contours of Acoustic Near Field Mae=0.85, Overall and Bandpassed at
Peak Frequency Denoted
70
0 1 2 3 4 5 6
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=0.0
x/D=1.0x/D=2.0x/D=3.0x/D=4.0x/D=5.0x/D=6.0
r/D=3.0
0 1 2 3 4 5 6
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=0.0
x/D=1.0x/D=2.0x/D=3.0x/D=4.0x/D=5.0x/D=6.0
r/D=4.0
4 5 6 7 8 9 10
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=4.0
x/D=5.0x/D=6.0x/D=7.0x/D=7.0x/D=9.0x/D=10.0
r/D=3.0
4 5 6 7 8 9 10
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=4.0
x/D=5.0x/D=6.0x/D=7.0x/D=7.0x/D=9.0x/D=10.0
r/D=4.0
7 8 9 10 11 12 13
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=7.0
x/D=8.0x/D=9.0x/D=10.0x/D=11.0x/D=12.0x/D=13.0
r/D=3.0
7 8 9 10 11 12 13
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=7.0
x/D=8.0x/D=9.0x/D=10.0x/D=11.0x/D=12.0x/D=13.0
r/D=4.0
Figure 66: Zero Time Lag Pressure Correlations, Mae=0.30
71
0 1 2 3 4 5 6
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=0.0
x/D=1.0x/D=2.0x/D=3.0x/D=4.0x/D=5.0x/D=6.0
r/D=3.0
0 1 2 3 4 5 6
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=0.0
x/D=1.0x/D=2.0x/D=3.0x/D=4.0x/D=5.0x/D=6.0
r/D=4.0
0 1 2 3 4 5 6
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=0.0
x/D=1.0x/D=2.0x/D=3.0x/D=4.0x/D=5.0x/D=6.0
r/D=6.0
0 1 2 3 4 5 6
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=0.0
x/D=1.0x/D=2.0x/D=3.0x/D=4.0x/D=5.0x/D=6.0
r/D=8.0
0 1 2 3 4 5 6
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=0.0
x/D=1.0x/D=2.0x/D=3.0x/D=4.0x/D=5.0x/D=6.0
r/D=10.0
0 1 2 3 4 5 6
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=0.0
x/D=1.0x/D=2.0x/D=3.0x/D=4.0x/D=5.0x/D=6.0
r/D=12.0
0 1 2 3 4 5 6
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=0.0
x/D=1.0x/D=2.0x/D=3.0x/D=4.0x/D=5.0x/D=6.0
r/D=14.0
0 1 2 3 4 5 6
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=0.0
x/D=1.0x/D=2.0x/D=3.0x/D=4.0x/D=5.0x/D=6.0
r/D=16.0
Figure 67: Zero Time Lag Pressure Correlations, Mae=0.60
72
4 5 6 7 8 9 10
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=4.0
x/D=5.0x/D=6.0x/D=7.0x/D=7.0x/D=9.0x/D=10.0
r/D=3.0
4 5 6 7 8 9 10
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=4.0
x/D=5.0x/D=6.0x/D=7.0x/D=7.0x/D=9.0x/D=10.0
r/D=4.0
4 5 6 7 8 9 10
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=4.0
x/D=5.0x/D=6.0x/D=7.0x/D=7.0x/D=9.0x/D=10.0
r/D=6.0
4 5 6 7 8 9 10
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=4.0
x/D=5.0x/D=6.0x/D=7.0x/D=7.0x/D=9.0x/D=10.0
r/D=8.0
4 5 6 7 8 9 10
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=4.0
x/D=5.0x/D=6.0x/D=7.0x/D=7.0x/D=9.0x/D=10.0
r/D=10.0
4 5 6 7 8 9 10
