Radiated Component of Nearfield Pressure Fluctuations

from Elliptical Jets

By K N. Murugan (Roll No: 06401004)

The experimental study reports the radiated component of nearfield pressure

fluctuations by jets emanating from an elliptical nozzle with Mach numbers of 0.5 and 0.8.

All these nozzles were made out by rapid prototype using ABS plastic material with same

equivalent exit diameter of 20 mm. Simultaneous measurements of both near and farfield

were carried out to estimate the radiated component of nearfield pressure fluctuations using

cross correlation technique. The nearfield and farfield microphone at 30 deg show strong

correlation as compared to microphone at farfield 90 deg. The strength of radiating

component from the near field pressure fluctuations to the farfield at 30 deg are observed to

be different in minor and major axis plane as compared to circular nozzle. This study

strongly suggests that an elliptical nozzle does have potential to redistribute the acoustic

energy along major and minor axis plane. The elliptical nozzle with V notch along minor

plane found to reduce the strength of radiated component in major plane as compared to

plain elliptical nozzle.

Nomenclature

AR = aspect ratio

a = major diameter

b = minor diameter

a0 = ambient sound

De = equivalent diameter

M = Mach number

t = time

pn = nearfield pressure fluctuations

pf = farfield pressure fluctuations

Rnf = cross-correlation coefficient between near and far field microphones

Rnn = cross-correlation coefficient between near and near field microphones

r0 = microphone locations from the jet center.

x = axial distance

y = minor axis

z = major axis

I. Introduction

The application of non-circular jets has improved large – and small scale mixing in low- and high speed flows,

and enhanced combustor performance, noise suppression, heat transfer and thrust vector control2. A range of non-

circular jets: including elliptical, rectangular, square, triangular and cruciform jets have been identified as an

efficient low cost passive device. Among these non-circular jets, the elliptical jet has the general flow characteristics

of two-dimensional plane and axisymmetric jets. There have been studies on the flow characteristics of elliptical

nozzles in the literature at low and higher Mach numbers. However, the noise characteristics of a jets issued by an

elliptical nozzle at high subsonic Mach number are very limited. This motivated to study the noise producing

mechanism and its propagation to the far field of the jet from elliptical nozzles. Also, the study has been extended to

understand the effect of V notches in an elliptical nozzle at Mach numbers of 0.8 and 0.5. The following section is

devoted to the brief background about the flow and noise characteristics of elliptical jets from perfectly expanded

nozzle.

The Crighton1

stability theory of elliptical jets was first to found interesting characteristics of elliptical jet along

major and minor axis plane. He suggests that the nature of instability along major and minor plane will have

potential benefit in noise reduction. This brought more attention towards the flow and noise characteristics of

elliptical jets at low and high Mach number. Husain and Hussain3 extensively studied the flow characteristics of an

elliptical jets issued from an aspect ratio (AR = major/minor) of 2 and 4 at low speed. This study reveals that the

unique nature of elliptical jet from the circular jet by means of different length scale, spread rate, different

momentum thickness around the nozzle azimuthal plane. The immediate downstream of the elliptical nozzle, the

vortex filament forms and continues to stretch and expand due the induced velocity along major and minor plane.

As the vortex filament move downstream, the major axis side’s rolls up and allow expanding in minor axis due to

induced velocity. As a result of this increase induced velocity, minor axis moves outwards. Consequently the major

become minor and minor become major and this process is termed as axis switching. This three dimensional

deformation was found to increase mass entrainment in elliptical jet as compared to circular jet.

Husain and Hussain7 further extended to this analysis on to investigate shear layer roll-up along major and minor

axis plane. It was reported that the shear layer roll –up are similar like circular jet and with an instability mode

frequency of St = 0.4 is termed as preferred column mode of instability. The azimuthal vortex deformation and

pairing process was the main mechanism to enhance the mixing in elliptical jets. Ho and Gutmark5

investigated the

coherent structure of the elliptic jet with a fifth order polynomial contoured nozzle of aspect ratio AR = 2 at exit

velocity of 25 m/s. They found that the entrainment rate of the elliptic jet is 55% higher than that circular jet with

same equivalent diameter in contrast with Zaman 11

elliptical jets. Also, it was noted smaller AR elliptical nozzle

mass entrainment are mainly due to self induction of vorticity present in the flow. However, this axis switching, and

mass entrainment are due to state of the initial boundary condition 11-13

.

