Aeroacoustic Data for a High Reynolds Number Axisymmetric ...Aeroacoustic Data for a High Reynolds...

NASA/TM-1999-209336

Aeroacoustic Data for a High ReynoldsNumber Axisymmetric Subsonic Jet

Michael K. Ponton

Langley Research Center, Hampton, Virginia

Lawrence S. Ukeiley


Sang W. Lee

The George Washington University Joint Institute for Advancement of Flight Sciences


May 1999

https://ntrs.nasa.gov/search.jsp?R=19990047088 2020-03-03T15:37:53+00:00Z

The NASA STI Program ONce... in Profile

Since its founding, NASA has been dedicatedto the advancement of aeronautics and spacescience. The NASA Scientific and Technical

Information (STI) Program Office plays a keypart in helping NASA maintain this

important role.

The NASA STI Program Office is operated byLangley Research Center, the lead center forNASA's scientific and technical information.

The NASA STI Program Office providesaccess to the NASA STI Database, the

largest collection of aeronautical and spacescience STI in the world. The Program Officeis also NASA's institutional mechanism for

disseminating the results of its research anddevelopment activities. These results are

published by NASA in the NASA STI Report

Series, which includes the following reporttypes:

TECHNICAL PUBLICATION. Reports of

completed research or a major significantphase of research that present the results

of NASA programs and include extensivedata or theoretical analysis. Includes

compilations of significant scientific andtechnical data and information deemed

to be of continuing reference value. NASAcounterpart and peer-reviewed formal

professional papers, but having lessstringent limitations on manuscriptlength and extent of graphic

presentations.

TECHNICAL MEMORANDUM.

Scientific and technical findings that arepreliminary or of specialized interest,

e.g., quick release reports, workingpapers, and bibliographies that containminimal annotation. Does not contain

extensive analysis.

CONTRACTOR REPORT. Scientific and

technical findings by NASA-sponsored

contractors and grantees.

CONFERENCE PUBLICATION.

Collected papers from scientific andtechnical conferences, symposia,

seminars, or other meetings sponsored orco-sponsored by NASA.

SPECIAL PUBLICATION. Scientific,

technical, or historical information fromNASA programs, projects, and missions,

often concerned with subjects havingsubstantial public interest.

TECHNICAL TRANSLATION. English-

language translations of foreign scientificand technical material pertinent toNASA's mission.

Specialized services that complement the STIProgram Office's diverse offerings include

creating custom thesauri, building customizeddatabases, organizing and publishing

research results.., even providing videos.

For more information about the NASA STI

Program Office, see the following:

Access the NASA STI Program HomePage at http-//www.sti.nasa.gov

E-mail your question via the Internet to

[email protected]

Fax your question to the NASA STI HelpDesk at (301) 621-0134

Phone the NASA STI Help Desk at (301)621-0390

Write to:

NASA STI Help Desk

NASA Center for AeroSpace Information7121 Standard Drive

Hanover, MD 21076-1320

NASA/TM-1999-209336

Aeroacoustic Data for a High ReynoldsNumber Axisymmetric Subsonic Jet

Michael K. Ponton


Lawrence S. Ukeiley


Sang W. Lee

The George Washington University Joint Institute for Advancement of Flight Sciences


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)7121 Standard Drive

Hanover, MD 21076-1320

(301) 621-0390

National Technical Information Service (NTIS)

5285 Port Royal Road

Springfield, VA 22161-2171

(703) 605-6000

Summary

The near field fluctuating pressure and

aerodynamic mean flow 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

fluctuating 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 flow velocity by assuming the sub-

sonic flow to be pressure-balanced with the

ambient field into which it exhausts. Pre-

sented are mean flow profiles 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 fluctuations in

the hydrodynamic near field and acoustic

far field regions of the jet flow. 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 flow

field. 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 field noise generation.

Michalke and Fuchs (1975) provide in-

sight into the azimuthal structure of the

turbulent pressure and velocity fields in a

subsonic jet (Mach 0.2) shear layer while

Arndt, Long, and Glauser (1997) use the

POD technique to define the structure of

the near field pressure fluctuations sur-

rounding a Mach 0.07 jet. The purpose

of this paper is to continue characterizing

the near fluctuating pressure field 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 flow field are also

presented.

Symbols

D

L

Ma e

OASPL

Pa

Pt

T

SPL

X

U

O

nozzle exit diameter, 2 in.

center frequency of the emitted

broadband jet noise

local jet Mach number at the

nozzle exit based upon the

nozzle pressure ratio

Overall SPL in dB

re 20 x 10 -6 N/m 2

test cell ambient pressure

local jet total pressure from

the pitot probe

radial coordinate perpendicular

to x; referenced from the jetcenterline

Sound Pressure Level in dB

re 20 x 10 .6 N/m 2

axial coordinate parallel to the

jet centerline; referenced from

the nozzle exit plane

local jet velocity

nozzle exit velocity

compressible momentumthickness

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 fluid dy-namic and acoustic characteristics associ-

ated with internal and external air flows.

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 flow 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 parallelexit flow. A 2 ft diameter circular duct

treated with fine mesh screen is positioned

concentric to the nozzle assembly thus fa-

cilitating co-flow 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 arraywastraversedin the r-direction. Data wereacquired using the semi-circular array atx/D = 0, 1, 2, 3, 4, 5, 6, 7 and 8. Forthe linear array,datawereacquiredat r/D= 3, 4, 6, 8, 10, 12, 14, 16 and 18 andthe array was traversed axially wherebythe upstream microphonevaried in posi-tion from x/D = 0, 4, 7 to 13. For thelinear array data, eachmicrophonesignalwasdigitized at 50 kHz and bandpassill-tered between160Hz and 20kHz. For thesemi-circular array data, the signalsweredigitized at 30 kHz and bandpassfilteredbetween160Hz and 12.5kHz. For all mi-crophonedata, 128independentblocks of1024usabledata points wererecorded.

Aerodynamic Results

Presented in figures 2 and 3 are the ra-dial distributions for the axial mean veloc-

ity profiles 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 difference 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

flow is assumed and the ratio of specific

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 figures 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 reflections from

the near field 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 fig-

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 field

pressure contour maps of OASPL as well

as SPL in select frequency bands, re, for

Ma_ = 0.6 and 0.85. The data were re-

duced by digitally filtering the FFT gener-

ated spectra in select 488.3 Hz bands. The

lowest f_ 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 f_ values plotted correspond to

3

Fig Mae r/D x/D4 0.30 3 0-5

5 0.30 3 8-11

6 0.30 4 0-5

7 0.30 4 8-11

8 0.30 6 0-5

9 0.30 6 8-11

10 0.60 3 0-5

11 0.60 3 8-11

12 0.60 3 12-17

13 0.60 4 0-5

14 0.60 4 8-11

15 0.60 4 12-17

16 0.60 6 0-5

17 0.60 6 8-11

18 0.60 6 12-17

19 0.60 8 0-5

20 0.60 8 8-11

21 0.60 8 12-17

22 0.60 10 0-5

23 0.60 10 8-11

24 0.60 10 12-17

25 0.60 12 0-5

26 0.60 12 8-11

27 0.60 12 12-17

28 0.60 14 0-5

29 0.60 14 8-11

30 0.60 14 12-17

31 0.60 16 0-5

32 0.60 16 8-11

33 0.60 16 12-17

Fig Mae r/D x/D Fig Mae r/D x/D34 0.60 18 0-5

35 0.60 18 8-11

36 0.60 18 12-17

37 0.85 3 0-5

38 0.85 3 8-11

39 0.85 3 12-17

40 0.85 4 0-5

41 0.85 4 8-11

42 0.85 4 12-17

43 0.85 6 0-5

44 0.85 6 8-11

45 0.85 6 12-17

46 0.85 8 0-5

47 0.85 8 8-11

48 0.85 8 12-17

49 0.85 10 0-5

50 0.85 10 8-11

51 0.85 10 12-17

52 0.85 12 0-5

53 0.85 12 8-11

54 0.85 12 12-17

55 0.85 14 0-5

56 0.85 14 8-11

57 0.85 14 12-17

58 0.85 16 0-5

59 0.85 16 8-11

60 0.85 16 12-17

61 0.85 18 0-5

62 0.85 18 8-11

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 figures 66 through 74 arethe cross-correlation coefficients 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 figures.

Figures 75 and 76 present the cross-correlation coefficients 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 filtered about the

66 0.30 3-4 0-13

67 0.60 3-16 0-6

68 0.60 3-16 4-10

69 0.60 3-16 7-13

70 0.60 3-16 13-19

Fig Mac r/D x/D71 0.85 3-16 0-6

72 0.85 3-16 4-10

73 0.85 3-16 7-13

74 0.85 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 unfiltered data,

figures 77 through 79 contain the cross-

spectra of the azimuthal cross-correlations

for Mae = 0.3, 0.6, and 0.85. These figures

provide insight into the spatial structure

of the azimuthal pressure field at r/D=2.The cross-correlation levels are consistent

with the limited measurements presented

by Pao and Maestrello (1976).

Concluding Remarks

Near field pressure and mean flow data,

acquired at the NASA Langley Research

Center, are presented for a contoured con-

vergent nozzle. Velocity profiles and too-

mentum thickness distributions are given

as well as spectra, contour maps, cross-

correlations, and cross-spectra of the fluc-

tuating pressure field. 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

field 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., & Port-

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

iiiiiiiiiii

iiiiiiiiiii_

Figure 1: Near Field Microphone Arrays

6

Ma_=0.30

-1 0

riD

Ma_=0.60

x/D=10

x/D=9

x/D=8

x/D=7

x/D=6

x/D=4

x/D=1

1 2

-1 0 1 2rid

Ma_=0.85

x/D=10

x/D=9

+ x/D=8

x/D=7

x/D=6

x/D=4

x/D=1

-1 0 1 2

rid

Figure 2: Mean Streamwise Velocity Profiles

7

0.15 -

0.14

0.13

0.12

0.11

0.1

0.09

0.08

0.07

0.06

0.05

0.04

0.03

[]

0.02

0.01

[]

[]

V

©V

[]

V

©

[]

V

©

[]

V

©

[]

V

©

[]

V

©

[]

[]

V

v ©

©

[] Mach 0.3

v Mach 0.6

© Mach 0.85

00 i i i i I i i i i I i i i i I i i i i I i i i i I2 4 6 8 10

Figure 3: Momentum Thickness

8

I_ 130

120

_ 110

I11100

N

90

CO 80

.N 7o

--1 60O.

U') illlll10"

r/D=3.0, x/D=0.0

10" 10_

Frequency, Hz

I_ 130

120

_ 110

IXI10O

N"1"

9O

_ 8o.N 7o

-J 6O

if)

r/D=3.0, x/D=3.0

i i i iI i i i i i i i iI i i i 11111"__7_%

10" 10" 10 _

Frequency, Hz

m 130

120

_ 110

I11100

N

90

CO 80

._ 70

•"J 60a.

U)

r/D=3.0, x/D=1.0

10" 10_

Frequency, Hz

104

m 130

120

_ 110

I11100

N

90

CO 80

._ 70

•"J 60a.

O3

r/D=3.0, x/D=4.0

i i i i I i i i i i i i i I i _'_'_7 '_''',

10" 10_ 104

Frequency, Hz

m 130

120

_ 110

I11100

IN

90

CO 80

._ 70

•"J 60a.

O3

r/D=3.0, x/D=2.0

illl i i i illll i i i illll10" 10" 10 _

Frequency, Hz

I_ 130

120

_ 110

I11100

N

90

_ 80

e- 70

-1 60o.

U')

r/D=3.0, x/D=5.0

illl i i i illlll i i i ii'_ I_"

10" 10" 10 _

Frequency, Hz

Figure 4: Near Field Pressure Spectra, Mae=0.30, r/D=3.0

9

at,, 130

"0120

"0

_ 110

I11100

N

90

_ 80

.N 7o

--1 60a.