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=4.0
x/D=5.0x/D=6.0x/D=7.0x/D=7.0x/D=9.0x/D=10.0
r/D=12.0
4 5 6 7 8 9 10
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=4.0
x/D=5.0x/D=6.0x/D=7.0x/D=7.0x/D=9.0x/D=10.0
r/D=14.0
4 5 6 7 8 9 10
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=4.0
x/D=5.0x/D=6.0x/D=7.0x/D=7.0x/D=9.0x/D=10.0
r/D=16.0
Figure 68: Zero Time Lag Pressure Correlations, Mae=0.60
73
7 8 9 10 11 12 13
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=7.0
x/D=8.0x/D=9.0x/D=10.0x/D=11.0x/D=12.0x/D=13.0
r/D=3.0
7 8 9 10 11 12 13
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=7.0
x/D=8.0x/D=9.0x/D=10.0x/D=11.0x/D=12.0x/D=13.0
r/D=4.0
7 8 9 10 11 12 13
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=7.0
x/D=8.0x/D=9.0x/D=10.0x/D=11.0x/D=12.0x/D=13.0
r/D=6.0
7 8 9 10 11 12 13
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=7.0
x/D=8.0x/D=9.0x/D=10.0x/D=11.0x/D=12.0x/D=13.0
r/D=8.0
7 8 9 10 11 12 13
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=7.0
x/D=8.0x/D=9.0x/D=10.0x/D=11.0x/D=12.0x/D=13.0
r/D=10.0
7 8 9 10 11 12 13
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=7.0
x/D=8.0x/D=9.0x/D=10.0x/D=11.0x/D=12.0x/D=13.0
r/D=12.0
7 8 9 10 11 12 13
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=7.0
x/D=8.0x/D=9.0x/D=10.0x/D=11.0x/D=12.0x/D=13.0
r/D=14.0
7 8 9 10 11 12 13
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=7.0
x/D=8.0x/D=9.0x/D=10.0x/D=11.0x/D=12.0x/D=13.0
r/D=16.0
Figure 69: Zero Time Lag Pressure Correlations, Mae=0.60
74
13 14 15 16 17 18 19
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=13.0
x/D=14.0x/D=15.0x/D=16.0x/D=17.0x/D=18.0x/D=18.0
r/D=3.0
13 14 15 16 17 18 19
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=13.0
x/D=14.0x/D=15.0x/D=16.0x/D=17.0x/D=18.0x/D=18.0
r/D=4.0
13 14 15 16 17 18 19
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=13.0
x/D=14.0x/D=15.0x/D=16.0x/D=17.0x/D=18.0x/D=18.0
r/D=6.0
13 14 15 16 17 18 19
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=13.0
x/D=14.0x/D=15.0x/D=16.0x/D=17.0x/D=18.0x/D=18.0
r/D=8.0
13 14 15 16 17 18 19
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=13.0
x/D=14.0x/D=15.0x/D=16.0x/D=17.0x/D=18.0x/D=18.0
r/D=10.0
13 14 15 16 17 18 19
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=13.0
x/D=14.0x/D=15.0x/D=16.0x/D=17.0x/D=18.0x/D=18.0
r/D=12.0
13 14 15 16 17 18 19
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=13.0
x/D=14.0x/D=15.0x/D=16.0x/D=17.0x/D=18.0x/D=18.0
r/D=14.0
13 14 15 16 17 18 19
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=13.0
x/D=14.0x/D=15.0x/D=16.0x/D=17.0x/D=18.0x/D=18.0
r/D=16.0