Although there have been vast amount of study devoted to flow characteristics of elliptical jet as explained in earlier

section, very limited data are available in the open literature to address the noise characteristics of an elliptical jets at

high subsonic Mach number. Nearfield noise measurement from AR 2 nozzle with exit velocity of 25 m/s by

Gutmark and Ho5, Far field noise measurement from Bridge and Hussain

4at low Mach number of small and

moderate AR elliptical jets reveal that, the noise generated by the elliptical jets are due to large scale interaction. At

supersonic shock free elliptical jet measurement carried out by Kinze and Mclaughlin14

attributed that there were two

planes existing in an elliptical jet in which the acoustic energy distributed over different planes. Tam and Zaman15

was first to carry out the experimental study on noise characteristics of AR 3 elliptical jet at high-subsonic Mach

number of 0.82 and 0.93 with the aim of validating universal similarity theory in non-circular jets. They found

from the systematic far field noise measurements, changing circular to non-circular jets would not give any

significant of noise reduction at high subsonic Mach numbers and the radiated noise is quite independent of nozzle

geometries. It was stated that, this was in contrast to previous literature of non-circular jets which was found to

significant noise reduction at high subsonic Mach numbers 2, 10

.

Recently, Sharma and Murugan16

carried out near field noise measurement on elliptical Nozzle with AR 3 at exit

Mach number of 0.8. They showed that, the strength of near field pressure level is different in minor axis plane

compared with major axis plane, thereby, proper control employing either axis will suppress noise. Also, it has been

concluded that the noise source locations are independent of the major and minor axis plane from the direct

measurement and Arndt17

decay law for noise source location using single microphone.

Since, elliptical nozzle has the capability of increasing mixing due to complex strain field arises due to perimeter

stretching we expect that the corresponding noise reduction can be achieved. Although, there have been studies on

elliptical jets far field noise characteristics towards the noise suppression point of view and there have been divided

opinion among the researcher about the beneficial of an elliptical jet at high subsonic Mach numbers when

compared to circular jet. Therefore, the present study aims to carry out a systematic investigation to further

understand the noise producing mechanism in elliptical jets with varying aspect ratio at exit Mach number of 0.5 and

0.8. Simultaneous near and far field pressure fluctuations were measured to quantify the acoustic energy transferred

from the nearfield to farfield.

II. Concepts and Experimental Methods

A. Concepts

The methodology of cross correlation technique has been adopted to estimate the amount of acoustic energy

converted from the nearfield pressure fluctuations to the farfield19

. And also, the near field pressure fluctuations are

the combination of hydrodynamic and acoustic component 17, 19, and 20

. The far field pressure fluctuations are only

component of acoustic energy. The peaks cross –correlation directly related to similar energy content of signal

measured pressure at different transducers. However, this energy is the dominant large-scale structure energy which

is radiating as an acoustic field from the near field pressure fluctuations. However, the degree of peak cross

correlation coefficient will decide the nature of structure which is responsible for the noise radiation from the near

field.

Near field microphone senses both hydrodynamic and acoustics pressure fluctuations

Far field microphone senses only acoustic pressure fluctuations

The cross-correlation coefficient is defined as

2 2

( ) ( )( ) (1)

( ) ( )

n f

nf

n f

p t p tR

p t p t

This cross-correlation has implemented for elliptical jets which is expected to behave different nature in near

field as compared to far field. The quantification of radiated near field pressure from elliptical jets are compared to

the circular with same equivalent diameter nozzle.