U')

r/D=3.0, x/D=6.0

,,4 , , , ,,,,,t , , , ,,_'_'/"_"%"

10 _ 10" 10"

Frequency, Hz

m 130

"0. 120

"0

_ 110

IXI10O

N"1"

9O

_ 8O

.N 7o

-J 6O

if)

r/D=3.0, x/D=9.0

i i i I i i i i i i "_,,..10" %° 10°

Frequency, Hz

m 130

"0120

"0

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

U)

r/D=3.0, x/D=7.0

\\\

,,,,I , , , , ,,,,I , _\\'_'_,,

10_ 10_ 10_

Frequency, Hz

00 130

"O120

"O

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

U)

r/D=3.0, x/D=10.0

\\\\\\

,,10 . , ...... 4_)_ 10_

Frequency, Hz

00 130

"O120

"O

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

U)

r/D=3.0, x/D=8.0

\\\\

.... , ........ , .... _'_ ,_...10 _ 10 _ 10 _

Frequency, Hz

at,, 130

"0120

"0

_ 110

I11100

N

90

_ 80

e" 70

--1 60a.

U')

r/D=3.0, x/D=11.0

10 _ "4_ 10 _

Frequency, Hz


10

I_ 130"0

1201:3

_ 110

I11100

N

90

CO 80

.N 7o

-1 60O.U')

1o"

r/D=4.0, x/D=O.O

I0_

Frequency, Hz

104

I_ 130"0

120"[3

_ 110IXI

10ON

"1"9O

_ 8O

.N 7o

"J 6O

if)

r/D=4.0, x/D=3.0

i i i i i i i i i i i i i i i i i i'_'_"_/_'_'_k10" 10" 104

Frequency, Hz

m 1301:3

1201:3

_ 110I11

100N

90

CO 80

._ 70

•"J 60a.U)

r/D=4.0, x/D=1.0

10" 10_

Frequency, Hz

104

m 1301:3

1201:3

_ 110I11

100N

90

CO 80

_ 7°

"J 60a.U)

r/D=4.0, x/D=4.0

i i i i i i i i i i i i i i i i i_t_ _'_lO . lO_ lO4

Frequency, Hz

00 1301:3

1201:3

_ 110I11

100IN

90

CO 80

._ 70

•"J 60a.U)

r/D=4.0, x/D=2.0

10" 10"

Frequency, Hz

104

I_ 130"O

1201:3

_ 110

I11100

N

90

CO 80

e" 70

--1 60O.U')

r/D=4.0, x/D=5.0

10" 10" 104

Frequency, Hz


11

I_ 130

"0120

"0

_ 110

I11100

N

90

_ 80

.N zo

--1 60a.

U'I

r/D=4.0, x/D=6.0

10 _ 10_ 10_

Frequency, Hz

I_ 130

"0120

"0

_ 110

IXI100

N"r

90

_ 80

.N zo

-J 60

ffl

r/D=4.0, x/D=9.0

illl i i i illlll i i i i_,,10 _ 10" 10 _

Frequency, Hz

m 130

"0120

"0

_ 110

O0100

N

90

_ 80

._ 70

=.1 60a.

if)

r/D=4.0, x/D=7.0

10" 10_ 10_

Frequency, Hz

00 130

'13120

'13

_ 110

O0100

N

90

_ 80

._ 70

=.1 60a.

if)

r/D=4.0, x/D=10.0

lllll i i i llllll i i \ _'_'_I_10 _ 10_ ' , ,, '_0_

Frequency, Hz

130

'13120

'13

_ 110

O0100

N

90

_ 80

._ 70

=.1 60a.

if)

r/D=4.0, x/D=8.0

10" 10" 10 _

Frequency, Hz

I_ 130

"0120

"0

_ 110

I11100

N

90

_ 8o

e- 70

-1 60a.

r/D=4.0, x/D=11.0

10 _ 10_ 10 _

Frequency, Hz

Figure 7: Near Field Pressure Spectra, Ma_=0.30, r/D=4.0

12

I_ 130"O

120

_ 110

I11100

N

90

CO 80

.N 7o

-1 600.U'I

r/D=6.0, x/D=0.0I_ 130

120

_ 110IXI

10ON

"1"9O

_ 8O

.N 7o

-J 6O

ffl

r/D=6.0, x/D=3.0

10" 10" 10" 10" 10_ 10"

Frequency, Hz Frequency, Hz

m 130

120

_ 110O0

100N

90

_ 80

._ 70

"J 60a.if)

r/D=6.0, x/D=1.0m 130

120

_ 110O0

100N

90

_ 80

e" 70

"J 60a.if)

r/D=6.0, x/D=4.0

10" 10_ 10_ 10. 10_ 10_


00 130

120

_ 110O0

100IN

90

_ 80

._ 70

•"J 60a.if)

r/D=6.0, x/D=2.0 r/D=6.0, x/D=5.0I_ 130"O

120

_ 110

I11100

N

90

CO 80

e" 70

--1 600.U'I

j-

10" 10" 10" 10" ' '1_)" 10"



13

I_ 130

120

_ 110

I11100

N

90

CO 80

.N 7o

--1 600.

U')

r/D=6.0, x/D=6.0

10" 10" 104

Frequency, Hz

m 130

120

_ 110

IXI10O

N"1"

9O

_ 8O

.N 7o

..I 6O

if)

r/D=6.0, x/D=9.0

illll i i i i illll i i i 1"_l_4,

10" 10" 104

Frequency, Hz

00 130

"O120

"O

_ 110

O0100

N

90

_ 80

._ 70

=.1 60a.

if)

r/D=6.0, x/D=7.0 r/D=6.0, x/D=10.000 130

"O120

"O

_ 110

O0100

N

90

_ 80

._ 70

=.1 60a.

if)iiiI i i i iii iiiiI i i i iiiiiI i i i _"%_"T'_Ilo_ '4_, _oo _o_ _o, _oo


00 130

"O120

"O

_ 110

O0100

IN

90

_ 80

._ 70

=.1 60a.

if)

r/D=6.0, x/D=8.0 r/D=6.0, x/D=11.0I_ 130

120

_ 110

I11100

N

90

CO 80

e" 70

--1 600.

,,,_ ...... _'_,_ ,,,_ ........10" '1_)" 10_' 10" 10" ' ' 104



14

I_ 130

"O120

"O

_ 110

I11100

N

90

_ 80

.N 7o--1 60a.

U')

r/D=3.0, x/D=0.0I_ 130

"O120

"O

_ 110

IXI10O

N"1"

9O

_ 8O

.N 7o

-J 6O

if)

r/D=3.0, x/D=3.0

/_ __

iiiii i i i iiiiii i i i ii iiiii i i i iiiiii i i i iiilo" lo° '%° lo" lo° %°


00 130

1:3120

1:3

_ 110

I11100

N

90

_ 80

._ 70

-J 60a.

U)

r/D=3.0, x/D=1.000 130

1:3120

1:3

_ 110

I11100

N

90

_ 80

._ 70

-J 60a.

U)

r/D=3.0, x/D=4.0

.....................10z 10_ 4_)............. 10 z 10_11 ....... 4_)4


00 130

1:3120

1:3

_ 110

I11100

N

90

_ 80

._ 70

-J 60a.

U)

r/D=3.0, x/D=2.0I_ 130

"O120

"O

_ 110

I11100

N

90

_ 80

e" 70

--1 60a.

U')

r/D=3.0, x/D=5.0

iiiii i i i iiiiii i i i ii iiii i i i iiiiii i i i iii10" 10" "_ 10 _ 10" 'I'__



15

at,, 130

"0120

"0

_ 110

121

N 100

•1- 90

CO

a_ 8O

.__ 70

.--I 6013.

08

r/D=3.0, x/D=6.0

,,,I , , , ,,,,,I , , , ,,10 _ 10" "4_

Frequency, Hz

I_ 130

"O120

"O

_ 110

IXI10O

N"r

9O

_ 8O

.N 7o

..I 6O

if)

r/D=3.0, x/D=9.0

,,,I , , , ,,,,,I , , , ,,,lo" lo° %°

Frequency, Hz

00 130

"O120

"O

t-" 1100=

100N

"1-90

CO

CO 80

._ 70

.--I 60O.

08

r/D=3.0, x/D=7.0

.... 10.' ........ 10_' ....... 4_)_

Frequency, Hz

00 130

"O120

"O

t-" 1100=

100N

"1-90

CO

CO 80

._ 70

.--I 60O.

08

r/D=3.0, x/D=10.0

.... 10.' ........ 10_' ....... 4_)_

Frequency, Hz

00 130

"O120

"O

_ 110

O0100

IN

90

_ 80

._ 70

..1 60Q.

if)

r/D=3.0, x/D=8.0IX) 130

"o120

"o

_ 110

121100

N

90

_ 80

e" 70

--1 60O.

0')

r/D=3.0, x/D=11.0

,,,,I , , , ,,,,,I , , , ,, ,,,I , , , ,,,,,I , , , ,,,10" 10" "_F 10 _ 10" 'I'_F



16

IX_ 130

"O120

"O

_ 110

I11100

N

90

CO 80

.N 7o

--1 60O.

U')

r/D=3.0, x/D=12.0

,,,I , , , ,,,,,I , , , ,,10 _ 10_ "4_

Frequency, Hz

I_ 130

"O120

"O

_ 110

IXI10O

N"1"

9O

_ 8O

.N 7o

..I 6O

if)

r/D=3.0, x/D=15.0

,,,,I , , , ,,,,,I , , , ,,,10" 10° %°

Frequency, Hz

m 130

"0120

"0

_ 110

I11100

N

90

CO 80

._ 70

..1 60a.

U)

r/D=3.0, x/D=13.0

J \\\\\

.... 10.' ........ 10_' ....... 4_)_

Frequency, Hz

m 130

"0120

"0

_ 110

I11100

N

90

CO 80

._ 70

..1 60a.

U)

r/D=3.0, x/D=16.0

.... 10.' ........ 10_' ....... 4_)_

Frequency, Hz

00 130

"O120

"O

_ 110

I11100

IN

90

CO 80

._ 70

..1 60a.

U)

r/D=3.0, x/D=14.0

_\\\\\

I_ 130

"O120

"O

_ 110

I11100

N

90

CO 80

e" 70

--1 60O.

U')

r/D=3.0, x/D=17.0

\\

,,,,I , , , ,,,,,I , , , ,, ,,,,I , , , ,,,,,I , , , ,,,10" 10" "_F 10" 10" 'I'_F



17

I_ 130

"O120

_ 110

I11100

N

90

_ 80

.N 7o

--1 60a.

U')

r/D=4.0, x/D=O.O

f

I_ 130

"O120

_ 110

IXI10O

N"1"

9O

_ 8O

.N 7o

-J 6O

if)

r/D=4.0, x/D=3.0



00 130

1:3120

1:3

_ 110

I11100

N

90

_ 80

._ 70

-J 60a.

U)

J/

r/D=4.0, x/D=1.000 130

1:3120

1:3

_ 110

I11100

N

90

_ 80

._ 70

-J 60a.

U)

r/D=4.0, x/D=4.0

/-

.....................10z 10_ 4_)............. 10 z 10_11 ....... 4_)4


00 130

1:3120

1:3

_ 110

I11100

N

90

_ 80

._ 70

-J 60a.

U)

r/D=4.0, x/D=2.0I_ 130

"O120

"O

_ 110

I11100

N

90

_ 80

e" 70

--1 60a.

U')

r/D=4.0, x/D=5.0

iiii i i i iiiiii i i i ii iiii i i i iiiiii i i i iii10" 10" "_ 10" 10" 'I'__



18

I_ 130

"0120

"0

_ 110

I11100

N

90

_ 80

.N 7o

--1 60a.

U'I

r/D=4.0, x/D=6.0I_ 130

"0120

"0

_ 110

IXI10O

N"1"

9O

_ 8O

.N zo

-J 6O

ffl

r/D=4.0, x/D=9.0

iiii i i i iiiiii i i i ii iiii i i i iiiiii i i i iiilo" lo° '%° lo" lo° %°


00 130

"O120

"O

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

if)

r/D=4.0, x/D=7.000 130

"O120

"O

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

if)

r/D=4.0, x/D=10.0

.....................lo_ lo" _............. 1o_ lo,'' ....... _°


00 130

"O120

"O

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

if)

r/D=4.0, x/D=8.0I_ 130

"O120

"O

_ 110

I11100

N

90

_ 80

e" 70

--1 60a.