Figure 70: Zero Time Lag Pressure Correlations, Mae=0.60
75
0 1 2 3 4 5 6
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=0.0
x/D=1.0x/D=2.0x/D=3.0x/D=4.0x/D=5.0x/D=6.0
r/D=3.0
0 1 2 3 4 5 6
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=0.0
x/D=1.0x/D=2.0x/D=3.0x/D=4.0x/D=5.0x/D=6.0
r/D=4.0
0 1 2 3 4 5 6
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=0.0
x/D=1.0x/D=2.0x/D=3.0x/D=4.0x/D=5.0x/D=6.0
r/D=6.0
0 1 2 3 4 5 6
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=0.0
x/D=1.0x/D=2.0x/D=3.0x/D=4.0x/D=5.0x/D=6.0
r/D=8.0
0 1 2 3 4 5 6
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=0.0
x/D=1.0x/D=2.0x/D=3.0x/D=4.0x/D=5.0x/D=6.0
r/D=10.0
0 1 2 3 4 5 6
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=0.0
x/D=1.0x/D=2.0x/D=3.0x/D=4.0x/D=5.0x/D=6.0
r/D=12.0
0 1 2 3 4 5 6
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=0.0
x/D=1.0x/D=2.0x/D=3.0x/D=4.0x/D=5.0x/D=6.0
r/D=14.0
0 1 2 3 4 5 6
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=0.0
x/D=1.0x/D=2.0x/D=3.0x/D=4.0x/D=5.0x/D=6.0
r/D=16.0
Figure 71: Zero Time Lag Pressure Correlations, Mae=0.85
76
4 5 6 7 8 9 10
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=4.0
x/D=5.0x/D=6.0x/D=7.0x/D=7.0x/D=9.0x/D=10.0
r/D=4.0
4 5 6 7 8 9 10
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=4.0
x/D=5.0x/D=6.0x/D=7.0x/D=7.0x/D=9.0x/D=10.0
r/D=6.0
4 5 6 7 8 9 10
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=4.0
x/D=5.0x/D=6.0x/D=7.0x/D=7.0x/D=9.0x/D=10.0
r/D=3.0
4 5 6 7 8 9 10
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=4.0
x/D=5.0x/D=6.0x/D=7.0x/D=7.0x/D=9.0x/D=10.0
r/D=8.0
4 5 6 7 8 9 10
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=4.0
x/D=5.0x/D=6.0x/D=7.0x/D=7.0x/D=9.0x/D=10.0
r/D=12.0
4 5 6 7 8 9 10
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=4.0
x/D=5.0x/D=6.0x/D=7.0x/D=7.0x/D=9.0x/D=10.0
r/D=10.0
4 5 6 7 8 9 10
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=4.0
x/D=5.0x/D=6.0x/D=7.0x/D=7.0x/D=9.0x/D=10.0
r/D=14.0
4 5 6 7 8 9 10
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=4.0
x/D=5.0x/D=6.0x/D=7.0x/D=7.0x/D=9.0x/D=10.0
r/D=16.0
Figure 72: Zero Time Lag Pressure Correlations, Mae=0.85
77
7 8 9 10 11 12 13
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=7.0
x/D=8.0x/D=9.0x/D=10.0x/D=11.0x/D=12.0x/D=13.0
r/D=3.0
7 8 9 10 11 12 13
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=7.0
x/D=8.0x/D=9.0x/D=10.0x/D=11.0x/D=12.0x/D=13.0
r/D=4.0
7 8 9 10 11 12 13
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=7.0
x/D=8.0x/D=9.0x/D=10.0x/D=11.0x/D=12.0x/D=13.0
r/D=6.0
7 8 9 10 11 12 13
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=7.0