B. Experimental Methods

A reservoir with volumetric capacity of 30 m3 and the maximum storage pressure of about 14 x 10

5 N/m

2

supplies compressed air to the plenum chamber of the test facility at a predetermined pressure through a 75 mm

diameter pressure regulating valve to ensure steady mass flow at a predetermined rate. The plenum chamber

measures 332 mm in diameter and 550 mm in length and has conical ends on both sides. At the free-end of the

plenum chamber, a 210 mm long pipe with 36 mm internal diameter facilitates mounting of different shape nozzles.

Figure 1 shows the solid model of the test nozzles smoothly transforming from a circular inlet of 36 mm

diameter (to match with the pipe) to an elliptical cross section at the exit over a length of about 150 mm. The

elliptical opening has an aspect ratio of 3 and 2 equivalent diameter, De, of 20 mm and the detailed dimensions are

given in Table.1. The nozzle was constructed out of ABS using rapid prototyping manufacturing process. The nozzle

wall thickness was tapered along its length to give a circumferentially uniform lip thickness of about 1 mm. A

computer controlled Dantec Dynamics traverse, having a traverse range of 610 mm along each of the three

orthogonal axes, was integrated with the test rig. The traverse moves at a speed of 25 mm/s and can be positioned at

a point with a resolution of 0.01 mm.

The present jet acoustic measurements were carried out in semi-anechoic facility. A 56 mm thick polyurethane

foam sheets were used to cover the ceiling and side walls to avoid sound reflections from other setup in the

laboratory. However, all the experiments were conducted during late night to minimize external noise and ambient

conditions. Figure 2 shows the simultaneous nearfield and farfield microphone arrangement for the present

investigation. In near field measurements one microphone was fixed at radial distance of 1.5 De from the jet center

and 0.25 De downstream from the nozzle exit plane. The second microphone was traversed along 7.013 deg. inclined

to outer edge of jet with respect to the radial distance of first microphone. Two microphones were kept at far field

at radial distance of 46 De facing nozzle exit plane with polar angle of 30 and 90 degree.

All the four microphones used in the present study are B&K 4939 free-field condenser microphones having 6.53

mm diameter were used in conjunction with B&K 2970 pre-amplifiers. The microphones were powered by two and

four channel NEXUS model 2690-0S2 and 2690-0S4 signal conditional amplifiers. Each microphone had an open

circuit sensitivity of 4.5mV/Pa and a flat frequency response from 4 Hz to 100 kHz. The microphones were

periodically calibrated using a B&K 4226 Multifunction acoustic calibrator. The output of conditional amplifier was

recorded by four channel National Instrument DAQ PCI-4462 card with Labview 7.1 software. The data were

sampled at the rate of 200 kHz with 8192 sample to have frequency band of 24.413 Hz.

The plenum chamber pressure was calculated with reference to the ambient pressure using isentropic flow

relations for a predetermined jet Mach number at the nozzle exit plane and was maintained by means of pressure

regulating valve. Pressures were registered by Pressure Systems transducers, PSI model 9116 with 16 channels.

Each of the pressure transducers is capable of measuring 103 kPa gauge pressure with an accuracy of ± 0.05% of

full scale. It uses NUSS software for acquiring the data at a scanning rate of 500 samples per second.

III. Results and Discussion

A. Far field pressure fluctuations

The comparison of farfield pressure spectra measured at radial distance of 46De, at polar angle of 30 deg and 90

deg were shown in Fig.3. It is observed that there is a little difference at lower and higher frequency in the spectra.

At polar angle of 30 deg, the characteristics frequency was about St (= fDe/Ue) 0.2, which is in good agreement with

the large scale coherent structure frequency15, 18

. At higher frequency, the spectra level changes are significant with

the nozzle geometry considered in the present study. At present, the discussion is underway for the reason behind

the change in spectral level at high frequency. It is interesting to note that, the spectra levels are redistributing along

the major and minor axis when we compared to the circular nozzle with same equivalent diameter. This change in

noise level was found insignificant when we look at the spectra at 90 deg to the jet axis. The effect of nozzle

geometry is not playing much role when sound propagates to higher angle with respect to jet axis and it was

observed irrespective of the nozzle plane.