U'I

r/D=4.0, x/D=11.0

iiiii i i i iiiiii i i i ii iiii i i i iiiiii i i i iii10" 10" "_ 10 _ 10" 'I'__



19

at,, 130

"0120

"0

_ 110

I11100

N

90

CO 80

.N 7o

--1 600.

U')

r/D=4.0, x/D=12.0

,,,I , , , ,,,,,I , , , ,,10 _ 10" "4_

Frequency, Hz

I_ 130

"O120

"O

_ 110

IXI10O

N"1"

9O

_ 8O

.N 7o

..I 6O

if)

r/D=4.0, x/D=15.0

,,,I , , , ,,,,,I , , , ,,,10" 10° %°

Frequency, Hz

m 130

"0120

"0

_ 110

I11100

N

90

CO 80

._ 70

..1 60a.

U)

r/D=4.0, x/D=13.0

.... 10.' ........ 10_' ....... 4_)_

Frequency, Hz

m 130

"0120

"0

_ 110

I11100

N

90

CO 80

._ 70

..1 60a.

U)

r/D=4.0, x/D=16.0

.... 10.' ........ 10_' ....... 4_)_

Frequency, Hz

00 130

"O120

"O

_ 110

I11100

IN

90

CO 80

._ 70

..1 60a.

U)

r/D=4.0, x/D=14.0I_ 130

"O120

"O

_ 110

I11100

N

90

CO 80

e" 70

--1 600.

U')

r/D=4.0, x/D=17.0

\\ \

,,,,I , , , ,,,,,I , , , ,, ,,,,I , , , ,,,,,I , , , ,,,10" 10" "_F 10 _ 10" 'I'_F



20

I_ 130"O

120

_ 110

I11100

N

90

_ 80

.N zo

-1 60a.U')

r/D=6.0, x/D=0.0 r/D=6.0, x/D=3.0I_ 130

120

_ 110IXI

100N

"1"90

_ 80

.N zo

-J 60

if)

J" j

iiiil i i i iiiiil i i i ii iiiil i i i iiiiil i i i illlo" lo° '%° lo" lo° %°


00 130"O

. 120"O

_ 110O0

100N

90

_ 80

._ 70

"J 60a.if)

r/D=6.0, x/D=1.0

_ J .... _/_ _.._ww._. '

00 130"O

120"O

_ 110O0

100N

90

_ 80

._ 70

"J 60a.if)

r/D=6.0, x/D=4.0

.....................lo_ lo, _............ 1o_ lo," ....... _°


00 130"O

120"O

_ 110O0

100IN

90

_ 80

._ 70

"J 60a.if)

r/D=6.0, x/D=2.0 r/D=6.0, x/D=5.0I_ 130"O

120"O

_ 110

I11100

N

90

_ 80

e" 70

--1 60a.U')iiiii i i i iiiiii i i i ii iiiii i i i iiiiii i i i iiiIo" Io° '%° lo" lo° %°



21

I_ 130

"O120

"O

_ 110

I11100

N

90

_ 80

.N 7o

--1 60a.

U')

r/D=6.0, x/D=6.0I_ 130

"O120

"O

_ 110

IXI10O

N"1"

9O

_ 8O

.N 7o

-J 6O

if)

r/D=6.0, x/D=9.0



00 130

"O120

"O

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

U)

r/D=6.0, x/D=7.000 130

"O120

"O

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

U)

r/D=6.0, x/D=10.0

.................... _)............ 10_10" 10_ 10" ,I ....... 4_)_


00 130

"O120

"O

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

U)

r/D=6.0, x/D=8.0

JJ

I_ 130

"O120

"O

_ 110

I11100

N

90

_ 80

e" 70

--1 60a.

U')

r/D=6.0, x/D=11.0

iiiii i i i iiiiii i i i ii iiii i i i iiiiii i i i iii10" 10" "_ 10" 10" 'I'__



22

I_ 130

"O120

"O

_ 110

I11100

N

90

_ 80

.N 7o--1 60a.

U'I

r/D=6.0, x/D=12.0I_ 130

"O120

"O

_ 110

IXI10O

N"1"

9O

_ 8O

.N zo

-J 6O

ffl

r/D=6.0, x/D=15.0



00 130

"O120

"O

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

if)

r/D=6.0, x/D=13.000 130

"O120

"O

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

if)

r/D=6.0, x/D=16.0

.....................10z 10_ 4_)............. 10 z 10_11 ....... 4_)4


00 130

"O120

"O

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

if)

r/D=6.0, x/D=14.0 r/D=6.0, x/D=17.0I_ 130

"O120

"O

_ 110

I11100

N

90

_ 80

e" 70,m

--1 60a.

U'Iiiiii i i i iiiiii i i i ii iiiii i i i iiiiii i i i iiiIo_ Io° '%° lo" lo° %°



23

I_ 130"O

120"O

_ 110

I11100

N

90

_ 80

.N 7o

-1 60a.U'I

r/D=8.0, x/D=O.O r/D=8.0, x/D=3.0I_ 130"O

120"O

_ 110IXI

10ON

"1"9O

_ 8O

.N zo

-J 6O

ffliiiii i i i iiiiii i i i ii iiiii i i i iiiiii i i i iiiio_ io° '%° lo_ lo° %°


00 1301:3

1201:3

_ 110O0

100N

90

_ 80

._ 70

"=J 60a.if)

r/D=8.0, x/D=1.0 r/D=8.0, x/D=4.000 1301:3

1201:3

_ 110O0

100N

90

_ 80

_ 7°

"=J 60a.if)....................lo_ lo, 4_............. 1o_ lo," ....... 4_°


00 1301:3

1201:3

_ 110O0

100N

90

_ 80

._ 70

"=J 60a.if)

r/D=8.0, x/D=2.0 r/D=8.0, x/D=5.0I_ 130"O

120"O

_ 110

I11100

N

90

_ 80

e" 70

--1 60a.U'Iiiiii i i i iiiiii i i i ii iiiii i i i iiiiii i i i iiiIo_ Io° '%° lo_ lo° %°



24

I_ 130

"0120

"0

_ 110

I11100

N

90

_ 80

.N 7o

--1 60a.

U'I

r/D=8.0, x/D=6.0I_ 130

"0120

"0

_ 110

IXI10O

N"r

9O

_ 8O

.N 7o

-J 6O

ffl

r/D=8.0, x/D=9.0

J



00 130

"O120

"O

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

if)

r/D=8.0, x/D=7.000 130

"O120

"O

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

if)

r/D=8.0, x/D=10.0

....................lo_ lo" _............. 1o_ lo,'' ....... _°


00 130

"O120

"O

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

if)

r/D=8.0, x/D=8.0 r/D=8.0, x/D=11.0I_ 130

"O120

"O

_ 110

I11100

N

90

_ 80

e" 70.m

--1 60a.

U'I

_s_

10" 10" 11_ 10 _ 10" 111__



25

I_ 130

"O120

"O

_ 110

I11100

N

90

_ 8o

.N 7o

--1 60a.

U')

r/D=8.0, x/D=12.0I_ 130

"O120

"O

_ 110

IXI10O

N"1"

9O

_ 8O

.N 7o

-J 6O

if)

r/D=8.0, x/D=15.0



00 130

"O120

"O

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

U)

r/D=8.0, x/D=13.000 130

"O120

"O

_ 110

O0100

N

90

._ 70

-J 60a.

U)

r/D=8.0, x/D=16.0

....................10z 10_ 4_)............. 10 z 10_11 ....... 4_)4


00 130

"O120

"O

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

U)

r/D=8.0, x/D=14.0

S _ _

I_ 130

"O120

"O

_ 110

I11100

N

90

_ 80

e" 70

--1 60a.

U')

r/D=8.0, x/D=17.0

iiii i i i iiiiii i i i ii iiiii i i i iiiiii i i i iii10" 10" "_ 10" 10" 'I'__



26

I_ 130"O

120

_ 110

I11100

N

90

_ 80

.N zo-1 60a.U'I

r/D=10.0, x/D=0.0 r/D=10.0, x/D=3.0I_ 130"O

120

_ 110IXI

100N

"1"90

_ 80

.N zo

-J 60

fflillll i i i illlll i i i ii illl i i i illlll i i i illlo" lo° '%° lo" lo° %°


t_ 1301:3

1201:3

_ 110O0

100N

90

_ 80

._ 70

"J 60a.if)

r/D=10.0, x/D=1.0 r/D=10.0, x/D=4.0t_ 1301:3

1201:3

_ 110O0

100N

90

_ 80

._ 70

"J 60a.if).....................lo_ lo, 4_............. 1o_ lo," ....... 4_°


t_ 1301:3

1201:3

_ 110O0

100IN

90

_ 80

._ 70

•"J 60a.if)

r/D=10.0, x/D=2.0 r/D=10.0, x/D=5.0I_ 130"O

120"O

_ 110

I11100

N

90

_ 80

e" 70

--1 60a.U'IIo" Io° '%° lo" lo° %°



27

I_ 130

"O120

_ 110

I11100

N

90

_ 80

.N 7o

--1 60a.

U'I

r/D=10.0, x/D=6.0

J

Jf

I_ 130

120

_ 110

IXI10O

N"1"

9O

_ 8O

.N zo

-J 6O

ffl

r/D=10.0, x/D=9.0



00 130

"O120

"O

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

if)

r/D=10.0, x/D=7.0

J

J

00 130

"O120

"O

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

if)

r/D=10.0, x/D=10.0

J

.....................lo_ lo" _............. 1o_ lo,'' ....... _°


00 130

"O120

"O

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

if)

r/D=10.0, x/D=8.0

f

JJ

I_ 130

"O120

"O

_ 110

I11100

N

90

_ 80

e" 70.m

--1 60a.

U'I

r/D=10.0, x/D=11.0

J

iiii i i i iiiiii i i i ii iiiii i i i iiiiii i i i iii10" 10" "_ 10 _ 10" 'I'__



28

I_ 130"O

120"O

_ 110

I11100

N

90

_ 80

.N 7o-1 60a.U'I

r/D=10.0, x/D=12.0 r/D=10.0, x/D=15.0I_ 130"O

120"O

_ 110IXI

10ON

"1"9O

_ 8O

.N zo

-J 6O

ffl

J /

iiiii i i i iiiiii i i i ii iiii i i i iiiiii i i i iiiio_ io° '%° lo_ lo° %°


00 130"O

120"O

_ 110O0

100N

90

_ 80

._ 70

-J 60a.if)

r/D=10.0, x/D=13.0 r/D=10.0, x/D=16.000 130"O

120"O

_ 110O0

100N

90

_ 80

._ 70

-J 60a.if).................... 4_............ lo,10" 10_ 10" ,I ....... 4_)_


/-

00 130"0

120"0

_ 110O0

100N

90

_ 80

._ 70

-J 60a.if)

r/D=10.0, x/D=14.0 r/D=lO.O, x/D=17.0I_ 130"O

120"O

_ 110

I11100

N

90

_ 80

e" 70

--1 60a.U'I,,,,i , , , ,,,,,i , , , ,, ,,,,i , , , ,,,,,i , , , ,,,

lO" lO" "_ lO" lO" 'I'__



29

I_ 130"O

120

_ 110

I11100

N

90

CO 80

.N 7o

-1 60a.U')

r/D=12.0, x/D=0.0I_ 130"O

120

_ 110IXI

10ON

"1"9O

_ 8O

.N 7o

-J 6O

if)

r/D=12.0, x/D=3.0

f

iiii i i i iiiiii i i i ii iiiii i i i iiiiii i i i iiilo" lo° %° 1o" lo° %°


00 130"O

120"O

_ 110O0

100N

90

CO 80

._ 70

-J 60a.U)

r/D=12.0, x/D=1.0 r/D=12.0, x/D=4.000 130"O

120"O

_ 110O0

100N

90

CO 80

._ 70

-J 60a.U)

jJ_ _

.................... _............ lo,10" 10_ 10" ,I ....... 4_)_


00 130"O

120"O

_ 110O0

100N

90

CO 80

._ 70

-J 60a.U)

r/D=12.0, x/D=2.0 r/D=12.0, x/D=5.000 130"O

120"O

_ 110

I11100

N

90

CO 80

e" 70

--1 60a.U')iiiii i i i iiiiii i i i ii iiiii i i i iiiiii i i i iiiIo" Io° '%° Io" Io° %°