x/D=8.0x/D=9.0x/D=10.0x/D=11.0x/D=12.0x/D=13.0
r/D=8.0
7 8 9 10 11 12 13
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=7.0
x/D=8.0x/D=9.0x/D=10.0x/D=11.0x/D=12.0x/D=13.0
r/D=10.0
7 8 9 10 11 12 13
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=7.0
x/D=8.0x/D=9.0x/D=10.0x/D=11.0x/D=12.0x/D=13.0
r/D=12.0
7 8 9 10 11 12 13
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=7.0
x/D=8.0x/D=9.0x/D=10.0x/D=11.0x/D=12.0x/D=13.0
r/D=14.0
7 8 9 10 11 12 13
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=7.0
x/D=8.0x/D=9.0x/D=10.0x/D=11.0x/D=12.0x/D=13.0
r/D=16.0
Figure 73: Zero Time Lag Pressure Correlations, Mae=0.85
78
13 14 15 16 17 18 19
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=13.0
x/D=14.0x/D=15.0x/D=16.0x/D=17.0x/D=18.0x/D=18.0
r/D=3.0
13 14 15 16 17 18 19
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=13.0
x/D=14.0x/D=15.0x/D=16.0x/D=17.0x/D=18.0x/D=18.0
r/D=4.0
13 14 15 16 17 18 19
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=13.0
x/D=14.0x/D=15.0x/D=16.0x/D=17.0x/D=18.0x/D=18.0
r/D=6.0
13 14 15 16 17 18 19
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=13.0
x/D=14.0x/D=15.0x/D=16.0x/D=17.0x/D=18.0x/D=18.0
r/D=8.0
13 14 15 16 17 18 19
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=13.0
x/D=14.0x/D=15.0x/D=16.0x/D=17.0x/D=18.0x/D=18.0
r/D=16.0
13 14 15 16 17 18 19
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=13.0
x/D=14.0x/D=15.0x/D=16.0x/D=17.0x/D=18.0x/D=18.0
r/D=14.0
13 14 15 16 17 18 19
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=13.0
x/D=14.0x/D=15.0x/D=16.0x/D=17.0x/D=18.0x/D=18.0
r/D=12.0
13 14 15 16 17 18 19
x/D
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Co
rrel
atio
nC
oef
ficie
nt x/D=13.0
x/D=14.0x/D=15.0x/D=16.0x/D=17.0x/D=18.0x/D=18.0
r/D=10.0
Figure 74: Zero Time Lag Pressure Correlations, Mae=0.85
79
0 50 100 150Azimuthal Separation (deg.)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1C
orr
elat
ion
Co
effic
ien
tx/D=0.0x/D=1.0x/D=2.0x/D=3.0x/D=4.0x/D=0.0, fc=732 Hzx/D=1.0, fc=732 Hzx/D=2.0, fc=732 Hzx/D=3.0, fc=732 Hzx/D=4.0, fc=732 Hz
0 50 100 150Azimuthal Separation (deg.)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Co
rrel
atio
nC
oef
ficie
nt
x/D=5.0x/D=6.0x/D=7.0x/D=8.0x/D=5.0, fc=732 Hzx/D=6.0, fc=732 Hzx/D=7.0, fc=732 Hzx/D=8.0, fc=732 Hz
Figure 75: Azimuthal Correlations, Mae=0.60
80
0 50 100 150Azimuthal Separation (deg.)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Co
rrel
atio
nC
oef
ficie
nt
x/D=5.0x/D=6.0x/D=7.0x/D=8.0x/D=5.0, fc=1123 Hzx/D=6.0, fc=1123 Hzx/D=7.0, fc=1123 Hzx/D=8.0, fc=1123 Hz
0 50 100 150Azimuthal Separation (deg.)