B. Near field pressure fluctuations

Figure 4 shows comparison of pressure fluctuations registered by microphones along the jet edge at several

locations starting from the just downstream of the nozzle exit plane. With increasing distance from the nozzle exit,

the spectral peak is seen to gain amplitude from about 90 dB to nearly 115 dB. Moreover, it also shifts towards the

lower frequency. At Mach number 0.8, the spectra in the major axis plane of the AR3 nozzle, AR 2 nozzle, and

circular nozzle at x/De = 0.25 are seen to have harmonic tones. These harmonic tones are due to the initial shear

layer roll up and eventually it disappears at x/De = 3.75. Interestingly, these behaviors are not seen along the minor

axis plane. At present the reason for the same is under discussion. This is consistent even at the lower Mach number

of 0.5.

C. Cross correlation of near and farfield pressure fluctuations

The sound pressure fluctuations measured by a farfield microphones are due to the sum of the radiation from all

turbulent eddies distributed in the entire jet. The cross-correlation between near and far field pressure fluctuations

reveal the common energy between two microphones placed at both the field. Figures 5 -10 show the cross

correlation between near field microphone to far field microphone placed at 30 and 90 deg respectively. It is

observed that, the correlation coefficient Rnf varies with the downstream nearfield microphone. And also the time

delay varies with downstream locations. These observations are similar as recent work carried out by Viswanathan

et al.21

. Figures 11a-b show the comparison of maximum cross-correlation coefficients obtained from an individual

near and farfield correlation at exit Mach number of 0.8 and 0.5 for all nozzles. The expected behavior of maximum

cross correlation varies with nozzle downstream distance when the traversing nearfield microphone correlates with

far field microphone of 30o polar angle. The dominant maximum cross correlation invariantly sits in the axial

distance between 5 to 10 De. This region is known as the dominant noise source region. However, the effect of Mach

number is clearly seen in the Fig.14 a. The dominant region shifts towards nozzle exit plane within the mixing layer

region. It is important to point out here that the radiated components of elliptical jets clearly indicate the existence of

an element to change the farfield noise characteristics. Further, the minor axis plane shows higher energy as

compared to major axis plane for both plain and AR 3 with notched nozzle.

Figure 11c shows the correlation between nozzle exit plane and nozzle downstream distance. It is observed that the

maximum cross correlation reduces as the microphone separates axially and parallel to jet edge. The high frequency

component of nozzle exit plane loses its coherence as the nozzle downstream movement of microphone.

References 1Crichton, D.G., “Instability of an elliptic jet,” Journal of Fluid Mechanics, Vol. 59, 1973, pp. 665-672. 2Gutmark, E.J. and Grinstein,F.F., “Flow control with non-circular jet,” Annual Review of Fluid Mechanics, Vol. 31, 1999

pp. 239-272. 3Husain, H. S., and Hussain, A. K. M. F., “Controlled excitation of elliptic jets,” Physics of Fluids, Vol. 26, 1983, pp. 2763-

2765. 4Bridges, J.E and Hussain, A.K.M.F.,“Roles of initial condition and vortex pairing in jet noise,” Journal of Sound and

Vibration, Vol. 117, Issue 2, 8. 1987, pp. 289-311 5Ho, C.M. and Gutmark, E., “Vortex induction and mass entrainment in a small-aspect-ratio elliptic jet” Journal of Fluid

Mechanics, Vol. 179, 1987, pp. 383-405. 6Gutmark, E. and Ho C. M., “Near-field Pressure Fluctuations of an Elliptic Jet,” AIAA Journal, Vol.23, No.3, 1985, pp.354-

358. 7Husain, H. S. and Hussain, A. K. M. F., “Elliptic jets. Part 1. Characteristics of unexcited and excited jets,” Journal of Fluid

Mechanics,Vol. 208, 1989, pp. 257-320. 8 Gutmark , E.J., Schadow, K C, Wilson, K.J., and Biker, C. J. “Near Field pressure variation and flow characteristics in low

supersonic circular and elliptical jet,” Physics of Fluids, 31(9), 1988, pp.2524-2532. 9Baty, R. S., Seiner, J. M. and Ponton, M. K., “Instability of a supersonic shock free elliptic jet,” AIAA paper 90-3959. 10Ahuja, K.K., Manes J, Massey, K. 1990 “An evaluation of various concepts of reducing supersonic jet noise,” AIAA 90–