3O

I_ 130"0

120"0

_ 110

I11100

N

90

_ 80

.N 7o

-1 60a.U'I

r/D=12.0, x/D=6.0 r/D=12.0, x/D=9.0m 130"0

120"0

_ 110IXI

10ON

"1"9O

_ 8O

.N zo

-J 6O

ffl

SJ

jJ

iiiii i i i iiiiii i i i ii iiii i i i iiiiii i i i iiiio_ io° '%° lo_ lo° %°


00 130"0

120"0

_ 110O0

100N

90

_ 80

._ 70

-J 60a.if)

r/D=12.0, x/D=7.000 130"0

120"0

_ 110O0

100N

90

_ 80

._ 70

-J 60a.if)

r/D=12.0, x/D=10.0

J

....................lo_ lo, 4_............. 1o_ lo,'' ....... 4_°


00 130"0

120"0

_ 110O0

100N

90

_ 80

._ 70

-J 60a.if)

r/D=12.0, x/D=8.0 r/D=12.0, x/D=11.0I_ 130"0

120"0

_ 110

I11100

N

90

_ 80

_ 7o

-1 60a.U'I,,,,i , , , ,,,,,i , , , ,, ,,,,i , , , ,,,,,i , , , ,,,

lO _ lO _ "_ lO _ lO_ 'I'__



31

I_ 130

"0120

"0

_ 110

I11100

N

90

_ 80

_ 7°

--1 60a.

U'I

r/D=12.0, x/D=12.0 r/D=12.0, x/D=15.0I_ 130

"0120

"0

_ 110

IXI10O

N"r

9O

_ 8O

-J 60

ffl,,,I , , , ,,,,,I , , , ,, ,,,,I , , , ,,,,,I , , , ,,,lo" lo° %° 1o" lo° %°


m 130

"0. 120

"0

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

if)

r/D=12.0, x/D=13.0m 130

"0120

"0

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

if)

r/D=12.0, x/D=16.0

.....................lo_ lo" _............. 1o_ lo,' ....... 4b


m 130

"0120

"0

_ 110

O0100

IN

90

_ 80

._ 70

-J 60a.

if)

r/D=12.0, x/D=14.0

J

I_ 130

"O120

"O

_ 110

I11100

N

90

_ 80

e" 70

--1 60a.

U'I

r/D=12.0, x/D=17.0

llll i i i llllll i i i ii lllll i i i llllll _ _ _ _10" 10" "_ 10" 10" 'I'__



32

I_ 130"O

120"O

_ 110

I11100

N

90

_ 80

.N 7o

-1 60a.U'I

r/D=14.0, x/D=0.0 r/D=14.0, x/D=3.0I_ 130"O

120"O

_ 110IXI

10ON

"1"9O

_ 8O

.N zo

-J 6O



I_ 130"O

120"O

_ 110O0

100N

90

_ 80

._ 70

-J 60a.if)

r/D=14.0, x/D=1.0 r/D=14.0, x/D=4.0I_ 130"O

120"O

_ 110O0

100N

90

_ 80

._ 70

-J 60a.if)

: i

10_ 10_ 10_ 10_ 10_ 10_


I_ 130"O

120"O

_ 110O0

100N

90

_ 80

._ 70

-J 60a.if)

r/D=14.0, x/D=2.0 r/D=14.0, x/D=5.0I_ 130"O

120"O

_ 110

I11100

N

90

_ 80

e" 70

--1 60a.U'I

10_ 10_ ' 'I_)_ 10_ ' ...... I0_ ' ...... 1'_)_



33

I_ 130"0

120"0

_ 110

I11100

N

90

_ 80

.N 7o-1 60a.U'I

r/D=14.0, x/D=6.0 r/D=14.0, x/D=9.0I_ 130"0

120"0

_ 110IXI

10ON

"1"9O

_ 8O

.N zo

-J 6O



00 130"0

120"0

_ 110O0

100N

90

_ 80

._ 70

-J 60a.if)

r/D=14.0, x/D=7.000 130"0

120"0

_ 110O0

100N

90

_ 80

._ 70

-J 60a.if)

r/D=14.0, x/D=10.0

....................lo_ lo, 4_............. 1o_ lo,'' ....... 4_°


00 130"0

120"0

_ 110O0

100N

90

_ 80

._ 70

-J 60a.if)

r/D=14.0, x/D=8.0 r/D=14.0, x/D=11.0I_ 130"0

120"0

_ 110

I11100

N

90

_ 80

e" 70

--1 60a.U'Iiiiii i i i iiiiii i i i ii iiii i i i iiiiii i i i iii1o_ 1o° '%° lo_ lo° %°



34

I_ 130

"0120

"0

_ 110

I11100

N

90

CO 80

.N 7o

--1 60D.

0'1

r/D=14.0, x/D=12.0I_ 130

"0120

"0

_ 110

IXI10O

N"1"

9O

_ 8O

.N 7o

-J 6O

ffl

r/D=14.0, x/D=15.0

iiiii i i i iiiiii i i i ii iiiii i i i iiiiii i i i iiilo" lo° %° 1o" lo° %°


00 130

"O120

"O

_ 110

O0100

N

90

_ 80

._ 70

-J 60D.

if)

r/D=14.0, x/D=13.0 r/D=14.0, x/D=16.000 130

"O120

"O

_ 110

O0100

N

90

_ 80

._ 70

-J 60D.

if)

JJz_

.....................lo_ lo, _............. 1o_ lo,' ....... _°


00 130

"O120

"O

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

if)

r/D=14.0, x/D=14.0 r/D=14.0, x/D=17.0I_ 130

"O120

"O

_ 110

I11100

N

90

CO 80

e" 70,m

--1 60D.

0'1,,,,I , , , ,,,,,I , , , ,, ,,,I , , , ,,,,,I , , , ,,,10" 10" "_ 10" 10" 'I'__



35

I_ 130"O

120"O

_ 110

I11100

N

90

CO 80

.N 7o

-1 60O.U')

r/D=16.0, x/D=0.0 r/D=16.0, x/D=3.0I_ 130"O

120"O

_ 110IXI

10ON

"1"9O

_ 8O

.N 7o

-J 6O

if)

JJ .

4" o ....... 1oo' ........ 1oo' ....1o" ........ 1oo' ....... lo"o


m 130"0

120"0

_ 110I11

100N

90

CO 80

._ 70

==1 60a.U)

r/D=16.0, x/D=1.0 r/D=16.0, x/D=4.0m 130"0

120"0

_ 110I11

100IN

90

CO 80

._ 70

==1 60a.U)

J J

I0 _ I0 _ i0 _ I0 _ I0 _


00 130"O

120"O

_ 110I11

100IN

90

CO 80

._ 70

==1 60a.U)

r/D=16.0, x/D=2.0 r/D=16.0, x/D=5.0I_ 130"O

120"O

_ 110

I11100

N

90

CO 80

e" 70

--1 60O.U')

7

10" 10_ ' 'I_)_ 10" ' ...... I_)_ ' ...... 1'_)_



36

I_ 130"0

120"0

_ 110

I11100

N

90

_ 80

.N 7o-1 60a.U')

r/D=16.0, x/D=6.0 r/D=16.0, x/D=9.0m 130"0

120"0

_ 110IXI

10ON

"1"9O

_ 8O

.N 7o

-J 6O

if)iiii i i i iiiiii i i i ii iiiii i i i iiiiii i i i iiiio_ io° '%° lo" lo° %°


00 130"0

120"0

_ 110O0

100N

90

_ 80

._ 70

-J 60a.U)

r/D=16.0, x/D=7.0 r/D=16.0, x/D=10.000 130"0

120"0

_ 110O0

100N

90

_ 80

._ 70

-J 60a.U)

T

:11111 i i i iiiiii i i i iiiiiilo_ lo_ lo° '%_ , ...... _ , ...... _o


00 130"O

120"O

_ 110O0

100N

90

_ 80

._ 70

-J 60a.U)

r/D=16.0, x/D=8.0 r/D=16.0, x/D=11.0I_ 130"0

120"0

_ 110

I11100

N

90

_ 80

e" 70

--1 60a.U')iiiii i i i iiiiii i i i ii iiii i i i iiiiii i i i iiiIo" Io° '%° lo" lo° '1'4°



37

IX_ 130

"O120

"O

_ 110

I11100

N

90

CO 80

.N 7o

--1 60O.

U')

r/D=16.0, x/D=12.0

,,,,I , , , ,,,,,I , , , ,,10" 10" "4_

Frequency, Hz

I_ 130

"O120

"O

_ 110

IXI10O

N"1"

9O

_ 8O

.N 7o

-J 6O

if)

r/D=16.0, x/D=15.0

J

,,,,I , , , ,,,,,I , , , ,,,10" 10° %°

Frequency, Hz

m 130

"0120

"0

_ 110

I11100

N

90

CO 80

._ 70

..1 60a.

U)

r/D=16.0, x/D=13.0

JJJ

.... , ........ , ....... ,,o10_ 10_ 10

Frequency, Hz

m 130

"0120

"0

_ 110

I11100

N

90

CO 80

._ 70

..1 60a.

U)

r/D=16.0, x/D=16.0

.... 10.' ........ 10_' ....... 4_)_

Frequency, Hz

00 130

"O120

"O

_ 110

I11100

IN

90

CO 80

._ 70

..1 60a.

U)

r/D=16.0, x/D=14.0IX_ 130

"O120

"O

_ 110

I11100

N

90

CO 80

e" 70

--1 60O.

U')

r/D=16.0, x/D=17.0

JJ

,,,I , , , ,,,,,I , , , ,, ,,,,I , , , ,,,,,I , , , ,,,10" 10" "_F 10" 10" 'I'_F



38

I_ 130"O

120"O

_ 110

I11100

N

90

_ 80

.N 7o

-1 60a.U'I

r/D=18.0, x/D=0.0 r/D=18.0, x/D=3.0I_ 130"O

120"O

_ 110IXI

10ON

"1"9O

_ 8O

.N zo

-J 6O



I_ 130"O

120"O

_ 110O0

100N

90

_ 80

._ 70

-J 60a.if)

r/D=18.0, x/D=1.0 r/D=18.0, x/D=4.0I_ 130"O

120"O

_ 110O0

100N

90

_ 80

._ 70

-J 60a.if)

s

10_ 10_ 10_ 10_ 10_ 10_


I_ 130"O

120"O

_ 110O0

100N

90

_ 80

._ 70

-J 60a.if)

r/D=18.0, x/D=2.0 r/D=18.0, x/D=5.0I_ 130"O

120"O

_ 110

I11100

N

90

_ 80

e" 70

--1 60a.U'I

j_ jJ_

7

10" 10_ ' 'I_)_ 10" ' ...... I0_ ' ...... 1'_)_



39

I_ 130"O

120"O

_ 110

I11100

N

90

_ 80

.N 7o

-1 60a.U'I

r/D=18.0, x/D=6.0 r/D=18.0, x/D=9.0I_ 130"O

120"O

_ 110IXI

10ON

"1"9O

_ 8O

.N zo

-J 6O



00 130"O

120"O

_ 110O0

100N

90

_ 80

._ 70

-J 60a.if)

r/D=18.0, x/D=7.0 r/D=18.0, x/D=10.000 130"O

120"O

_ 110O0

100N

90

_ 80

._ 70

-J 60a.if)

J j

....................lOz lO_ 4_)............. 1oz lO_11 ....... 4_)4


00 130"0

120"0

_ 110O0

100N

90

_ 80

._ 70

-J 60a.if)

r/D=18.0, x/D=8.0 r/D=18.0, x/D=11.0I_ 130"O

120"O

_ 110

I11100

N

90

_ 80

e" 70

--1 60a.U'I

10" 10_ ' 'I_)_ 10" ' ...... I0_ ' ...... 1'_)_



40

I_ 130"0

120"0

_ 110

I11100

N

90

_ 80

.N 7o

-1 60a.U')

r/D=18.0, x/D=12.0I_ 130"0

120"0

_ 110IXI

10ON

"1"9O

_ 8O

.N 7o

-J 6O

if)

r/D=18.0, x/D=15.0

IIIII I I I IIIIII I I I II IIII I I I IIIIII I I I IIIlo" lo° %° 1o" lo° %°


00 130"O

120"O

_ 110O0

100N

90

_ 80

._ 70

-J 60a.U)

r/D=18.0, x/D=13.0

J

r/D=18.0, x/D=16.000 130"O

120"O

_ 110O0

100N

90

_ 80

._ 70

-J 60a.U)I llll I I I llllll I

I0 _ I0 _ i0 _ I0 _ I0 _


00 130"O

120"O

_ 110O0

100N

90

_ 80

._ 70

-J 60a.U)

r/D=18.0, x/D=14.0

z_

m 130"0

120"0

_ 110

I11100

N

90

_ 80

e" 70.m

--1 60a.U')

r/D=18.0, x/D=17.0

IIII I I I IIIIII I I I II IIII I I I IIIIII I I I III

lO" lO" "_ lO" lO" 'I'__



41

I_ 130

"0120

"0

_ 110

I11100

N

90

_ 80

.N 7o

--1 60a.