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1C
orr
elat
ion
Co
effic
ien
tx/D=0.0x/D=1.0x/D=2.0x/D=3.0x/D=4.0x/D=0.0, fc=1123 Hzx/D=1.0, fc=1123 Hzx/D=2.0, fc=1123 Hzx/D=3.0, fc=1123 Hzx/D=4.0, fc=1123 Hz
Figure 76: Azimuthal Correlations, Mae=0.85
81
0 1 2 3 4 5 6Azimuthal Mode Number
0
0.1
0.2
0.3
0.4
0.5
0.6
Cro
ss-S
pec
tra
x/D=4.0x/D=3.0x/D=2.0x/D=1.0x/D=0.0
0 1 2 3 4 5 6Azimuthal Mode Number
0
0.1
0.2
0.3
0.4
0.5
0.6
Cro
ss-S
pec
tra
x/D=8.0x/D=7.0x/D=6.0x/D=5.0
Figure 77: Azimuthal Cross-Spectra, Mae=0.30
82
0 1 2 3 4 5 6Azimuthal Mode Number
0
0.1
0.2
0.3
0.4
0.5
0.6
Cro
ss-S
pec
tra
x/D=0.0x/D=1.0x/D=2.0x/D=3.0x/D=4.0
0 1 2 3 4 5 6Azimuthal Mode Number
0
0.1
0.2
0.3
0.4
0.5
0.6
Cro
ss-S
pec
tra
x/D=5.0x/D=6.0x/D=7.0x/D=8.0
Figure 78: Azimuthal Cross-Spectra, Mae=0.60
83
0 1 2 3 4 5 6Azimuthal Mode Number
0
0.1
0.2
0.3
0.4
0.5
0.6
Cro
ss-S
pec
tra
x/D=0.0x/D=1.0x/D=2.0x/D=3.0x/D=4.0
0 1 2 3 4 5 6Azimuthal Mode Number
0
0.1
0.2
0.3
0.4
0.5
0.6
Cro
ss-S
pec
tra
x/D=5.0x/D=6.0x/D=7.0x/D=8.0
Figure 79: Azimuthal Cross-Spectra, Mae=0.85
84
REPORT DOCUMENTATION PAGE Form ApprovedOMB No. 0704–0188
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NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89)Prescribed by ANSI Std. Z39-18298-102
1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE
May 19993. REPORT TYPE AND DATES COVERED
Technical Memorandum
4. TITLE AND SUBTITLE
Aeroacoustic Data for a High Reynolds Number Axisymmetric SubsonicJet
5. FUNDING NUMBERS
522-32-31-02
6. AUTHOR(S)
Michael K. Ponton, Lawrence S. Ukeiley and Sang W. Lee
7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)
NASA Langley Research CenterHampton, VA 23681–2199
8. PERFORMING ORGANIZATIONREPORT NUMBER
L–17870
9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)
National Aeronautics and Space AdministrationWashington, DC 20546–0001
10. SPONSORING/MONITORINGAGENCY REPORT NUMBER
NASA/TM–1999–209336
11. SUPPLEMENTARY NOTES
Ponton: Langley Research Center, Hampton VA; Ukeiley: NRC-Resident Research Associate, Langley ResearchCenter, Hampton VA; Lee: The George Washington University, Joint Institute for Advancement of Flight Sciences,Langley Research Center, Hampton VA.
12a. DISTRIBUTION/AVAILABILITY STATEMENT
Unclassified-UnlimitedSubject Category 71 Distribution: StandardAvailability: NASA CASI (301) 621–0390
12b. DISTRIBUTION CODE
13. ABSTRACT (Maximum 200 words)
The near field fluctuating pressure and aerodynamic mean flow characteristics of a cold subsonic jet issuing from acontoured convergent nozzle are presented. The data are presented for nozzle exit Mach numbers of 0.30, 0.60,and 0.85 at a constant jet stagnation temperature of 104�F. The fluctuating pressure measurements were acquiredvia linear and semi-circular microphone arrays and the presented results include plots of narrowband spectra,contour maps, streamwise/azimuthal spatial correlations for zero time delay, and cross-spectra of the azimuthalcorrelations. A pitot probe was used to characterize the mean flow velocity by assuming the subsonic flow to bepressure-balanced with the ambient field into which it exhausts. Presented are mean flow profiles and themomentum thickness of the free shear layer as a function of streamwise position.
14. SUBJECT TERMS
Aeroacoustics, Subsonic, Jet, Fluctuating Pressure15. NUMBER OF PAGES
89
16. PRICE CODE
A05
17. SECURITY CLASSIFICATIONOF REPORT
Unclassified
18. SECURITY CLASSIFICATIONOF THIS PAGE
Unclassified
19. SECURITY CLASSIFICATIONOF ABSTRACT
Unclassified
20. LIMITATION OF ABSTRACT