3982 11Zaman. K.M.B.Q., “Axis switching and spreading of an asymmetric jet: the role of coherent structure dynamics” Journal of

Fluid Mechanic, Vol. 316, 1996, pp. 1-27. 12Kinze, K.W., “Azimuthal mode measurement of elliptical jets,” Physics of Fluids 9, 1997, pp. 2000-2008. 13Zaman, K.B.M.Q, “Spreading characteristics of compressible jets from nozzles of various geometries,” Journal of Fluid

Mechanics, Vol. 383, 1999 pp 197-228.. 14Kinzie K W and Mclaughlin,D.K., “Aeroacoustics properties of supersonic elliptical jets,” Journal of Fluid Mechanics.

Vol. 395, 1999, pp. 1-28. 15Tam, C.K.W.,and Zaman, K.B.M.Q.,“Subsonic Jet noise from Non-axisymmetric and Tabbed Nozzle,” AIAA Journal, Vol.

38, No 4, 2000, pp.591-599. 16

Sharma, S.D., and Murugan, K. N., “Near Field Aeroacoustics of a Jet from Elliptical Nozzle at M=0.8,” AIAA/CEAS

Aeroacoustics Conference, AIAA paper No. 2010-3955, June 2010. 17Arndt,R., E, A,.D. F. Long, and M. N. Glauser, “The Proper Orthogonal Decomposition of Pressure Fluctuations

Surrounding a Turbulent Jet,” Journal of Fluid Mechanics, Vol. 340, 1997, pp. 1-33. 18Tam, C K W, Viswanathan,K., Ahuja, K. K., and Panda, J. “The sources of jet noise: experimental evidence,” Journal of

Fluid Mechanics, Vol. 615, 2008. Pp. 253-292. 19Lauendeau, E., Jordon, P., Delville, and Bonnet, J.-P., “Source-mechanism identification by nearfield-farfield pressure

correlations in subsonic jets,” International Journal of Aeroacoustics, Vol. 7, No.1, 2008, pp.41-68. 20Hall, J. W., Hall, A. M., Piner, J. T, and Glauser, M. N., “Cross-spectral analysis of the pressure in Mach 0.85 turbulent

jet,” AIAA Journal, Vol.47, 1, 2009, pp.54-59. 21Viswanathan, K., Underbrink, J. R., and Brusniak, L., “Space–Time Correlation Measurements in Near Fields of Jets”

AIAA Journal Vol. 49, No. 8, 2011, pp. 1577-1599.

Figure 1. Pictorial view of ABS Nozzle Models: a) Circular (AR 1), b) AR 2 elliptical, c) AR 3 elliptical, and

d) AR 3 elliptical with V notch.

Table 2 Nozzle dimensions

Nozzles Aspect

Ratio(AR)

Equivalent

Diameter

(mm)

Major axis

(mm)

Minor axis

(mm)

Exit Area

(mm2)

Mach

number

Circular 1 20 NA NA 314.16 0.8,and 0.5

Elliptical 2 20 28.28 14.14 314.13 0.8,and 0.5

Elliptical 3 20 34.62 11.54 314.13 0.8,and 0.5

Elliptical with

V notch

3

With V notch

20 34.62 11.54 314.13

0.8,and 0.5

V notch were made normal to major axis ( 3mm by 3mm)

x

y

z

(b) (a)

(c) (d)

x/De

r 0/D

e

-10 0 10 20 30 40 50 60 70 80-80

-70

-60

-50

-40

-30

-20

-10

0

10

Traversing microphone locations

Mic 2(

Mic 1 (

Near field Grid with 7.06o

Rmic = 46 D

e

Fixed microphone locations

Figure 2. Microphone arrangement for near and far field pressure measurements

Figure 3 Far field sound pressure level spectra at distance of 46 De from nozzle exit plane.