U'I

r/D=3.0, x/D=0.0I_ 130

"0120

"0

_ 110

IXI10O

N"1"

9O

_ 8O

.N zo

-J 6O

ffl

r/D=3.0, x/D=3.0



00 130

1:3120

1:3

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

if)

r/D=3.0, x/D=1.000 130

1:3120

1:3

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

if)

r/D=3.0, x/D=4.0

.....................lo_ lo" _............. 1o_ lo,'' ....... 4b


00 130

1:3120

1:3

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

if)

r/D=3.0, x/D=2.0

J

I_ 130

"O120

"O

_ 110

I11100

N

90

_ 80

e" 70.m

--1 60a.

U'I

r/D=3.0, x/D=5.0

iiiii i i i iiiiii i i i ii iiiii i i i iiiiii i i i iii10" 10" "_ 10 _ 10" 'I'__



42

I_ 130

120

_ 110

I11100

N

90

_ 80

.N 7o

"J 60a.

U')

r/D=3.0, x/D=6.0I_ 130

120

_ 110

IXI10O

N"1"

9O

_ 8O

.N zo

-J 6O

if)

r/D=3.0, x/D=9.0



00 130

"O120

"O

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

U)

r/D=3.0, x/D=7.0

JJ

00 130

"O120

"O

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

U)

r/D=3.0, x/D=10.0

.................... _)............ 10_10" 10" 10" ,I ....... 4_)_


00 130

"O120

"O

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

U)

r/D=3.0, x/D=8.0I_ 130

"O120

"O

_ 110

I11100

N

90

_ 80

e" 70

"J 60a.

U')

r/D=3.0, x/D=11.0




43

00 130

"O120

"O

_ 110

O0100

N

90

CO 80

.N 7o

--1 600.

U')

r/D=3.0, x/D=1 2.0

,,,,I , , , ,,,,,I , , , ,,10 _ 10_ "4_

Frequency, Hz

r/D=3.0, x/D=15.0n"= 130.

N 100 _= _

._ 78_-

681 , ,,,, ........ ,18 _ 18 _ 18 _

Frequency, Hz

m 130

"0120

"0

_ 110

O0100

N

90

CO 80

._ 70

"J 600.

if)

r/D=3.0, x/D=13.0

''"10_ ........ 10_' ....... 4_

Frequency, Hz

m 130

"0120

"0

_ 110

O0100

N

90

CO 80

._ 70

"J 600.

if)

r/D=3.0, x/D=16.0

.... 10_' ........ 10_' ....... 4_)_

Frequency, Hz

m 130

"0120

"0

_ 110

O0100

N

90

CO 80

._ 70

"J 600.

if)

r/D=3.0, x/D=14.0

\

r/D=3.0, x/D=17.0

\


44

I_ 130

120

_ 110

I11100

N

90

_ 80

.N 7o--1 60a.

U'I

r/D=4.0, x/D=O.OI_ 130

120

_ 110

IXI10O

N"1"

9O

_ 8O

.N zo

-J 6O

ffl

r/D=4.0, x/D=3.0

/-

iiii i i i iiiiii i i i ii iiiii i i i iiiiii i i i iiilo" lo° '%° lo" lo° %°


m 130

1:3120

1:3

_ 110

In100

N

90

_ 80

._ 70

-J 60a.

if)

r/D=4.0, x/D=1.0

//

m 130

1:3120

1:3

_ 110

In100

N

90

_ 80

._ 70

-J 60a.

if)

r/D=4.0, x/D=4.0

....................lo_ lo" 4_............. 1o_ lo,'' ....... 4_°


m 130

1:3120

1:3

_ 110

In100

N

90

_ 80

._ 70

-J 60a.

if)

r/D=4.0, x/D=2.0

//

I_ 130

"O120

"O

_ 110

I11100

N

90

_ 80

e" 70

--1 60a.

U'I

r/D=4.0, x/D=5.0

iiiil i i i iiiiil i i i ii fill i i i iiiiil i i i illIo_ Io° '%° lo" lo° %°



45

I_ 130

"O120

"O

_ 110

I11100

N

90

_ 80

.N 7o

--1 60a.

U')

r/D=4.0, x/D=6.0I_ 130

"O120

"O

_ 110

IXI10O

N"1"

9O

_ 8O

.N 7o

-J 6O

if)

r/D=4.0, x/D=9.0



m 130

"0120

"0

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

U)

r/D=4.0, x/D=7.0m 130

"0120

"0

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

U)

r/D=4.0, x/D=10.0

.................... _)............ 10_10" 10_ 10" ,I ....... 4_)_


m 130

"0120

"0

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

U)

r/D=4.0, x/D=8.0I_ 130

"O120

"O

_ 110

I11100

N

90

_ 80

e" 70

--1 60a.

U')

r/D=4.0, x/D=11.0




46

I_ 130

"0120

"0

_ 110

I11100

N

90

_ 80

.N 7o

--1 60a.

U'I

r/D=4.0, x/D=12.0I_ 130

"0120

"0

_ 110

IXI10O

N"1"

9O

_ 8O

.N zo

-J 6O

ffl

r/D=4.0, x/D=15.0

iiiii i i i iiiiii i i i ii iiii i i i iiiiii i i i iiilo" lo° '%° lo" lo° %°


00 130

"O120

"O

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

if)

r/D=4.0, x/D=13.000 130

"O120

"O

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

if)

r/D=4.0, x/D=16.0

....................lo_ lo" _............. 1o_ lo,'' ....... _°


00 130

"O120

"O

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

if)

r/D=4.0, x/D=14.0m 130

"0120

"0

_ 110

I11100

N

90

_ 80

e" 70

--1 60a.

U'I

r/D=4.0, x/D=17.0




47

I_ 130"O

120"O

_ 110

I11100

N

90

_ 80

.N 7o

-1 60a.U'I

r/D=6.0, x/D=0.0I_ 130"O

120"O

_ 110IXI

10ON

"r9O

_ 8O

.N 7o

-J 6O

ffl

r/D=6.0, x/D=3.0



00 130"O

120"O

_ 110QI

100N

90

_ 80

._ 70

-J 60a.U)

r/D=6.0, x/D=1.0

f

00 130"O

120"O

_ 110QI

100N

90

_ 80

._ 70

-J 60a.U)

r/D=6.0, x/D=4.0

__ _v ,.,_._ww_, _

.....................10" 10_ _)............. I0" 10_'t ....... _)_


00 130"O

120"O

_ 110QI

100N

90

._ 70

-J 60a.U)

r/D=6.0, x/D=2.0I_ 130"O

120"O

_ 110

I11100

N

90

_ 8o

e- 70.m

-1 60a.U'I

r/D=6.0, x/D=5.0

iiiii i i i iiiiii i i i ii iiiii i i i iiiiii i i i iiilO" lO" "_ lO _ lO" 'I'__



48

I_ 130

"O120

"O

_ 110

I11100

N

90

_ 80

.N 7o

--1 60a.

U')

r/D=6.0, x/D=6.0I_ 130

"O120

"O

_ 110

IXI10O

N"1"

9O

_ 8O

.N 7o

-J 6O

if)

r/D=6.0, x/D=9.0

JJ

iiiii i i i iiiiii i i i ii iiii i i i iiiiii i i i iiilo" lo° %° lo" lo° %°


m 130

"0120

"0

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

U)

r/D=6.0, x/D=7.0m 130

"0120

"0

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

U)

r/D=6.0, x/D=10.0

J

.....................10z 10_ 4_)............. 10 z 10_11 ....... 4_)4


m 130

"0120

"0

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

U)

r/D=6.0, x/D=8.0I_ 130

"O120

"O

_ 110

I11100

N

90

_ 80

e" 70

--1 60a.

U')

r/D=6.0, x/D=11.0

J




49

I_ 130

120

_ 110

I11100

N

90

CO 80

.N zo

--1 60a.

U')

r/D=6.0, x/D=12.0

/-

I_ 130

120

_ 110

IXI100

N"1"

90

_ 80

.N zo

..I 60

if)

r/D=6.0, x/D=15.0

J

iiiii i i i iiiiii i i i ii iiiii i i i iiiiii i i i iiilo_ lo° '%° lo_ lo° %°


m 130

"0120

"0

_ 110

I11100

N

90

CO 80

._ 70

..1 60a.

U)

r/D=6.0, x/D=13.0

/

m 130

"O120

"O

_ 110

I11100

IN

90

CO 80

._ 70

..1 60a.

U)

r/D=6.0, x/D=16.0

10" 10" 10" ,I ....... 4_)_


m 130

"0120

"0

_ 110

I11100

IN

90

CO 80

._ 70

..1 60a.

U)

r/D=6.0, x/D=14.000 130

"O120

"O

_ 110

I11100

N

90

CO 80

e" 70

--1 60a.

U')

r/D=6.0, x/D=17.0

iiiii i i i iiiiii i i i ii iiiii i i i iiiiii i i i iiiIo" Io° '%° lo" lo° %°



5O

I_ 130"0

120"0

_ 110

I11100

N

90

_ 80

.N 7o-1 60a.U'I

r/D=8.0, x/D=O.O

J

I_ 130"0

120"0

_ 110IXI

10ON

"1"9O

_ 8O

.N zo

-J 6O

ffl

r/D=8.0, x/D=3.0

iiii i i i iiiiii i i i ii iiii i i i iiiiii i i i iiiio" io° '%° lo" io° %°


m 1301:3

1201:3

_ 110O0

100N

90

_ 80

._ 70

-J 60a.if)

r/D=8.0, x/D=1.0m 1301:3

1201:3

_ 110O0

100N

90

_ 80

._ 70

-J 60a.if)

r/D=8.0, x/D=4.0

....................Io. Io. _8............. Io. Io."......._8°


m 1301:3

1201:3

_ 110O0

100N

90

_ 80

._ 70

-J 60a.if)

r/D=8.0, x/D=2.0I_ 130"O

120"O

_ 110

I11100

N

90

_ 80

e" 70.m

--1 60a.U'I

r/D=8.0, x/D=5.0

iiii i i i iiiiii i i i ii iiiii i i i iiiiii i i i iiilO" lO" "_ lO _ lO" 'I'__



51

I_ 130

"0120

"0

_ 110

I11100

N

90

_ 8o

.N 7o

--1 60a.

U'I

r/D=8.0, x/D=6.0I_ 130

"0120

"0

_ 110

IXI10O

N"1"

9O

_ 8O

.N zo

-J 6O

ffl

r/D=8.0, x/D=9.0

fJ

yJ

iiiii i i i iiiiii i i i ii iiii i i i iiiiii i i i iiilo" lo° '%° lo" lo° %°


00 130

"O120

"O

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

if)

r/D=8.0, x/D=7.0

.v_W_._,_ '

00 130

"O120

"O

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

if)

r/D=8.0, x/D=10.0

.....................lo_ lo" _............. 1o_ lo,'' ....... 4b


00 130

"O120

"O

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

if)

r/D=8.0, x/D=8.0I_ 130

"O120

"O

_ 110

I11100

N

90

_ 80

e" 70.m

--1 60a.

U'I

r/D=8.0, x/D=11.0

JJ

iiii i i i iiiiii i i i ii iiii i i i iiiiii i i i iii10" 10" "_ 10 _ 10" 'I'__



52

I_ 130

"0120

"0

_ 110

I11100

N

90

_ 80

.N 7o--1 60a.

U'I

r/D=8.0, x/D=12.0I_ 130

"0120

"0

_ 110

IXI10O

N"1"

9O

_ 8O

.N zo

-J 6O

ffl

r/D=8.0, x/D=15.0

J



m 130

"0120

"0

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

if)

r/D=8.0, x/D=13.0

J

m 130

"O120

"O

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

if)

r/D=8.0, x/D=16.0

....................lo_ lo" _............. 1o_ lo,'' ....... _°


m 130

"0120

"0

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

if)

r/D=8.0, x/D=14.0m 130

"0120

"0

_ 110

I11100

N

90

_ 80

e" 70,m

--1 60a.

U'I

r/D=8.0, x/D=17.0




53

I_ 130

"O120

"O

_ 110

I11100

N

90

_ 80

.N 7o

--1 60a.

U'I

r/D=10.0, x/D=0.0

JJ

I_ 130

"O. 120

"O

_ 110

IXI10O

N"1"

9O

_ 8O

.N zo

-J 6O

ffl

r/D=10.0, x/D=3.0



I_ 130

"O120

"O

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

if)

r/D=10.0, x/D=1.0I_ 130

"O120

"O

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

if)

r/D=10.0, x/D=4.0

J

....................10z 10_ 4_)............. 10 z 10_11 ....... 4_)4


I_ 130

"O120

"O

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

if)

r/D=10.0, x/D=2.0

j-

I_ 130

"O120

"O

_ 110

I11100

N

90

_ 80

e" 70.m

--1 60a.

U'I

r/D=10.0, x/D=5.0




54

I_ 130

"O120

"O

_ 110

I11100

N

90

_ 80

.N 7o

--1 60a.

U'I

r/D=10.0, x/D=6.0I_ 130

"O120

"O

_ 110

IXI10O

N"1"

9O

_ 8O

.N zo

-J 6O

ffl

r/D=10.0, x/D=9.0

J

iiii i i i iiiiii i i i ii iiiii i i i iiiiii i i i iiilo" lo° '%° lo" lo° %°


00 130

"O120

"O

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

if)

r/D=10.0, x/D=7.0

f---J

JJJ

00 130

"O120

"O

_ 110

O0100

N

90

._ 70

-J 60a.

if)

r/D=10.0, x/D=10.0

.....................lo_ lo" _............ 1o_ lo,'' ....... _°


00 130

"O120

"O

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

if)

r/D=10.0, x/D=8.0I_ 130

"O120

"O

_ 110

I11100

N

90

_ 80

e" 70.m

--1 60a.

U'I

r/D=10.0, x/D=11.0

JJJ




55

I_ 130

"O120

"O

_ 110

I11100

N

90

_ 80

.N 7o

--1 60a.

U')

r/D=10.0, x/D=12.0

z_

I_ 130

"O120

"O

_ 110

IXI10O

N"1"

9O

_ 8O

.N 7o

-J 6O

if)

r/D=10.0, x/D=15.0



m 130

"0120

"0

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

U)

r/D=10.0, x/D=13.0

/

m 130

"0120

"0

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

U)

r/D=10.0, x/D=16.0

J

.....................10z 10_ 4_)............. 10 z 10_11 ....... 4_)4


m 130

"0120

"0

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

U)

r/D=10.0, x/D=14.0

f--J/

JJ

I_ 130

"O120

"O

_ 110

I11100

N

90

_ 80

e" 70

--1 60a.

U')

r/D=10.0, x/D=17.0




56

I_ 130"O

120"O

_ 110

I11100

N

90

_ 80

.N 7o

-1 60a.U')

r/D=12.0, x/D=0.0

z_

I_ 130"O

120"O

_ 110IXI

10ON

"1"9O

_ 8O

.N 7o

-J 6O

if)

r/D=12.0, x/D=3.0

J

iiiii i i i iiiiii i i i ii iiii i i i iiiiii i i i iiilo" lo° %° 1o" lo° %°


00 130"O

120"O

_ 110O0

100N

90

_ 80

._ 70

-J 60a.U)

r/D=12.0, x/D=1.0

J

00 13o"O

12o"O

_ 110O0

100N

90

_ 80

._ 70

-J 60a.U)

r/D=12.0, x/D=4.0

jr

J

....................lo_ lo, _............. 1o_ lo,' ....... _°


00 130"O

120"O

_ 110O0

100N

90

_ 80

._ 70

-J 60a.U)

r/D=12.0, x/D=2.000 130"O

120"O

_ 110

I11100

N

90

_ 80

e" 70.m

--1 60a.U')

r/D=12.0, x/D=5.0

iiiii i i i iiiiii i i i ii iiiii i i i iiiiii i i i iiilO" lO" "_ lO" lO" 'I'__



57

I_ 130"0

120"0

_ 110

I11100

N

90

CO 80

.N 7o-1 60a.U')

r/D=12.0, x/D=6.0I_ 130"0

120"0

_ 110IXI

10ON

"1"9O

_ 8O

.N 7o

-J 6O

if)

r/D=12.0, x/D=9.0

iiiii i i i iiiiii i i i ii iiii i i i iiiiii i i i iiilo" lo° %° 1o" lo° %°


00 130"O

120"O

_ 110O0

100N

90

CO 80

._ 70

-J 60a.U)

r/D=12.0, x/D=7.000 130"O

120"O

_ 110O0

100N

90

CO 80

._ 70

-J 60a.U)

r/D=12.0, x/D=10.0

J

.....................lo_ lo, _............ 1o_ lo,' ....... _°


00 130"O

120"O

_ 110O0

100N

90

CO 80

._ 70

-J 60a.U)

r/D=12.0, x/D=8.0I_ 130"O

120"O

_ 110

I11100

N

90

CO 80

e" 70,m

--1 60a.U')

r/D=12.0, x/D=11.0

iiiii i i i iiiiii i i i ii iiii i i i iiiiii i i i iiilO" lO" "_ lO" lO" 'I'__



58

I_ 130"O

120"O

_ 110

I11100

N

90

_ 80

.N 7o

-1 60a.U')

r/D=12.0, x/D=12.0I_ 130"O

120"O

_ 110IXI

10ON

"1"9O

_ 8O

.N 7o

-J 6O

if)

r/D=12.0, x/D=15.0

J



m 130"0

120"0

_ 110O0

100N

90

_ 80

._ 70

-J 60a.U)

r/D=12.0, x/D=13.0m 130"0

120"0

_ 110O0

100N

90

_ 80

._ 70

-J 60a.U)

r/D=12.0, x/D=16.0

z_

.................... _............ lo,10" 10_ 10" ,t ....... 4_)_


m 130"0

120"0

_ 110O0

100N

90

_ 80

._ 70

-J 60a.U)

r/D=12.0, x/D=14.0I_ 130"O

120"O

_ 110

I11100

N

90

_ 80

e" 70,m

--1 60a.U')

r/D=12.0, x/D=17.0

J




59

I_ 130"O

120

_ 110

I11100

N

90

CO 80

.N 7o-1 60a.U')

r/D=14.0, x/D=0.0I_ 130"O

120

_ 110IXI

10ON

"1"9O

_ 8O

.N 7o

-J 6O

if)

r/D=14.0, x/D=3.0

JjJ



m 130"0

120"0

_ 110O0

100N

90

CO 80

._ 70

-J 60a.U)

r/D=14.0, x/D=1.0

J

m 130"0

120"0

_ 110O0

100N

90

CO 80

._ 70

-J 60a.U)

r/D=14.0, x/D=4.0

J

.....................lo_ lo, _............. 1o_ lo,' ....... _°


m 130"0

120"0

_ 110O0

100N

90

CO 80

._ 70

-J 60a.U)

r/D=14.0, x/D=2.0 r/D=14.0, x/D=5.0I_ 130"O

120"O

_ 110

I11100

N

90

CO 80

e" 70.m

--1 60a.U')iiiii i i i iiiiii i i i ii iiii i i i iiiiii i i i iiiIo" Io° '%° Io" Io° %°



6O

I_ 130"O

120"O

_ 110

I11100

N

90

CO 80

.N 7o

-1 60a.U')

r/D=14.0, x/D=6.0

J

I_ 130"O

120"O

_ 110IXI

10ON

"1"9O

_ 8O

.N 7o

-J 6O

if)

r/D=14.0, x/D=9.0



m 130"0

120"0

_ 110O0

100N

90

CO 80

._ 70

-J 60a.U)

r/D=14.0, x/D=7.0m 130"0

120"0

_ 110O0

100N

90

CO 80

._ 70

-J 60a.U)

r/D=14.0, x/D=10.0

JJ

JJ

.....................lOz lO_ 4_)............. 1oz lO_11 ....... 4_)4


m 130"0

120"0

_ 110O0

100N

90

CO 80

._ 70

-J 60a.U)

r/D=14.0, x/D=8.0

z_

I_ 130"O

120"O

_ 110

I11100

N

90

CO 80

e" 70.m

--1 60a.U')

r/D=14.0, x/D=11.0




61

I_ 130"O

120"O

_ 110

I11100

N

90

_ 80

.N 7o

-1 60a.U')

r/D=14.0, x/D=12.0I_ 130"O

120"O

_ 110IXI

10ON

"1"9O

_ 8O

.N 7o

-J 6O

if)

r/D=14.0, x/D=15.0

iiiii i i i iiiiii i i i ii iiiii i i i iiiiii i i i iiilo" lo° %° lo" lo° %°


m 130"0

120"0

_ 110O0

100N

90

_ 80

._ 70

-J 60a.U)

r/D=14.0, x/D=13.0m 130"0

120"0

_ 110O0

100N

90

_ 80

._ 70

-J 60a.U)

r/D=14.0, x/D=16.0

J

.....................lOz lO_ 4_)............ 1oz lO_11 ....... 4_)4


m 130"0

120"0

_ 110O0

100N

90

_ 80

._ 70

-J 60a.U)

r/D=14.0, x/D=14.0I_ 130"O

120"O

_ 110

I11100

N

90

_ 80

e" 70

--1 60a.U')

r/D=14.0, x/D=17.0

Fj J_ _\_

iiii i i i iiiiii i i i ii iiiii i i i iiiiii i i i iiilO" lO" "_ lO _ lO" 'I'__



62

I_ 130

"O120

"O

_ 110

I11100

N

90

_ 80

.N 7o

--1 60a.

U'I

r/D=16.0, x/D=0.0 r/D=16.0, x/D=3.0

z_

I_ 130

"O120

"O

_ 110

IXI10O

N"1"

9O

_ 8O

.N zo

-J 6O



m 130

"0120

"0

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

if)

r/D=16.0, x/D=1.0m 130

"0120

"0

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

if)

r/D=16.0, x/D=4.0

JJ

J

.....................10z 10_ 4_)............. 10 z 10_11 ....... 4_)4


m 130

"0120

"0

_ 110

O0100

N

90

_ 80

._ 70

-J 60a.

if)

r/D=16.0, x/D=2.0 r/D=16.0, x/D=5.0I_ 130

"O120

"O

_ 110

I11100

N

90

_ 80

e" 70

--1 60a.

U'I

JJ

iiiii i i i iiiiii i i i ii iiiii i i i iiiiii i i i iiiIo_ Io° '%° lo_ lo° %°



63

I_ 130"0

120"0

_ 110

I11100

N

90

_ 80

--1 60a.U'I

r/D=16.0, x/D=6.0I_ 130"0

120"0

_ 110IXI

10ON

"r9O

_ 8O

.N 7o

-J 6O

ffl

r/D=16.0, x/D=9.0

lllll i i i llllll i i i ii llll i i i llllll i i i illlo" lo° %° 1o" lo° %°


m 130"0

120"0

_ 110O0

100N

90

_ 80

._ 70

-J 60a.if)

r/D=16.0, x/D=7.0m 130"0

120"0

_ 110O0

100N

90

_ 80

._ 70

-J 60a.if)

r/D=16.0, x/D=10.0

J

....................lo_ lo, _............. 1o_ lo,' ....... _°


m 130"0

120"0

_ 110O0

100N

90

_ 80

._ 70

-J 60a.if)

r/D=16.0, x/D=8.0

Y

I_ 130"O

120"O

_ 110

I11100

N

90

_ 80

e" 70

--1 60a.U'I

r/D=16.0, x/D=11.0

lO" lO" "_ lO" lO" 'I'__



64

I_ 130"0

120"0

_ 110

I11100

N

90

CO 80

.N 7o-1 60a.U')

r/D=16.0, x/D=12.0I_ 130"0

120"0

_ 110IXI

10ON

"1"9O

_ 8O

.N 7o

-J 6O

if)

r/D=16.0, x/D=15.0



m 130"0

120"0

_ 110O0

100N

90

CO 80

._ 70

-J 60a.U)

r/D=16.0, x/D=13.0m 130"0

120"0

_ 110O0

100N

90

CO 80

._ 70

-J 60a.U)

r/D=16.0, x/D=16.0

.....................lo_ lo, _............. 1o_ lo,' ....... _o


m 130"0

120"0

_ 110O0

100N

90

CO 80

._ 70

-J 60a.U)

r/D=16.0, x/D=14.0

j_J

m 130"0

120"0

_ 110

I11100

N

90

CO 80

e" 70.m

--1 60a.U')

r/D=16.0, x/D=17.0




65

I_ 130"O

120"O

_ 110

I11100

N

90

_ 80

.N 7o-1 60a.U'I

r/D=18.0, x/D=0.0 r/D=18.0, x/D=3.0I_ 130"O

120"O

_ 110IXI

10ON

"1"9O

_ 8O

.N zo

-J 6O

ffl

_ j_j

iiiii i i i iiiiii i i i ii iiiii i i i iiiiii i i i iiiio_ io° '%° lo_ lo° %°


I_ 130"O

120"O

_ 110I11

100N

90

_ 80

._ 70

-J 60a.if)

r/D=18.0, x/D=1.0

JJ

I_ 130"O

120"O

_ 110I11

100N

90

_ 80

._ 70

-J 60a.if)

r/D=18.0, x/D=4.0

J

.....................lo_ lo, 4_............. 1o_ lo,' ....... 4_°


I_ 130"O

120"O

_ 110I11

100N

90

_ 80

._ 70

-J 60a.if)

r/D=18.0, x/D=2.0I_ 130"O

120"O

_ 110

I11100

N

90

_ 80

e" 70

--1 60a.U'I

r/D=18.0, x/D=5.0

J




66

I_ 130"O

120"O

_ 110

I11100

N

90

_ 80

.N 7o

-1 60a.U')

r/D=18.0, x/D=6.0I_ 130"O

120"O

_ 110IXI

10ON

"1"9O

_ 8O

.N 7o

-J 6O

if)

r/D=18.0, x/D=9.0

j_



00 130"O

120"O

_ 110O0

100N

90

_ 80

._ 70

-J 60a.U)

r/D=18.0, x/D=7.0

J

00 13o"O

12o"O

_ 110O0

100N

90

_ 80

._ 70

-J 60a.U)

r/D=18.0, x/D=10.0

jJ

.................... _)............ lO_lO" lO_ lO" ,t ....... 4_)_


00 130"O

120"O

_ 110O0

100N

90

_ 80

._ 70

-J 60a.U)

r/D=18.0, x/D=8.0

J

I_ 130"O

120"O

_ 110

I11100

N

90

_ 80

e" 70.m

--1 60a.U')

r/D=18.0, x/D=11.0

J

J




67

I_ 130"0

120"0

_ 110

I11100

N

90

CO 80

.N 7o-1 60a.U')

r/D=18.0, x/D=12.0I_ 130"0

120"0

_ 110IXI

10ON

"1"9O

_ 8O

.N 7o

-J 6O

if)

r/D=18.0, x/D=15.0



00 130"O

120"O

_ 110O0

100N

90

CO 80

._ 70

-J 60a.U)

r/D=18.0, x/D=13.0

J

00 13o"O

12o"O

_ 110O0

100N

90

CO 80

._ 70

-J 60a.U)

r/D=18.0, x/D=16.0

j_

.....................lo_ lo, _............. 1o_ lo,' ....... _°


00 130"O

120"O

_ 110O0

100N

90

CO 80

._ 70

-J 60a.U)

r/D=18.0, x/D=14.0

j J_J_ _ _v_Wv_v _

m 130"0

120"0

_ 110

I11100

N

90

CO 80

e" 70

--1 60a.U')

r/D=18.0, x/D=17.0




68

Overall fc = 732 Hz

.°I18

16

14

a 12

10

i i i i I i i i i I i i i i I i i i5 10 15

x/D

fc = 1465 Hz

'°I.18 .e_

_o Y _ _

2 i i i i I i i i i I i i i i I i i i5 10 15

x/D

fc = 2930 Hz

2O

18

16

14

12

10

8

6

4

25 10 15

x/D

f_ = 4395 Hz

e_L;

20

18

16

14

12

10

8

6

4

2IIIlllllllllll_l

5 10 15

_D

20

18

16

14

¢'_ 12

10

8

6

4

2 i i i i I i i i i I I i i i I i i i5 10 15

xJD

Figure 64: Contours of Acoustic Near Field for Mae=0.60, Overall and Bandpassed atCenter Frequency Denoted

69

Overall re= l123Hz

2°L18 j

14

118_

2(_ i i i i 51 i i i i 101 i i i i 151 i i i

x/D

re= 2246Hz

a

2O

18

16

14

12

10

8

6

4

2; i i i i I i i i i I i i i i I i i i5 10 15

x/D

re= 4492Hz

2O

18

16

14

a12

10

8

6

4

5 10

x/D

re= 6738Hz

\

15

2O

18

16

14

a12

10

5 10 15

x/D

2O

18

16

14

a12

10

8

6

4

5 10 15

x/D

Figure 65: Contours of Acoustic Near Field Ma¢=0.85, Overall and Bandpassed at

Peak Frequency Denoted

70

r/D=3.0

xJD=0.0

xJD=1.0

xJD=2.0

xJD=3.0XJD=4.0

_do:_.0XJD:6.0

r/D=4.0

xJD=0.0

xJD=1.0

xJD=2.0

xJD=3.0x,'o:4.0

X/D=6.0

11

O8

.£

8O

8

O

O

0 1 2 3 4 5 6

x/D

riD=3.0

x/D=4.0

x/D=5.0

+ x/D= 6.0

x/D=7.0

x/D=7.0

:,dD=l 0.0

0 1 2 3 4 5 6

x/D

riD=4.0

=

O

8

O

x/D=4.0x/D=5.0

x/D=6.0

x/D=7.0

x/D=7.0

:,dD=l 0.0

4 5 6 7 8 9 10

x/D4 5 6 7 8 9 10

x/O

r/D=3.0

7 a 9 10 11 12 13

x/D

dD=4.0

7 8 9 10 11 12 13

x/D

Figure 66: Zero Time Lag Pressure Correlations, Mae=0.30

71

r/D=3.0

x/D=0.0

x/D=1.0

x/D=2.0

:,dD=3.0X/D=4.0

_do:_.0X/D:6.0

r/D=4.0

x/D=0.0

x/D=1.0

x/D=2.0

xZD=3.0xZo:4.0

X/D=6.0

2 3

x/D

r/D=6.0

x/D=0.0

x/D=1.0

x/D=2.0

:,dD=3.0:,dO:4.0_dO=_.0X/D=6.0

2 3

x/D

r/D=8.0

x/D=0.0

x/D=1.0

x/D=2.0

xZD:3.0xZO=4.0

_O=_.0

0 2 3 4 5 6

x/D2 3 4 5 6

x/D

r/D=10.0

x/D=0.0

x/D=1.0

+ x/D=2.0

:,dD=3.0X/D=4.0

_do:_.0XJD:6.0

="6

88

O

O

r/D=12.0

x/D=0.0

x/D=1.0

x/D=2.0

xZD:3.0X/D=4.0

X/D=6.0

0 2 3

x/D

r/D=14.0

x/D=0.0

x/D=1.0

x/D=2.0

x/D=3.0

X/D=4.0

X/D=5.0

X/D=6.0

2 3

x/D

r/D=16.0

x/D=0.0

x/D=1.0

x/D=2.0

xZD:3.0X/D=4.0

X/D=6.0

0 2 3 4 5 6

x/D2 3 4 5 6

x/D


72

r/D=3.0

x/D=4.0x/D=5.0

x/D=6.0

x/D=7.0x/D=7.0

x_D=9.0x/D=10.0 8

._8

.==O

O

r/D=4.0

x/D=4.0

x/D=5.0

x/D=6.0x/D=7.0

x/D=7.0

x_o=9.0x/D=10.0

4 5 6 7 8 9 10

x/D

riD=6.0

:,OrD=4.0X/D=5.0

X/D=6.0X/D=7.0

X/D=7.0

_D=9.0X/D=10.0

4 5 6 7 8 9 10

x/D

riD=8.0

x/D=4.0x/D=5.0

x/D=6.0x/D=7.0

x/D=7.0

x_o:9.0x/D=10.0

4 5 6 7 8 9 10

x/D4 5 6 7 8 9 10

x/D

C

0

0

i 02

0

0

r/D=10.0

x/D=4.0x/D=5.0

x/D=6.0

x/D=7.0

x/D=7.0

x_D=9.0x/D=10.0

=

88

.==O

O

r/D=12.0

x/D=4.0x/D=5.0

x/D=6.0x/D=7.0

x/D=7.0

x_o=9.0x/D=10.0

C0_

:_e

O

8

.==O

O

4 5 6 7 8 9 lo

x/D

r/D=14.0

:,OrD=4.0X/D=5.0

X/D=6.0:,OrD=7.0

:,OrD=7.0

X/D=9.0

X/D=10.0

4 5 6 7 8 9 10

x/D

r/D=16.0

x/D=4.0x/D=5.0

x/D=6.0x/D 7.0

x/D 7.0

x_D9.0x/O 1o.o

4 5 6 7 8 9 10

x/D4 5 6 7 8 9 10

x/D


73

r/D=3.0

x/D=7.0x/D=8.0

x/D=9.0

_D=10.0_D=11.0

_D=12.0x/D=13.0

_D=7.0

_O=8.0

_D=I0.0

_D=11.0

_D=12.0x/D=13.0

8.I

O

O

r/D=4.0

7 8 9 10 11 12 13

x/D

riD=8.0

:¢ID=I0.0

:¢ID=I1.0

_D=12.0_D=13.0

:¢ID=I0.0

:¢ID=I1.0

_D=12.0_D=13.0

7 8 9 10 11 12 13

x/D7 8 9 10 11 12 13

x/O

r/D=10.0

_D=7.0

_D=8.0

_D=9.0

_D=I0.0

_D=11.0

_D=12.0x/D=13.0

"6

8

O

O

r/D=12.0

:¢ID=I0.0

:¢ID=I1.0

_D=12.0x/D=13.0

C

O

O

O

7 8 9 lO 11 12 13

x/D

r/D=14.0

_o=1o.o

_D=11.0

_D=12.0

x/D=13.0

7 8 9 10 11 12 13

x/D

t/D=16.0

x/D=?.0x/D=8.0

x/D=9.0x]D lO.O

X]D 11.o

_D 12.0x/D 13.0

7 8 9 10 11 12 13

x/D7 8 9 10 11 12 13

x/O


74

r/D=3.0

x]D=13.0x]D=l 4.0

x]D=15.0

+'_0=16.0+ x/D= 17.0

+,_0=18.ox]D=l 8.0

++8

O

+J

r/D=4.0

xZD=13.0

xZD=14.0

xZD=15.0xZD=l 6.0

X]D=I 7.0

_D=18.0xZD=l 8.0

13 14 15 16 17 18 19

x/D

riD=6.0

+D=13.0x/D=14.0

+D=15.0+D=16.0

X/[):17.0

_D=18.0x/D=18.0

13 14 15 16 17 18 19

x/D

riD=8.0

=

O

0

_o_O

xZD=13.0xZD=14.0

xZD=15.0xZD=l 6.0

x]D=I 7.0

_D=18.0xZD=l 8.0

13 14 15 16 17 18 19

x/D13 14 15 16 17 18 19

x/D

r/D=10.0

x]D=18.0x]D=l 4.0

x]D=15.0

+'_0=16.0

x/D=17.0

+,_0=18.ox]D=l 8.0

=

8

_m

O

O

r/D=12.0

xZD=13.0xlD=l 4.0

xZD=15.0xZD=l 6.0

xlD=l 7.0

_D=18.0xZD=l 8.0

C_3

:_e

O

_m

O

O

13 14 15 16 17 18 19

x/D

r/D=14.0

+D=13.0x/D=14.0

+D=15.0+D=16.0

X/[):17.0

x/D=18.0

x/D=18.0

13 14 15 16 17 18 19

x/D

r/D=16.0

xZD=13.0xlD=l 4.0

xZD=15.0xJD 16.0

X/D 17.0

_o 18.oxJD 18.0

13 14 15 16 17 18 19

x/D13 14 15 16 17 18 19

x/D


75

r/D=3.0

x/D=0.0

x/D=1.0

x/D=2.0

:,dD=3.0X/D=4.0

_do:_.0X/D:6.0

r/D=4.0

x/D=0.0

x/D=1.0

x/D=2.0

xZD=3.0xZo:4.0

X/D=6.0

2 3

x/D

r/D=6.0

x/D=0.0

x/D=1.0

x/D=2.0

:,dD=3.0:,dO:4.0_dO=_.0X/D=6.0

2 3

x/D

r/D=8.0

x/D=0.0

x/D=1.0

x/D=2.0

xZD:3.0xZO=4.0

_O=_.0

0 2 3 4 5 6

x/D2 3 4 5 6

x/D

r/D=10.0

x/D=0.0

x/D=1.0

+ x/D=2.0

:,dD=3.0X/D=4.0

_do:_.0XJD:6.0

r/D=12.0

x/D=0.0

x/D=1.0

x/D=2.0

xZD:3.0X/D=4.0

X/D=6.0

0 2 3

x/D

r/D=14.0

x/D=0.0

x/D=1.0

x/D=2.0

x/D=3.0

X/D=4.0

X/D=5.0

X/D=6.0

2 3

x/D

r/D=16.0

x/D=0.0

x/D=1.0

x/D=2.0

xZD:3.0X/D=4.0

X/D=6.0

0 2 3 4 5 6

x/D2 3 4 5 6

x/D


76

r/D=3.0

x/D=4.0x_D=5.0

x_D=6.0

x_D=7.0x_D=7.0

*'dD=10.0 8_8

O

O

r/D=4.0

xJD=4.0

xJD=5.0

xJD=6.0xJD=7.0

xJD=7.0

_o=9.0X/D=I 0.0

4 5 6 7 8 9 10

x/D

r/D=6.0

11

o8

8O

800

O

O

x/D=4.0

x/D=5.0

x/D=6.0

:(/D:7.0

:(/D:7.0

_D=9.0X/D=10.0

4 5 6 7 8 9 10

x/D

riD=8.0

x/D=4.0

x/D=5.0

x/D=6.0

x/D=7.0

x/D=7.0

_o=9.0X/D=10.0

4 5 6 7 8 9 10

x/D4 5 6 7 8 9 10

x/D

r/D=10.0

x/D=4.0

x/D=5.0

x/D=6.0

x/D=7.0

x/D=7.0

_D=9.0X/D=10.0

"6

88

O

O

r/D=12.0

x/D=4.0

x/D=5.0

x/D=6.0

x/D=7.0

x/D=7.0

_o=9.0X/D=10.0

4 5 6 7 8 9 10

x/D

r/D=14.0

x/D=4.0

x/D=5.0

x/D=6.0

x/D=7.0

x/D=7.0

x/D=9.0

X/D=10.0

4 5 6 7 8 9 10

x/D

r/D=16.0

x/D=4.0x/D=5.0

x/D=6.0x/D 7.0

x/D 7.0

_D 9.0XJD 10.0

4 5 6 7 8 9 10

x/D4 5 6 7 8 9 10

x/D


77

r/D=3.0

x/D=7.0x/D=8.0

x/D=9.0

_D=10.0_D=11.0

_D=12.0x/D=13.0 8

O

O

r/D=4.0

x/D=7.0

x/D=8.0

x/D=9.0:,dD=l 0.0

:,dD=l 1.0

_D=12.0x/D=13.0

7 8 9 10 11 12 13

x/D

riD=6.0

11

o8

@O

O

O

_D=7.0

_O=8.0

_O=9.0

_D=I0.0

_D=11.0

_D=12.0x/D=13.0

7 8 9 10 11 12 13

x/D

riD=8.0

:¢ID=I0.0

:¢ID=I1.0

_D=12.0_D=13.0

7 8 9 10 11 12 13

x/D7 8 9 10 11 12 13

x/O

r/D=10.0

_D=7.0

_D=8.0

_D=9.0

_D=I0.0

_D=11.0

_D=12.0x/D=13.0

"6

8

O

O

r/D=12.0

:¢ID=I0.0

:¢ID=I1.0

_D=12.0x/D=13.0

7 8 9 10 11 12 13

x/D

r/D=14.0

_o=9.o

_o=1o.o

_D=11.0

_D=12.0

x/D=13.0

7 8 9 10 11 12 13

x/D

t/D=16.0

x/D=?.0x/D=8.0

x/D=9.0x]D lO.O

X]D 11.o

_D 12.0x/D 13.0

7 8 9 10 11 12 13

x/D7 8 9 10 11 12 13

x/O


78

r/D=3.0

C

<9

OO

o'

o2

O

O4

13 14 15 16 17 18 19

x/D

r/D=6.0

x]D=13.0x]D=l 4.0

x]D=15.0

+'_0=16.0+ X/D= 17.0

+,_0=18.ox]D=l 8.0

+D=13.0x/D=14.0

+D=15.0+D=16.0

x/[):17.0

_D=18.0xfD=18.0

r/D=4.0

13 14 15 16 17 18 19

x/D

riD=8.0

=

O

0

_o_O

xZD=13.0

xZD=14.0

xZD=15.0xZD=l 6.0

x]D=I 7.0

_D=18.0xZD=l 8.0

xZD=13.0xZD=14.0

xZD=15.0xZD=l 6.0

xZD=17.0

_D=18.0xZD=l 8.0

13 14 15 16 17 18 19

x/D13 14 15 16 17 18 19

x/D

r/D=10.0

x]D=18.0x]D=l 4.0

x]D=15.0

+'_0=16.0

X/D=17.0

+,_0=18.ox]D=l 8.0

=

8

_m

O

O

r/D=12.0

xZD=13.0xID=I 4.0

xZD=15.0xZD=l 6.0

xID=I 7.0

_D=18.0xZD=l 8.0

C_3

:_e

O

_m

O

O

13 14 15 16 17 18 19

x/D

r/D=14.0

+D=13.0x/D=14.0

+D=15.0+D=16.0

x/[):17.0

xfD=18.0

xfD=18.0

13 14 15 16 17 18 19

x/D

r/D=16.0

xZD=13.0XID=I 4.0

xZD=15.0xJD 16.0

X/D 17.0

_o 18.oxJD 18.0

13 14 15 16 17 18 19

x/D13 14 15 16 17 18 19

x/D


79

° o

x/D=0.0

x/D=1.0x/D=2.0x/D=3.0

x/D=4.0

50 100 150

Azimuthal Separation (deg.)

x/D=5.0

x/D=6.0

x/D=7.0x/D=8.0

--=_ x/D=5.0, f=732 Hz

--_ x/D=6.0, f=732 Hz--,-- x/D=7.0,f_=732 Hz

x/D=8.0, f=732 Hz

00 50 100 150

Azimuthal Separation {deg.)

Figure 75: Azimuthal Correlations, Ma_=0.60

80

x/D=0.0

x/D=1.0x/D=2.0x/D=3.0

x/D=4.0x/D=0.0, f_=l 123 Hz

x/D=1.0, f_=l 123 Hz--I_ x/D=2.0, f_=1123 Hz

x/D=3.0, f_=l 123 Hzx/D=4.0, f_=l 123 Hz

50 100 150


0.1

00

x/D=5.0

x/D=6.0x/D=7.0

x/D=8.0

x/D=5.0, fo=1123 Hzx/D=6,0, Io=1123 Hzx/D=7.0, fo=1123 Hz

x/D=8.0, fo=1123 Hz

50 100 150


Figure 76: Azimuthal Correlations, Ma_=0.85

81

x/D=4.0x/D=3.0

x/D=2.0

x/D=1.0x/D=0.0

00 1 2 3 4 5

Azimuthal Mode Number

oQ.

£O

00 1 2 3 4 5


x/D=8.0

x/D=7.0

x/D=6.0x/D=5.0

Figure 77: Azimuthal Cross-Spectra, Mae=0.30

82

x/D=0.0

x/D=1.0x/D=2.0x/D=3.0

x/D=4.0

00 1 2 3 4 5


x/D=5.0

@ x/D=6.0x/D=7.0x/D=8.0

00 1 2 3 4 5



83

0.6

0.5

x/D=0.0

x/D=1.0x/D=2.0x/D=3.0

x/D=4.0

00 1 2 3 4 5


Q.

£O

oo 1 2 3 4 5


x/D=5.0

@ x/D=6.0x/D=7.0x/D=8.0


84

REPORT DOCUMENTATION PAGE FormApprovedOMB No. 0704_188

Public reporting burden for this collection of information isestimated to average 1 hour per response, including the time for reviewing instructions, searching existingdata sources,gathering and maintainingthe data needed, and completing and reviewingthe collection of information. Send comments regarding this burden estimate or any other aspect of thiscollection of information, including suggestions for reducing this burden, to Washington HeadquartersServices, Directoratefor Information Operationsand Reports, 1215 Jefferson DavisHighway,Suite 1204, Arlington, VA 22202-4302, and to the Office of Management and Budget, Paperwork Reduction Project (0704-0188), Washington, DC 20503.

1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE 3. REPORT TYPE AND DATES COVERED

May 1999 Technical Memorandum

5. FUNDING NUMBERS

522-32-31-02

4. TITLE AND SUBTITLE

Aeroacoustic Data for a High Reynolds Number Axisymmetric SubsonicJet

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

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

National Aeronautics and Space AdministrationWashington, DC 20546-0001

8. PERFORMING ORGANIZATIONREPORT NUMBER

L-17870

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,Lan.qley Research Center, Hampton VA.

12a. DISTRIBUTION/AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE

Unclassified-UnlimitedSubject Category 71 Distribution: StandardAvailability: NASA CASI (301) 621-0390

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 Pressure

17. SECURITY CLASSIFICATIONOF REPORT

Unclassified

18. SECURITY CLASSIFICATIONOF THIS PAGE

Unclassified

19. SECURITY CLASSIFICATIONOF ABSTRACT

Unclassified

15. NUMBER OF PAGES

89

16. PRICE CODE

A05

20. LIMITATION OF ABSTRACT

NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89)PrescribedbyANSI Std. Z39-18298-102

Aeroacoustic Data for a High Reynolds Number Axisymmetric ...Aeroacoustic Data for a High Reynolds...

Documents

Transcript of Aeroacoustic Data for a High Reynolds Number Axisymmetric ...Aeroacoustic Data for a High Reynolds...