Frequency, Hz

SP

L,

dB

102

103

10440

50

60

70

80

90M = 0.8 = 90

o

Frequency, Hz

SP

L,

dB

102

103

10440

50

60

70

80

90

Circular Nozzle

AR 3 V notch minor

AR 3 V notch major

AR 3 minor

AR 3 major

AR 2 minor

AR 2 major

M = 0.8 = 30o

SP

L,

dB

Frequency, Hz

60

70

80

90

100

110

120

x/De

= 0.25

M = 0.8

60

70

80

90

100

110

120

x/De

= 3.75

102

103

10460

70

80

90

100

110

120

x/De= 6.75

SP

L,

dB

102

103

10460

70

80

90

100

110

120

Circular Nozzle

AR 3 Vnotch minor

AR 3 Vnotch major

AR 3 minor

AR 3 major

AR 2 minor

AR2 major

x/De

= 9.75

Figure 4 Streamwise pressure evolutions at jet downstream

, ms

Rnf

0 1 2 3

-0.2

-0.1

0

0.1

0.2

x/De=0.25

x/De=1.75

x/De=2.75

x/De=3.75

x/De=4.75

x/De=5.75

x/De=6.75

x/De=7.75

x/De=8.75

x/De=9.75

x/De=10.75

x/De=11.75

x/De=12.75

x/De=13.75

x/De=14.75

x/De=15.75

x/De=16.75

M= 0.8

Circular Nozzle

, ms

Rnf

0 1 2 3

-0.2

-0.1

0

0.1

0.2

x/De=0.25

x/De=1.75

x/De=2.75

x/De=3.75

x/De=4.75

x/De=5.75

x/De=6.75

x/De=7.75

x/De=8.75

x/De=9.75

x/De=10.75

x/De=11.75

x/De=12.75

x/De=13.75

x/De=14.75

x/De=15.75

x/De=16.75

M= 0.8

Circular Nozzle

Figure 5. Near and far field cross correlation coefficient for circular nozzle with far field microphone at 30o

and 90o.

, ms

Rnf

0 1 2 3

-0.2

-0.1

0

0.1

0.2

x/De=0.25

x/De=1.75

x/De=2.75

x/De=3.75

x/De=4.75

x/De=5.75

x/De=6.75

x/De=7.75

x/De=8.75

x/De=9.75

x/De=10.75

x/De=11.75

x/De=12.75

x/De=13.75

x/De=14.75

x/De=15.75

x/De=16.75

M= 0.8

AR 2 major plane

, ms

Rnf

0 1 2 3

-0.2

-0.1

0

0.1

0.2

x/De=0.25

x/De=1.75

x/De=2.75

x/De=3.75

x/De=4.75

x/De=5.75

x/De=6.75

x/De=7.75

x/De=8.75

x/De=9.75

x/De=10.75

x/De=11.75

x/De=12.75

x/De=13.75

x/De=14.75

x/De=15.75

x/De=16.75

M= 0.8

AR 2 major plane

Figure 5.Near and far field cross correlation coefficient for AR2 elliptical nozzle major plane with far field

microphone at 30o and 90

o.

, ms

Rnf

0 1 2 3

-0.2

-0.1

0

0.1

0.2

x/De=0.25

x/De=1.75

x/De=2.75

x/De=3.75

x/De=4.75

x/De=5.75

x/De=6.75

x/De=7.75

x/De=8.75

x/De=9.75

x/De=10.75

x/De=11.75

x/De=12.75

x/De=13.75

x/De=14.75

x/De=15.75

x/De=16.75

M= 0.8

AR 2 minor plane

, ms

Rnf

0 1 2 3

-0.2

-0.1

0

0.1

0.2

x/De=0.25

x/De=1.75

x/De=2.75

x/De=3.75

x/De=4.75

x/De=5.75

x/De=6.75

x/De=7.75

x/De=8.75

x/De=9.75

x/De=10.75

x/De=11.75

x/De=12.75

x/De=13.75

x/De=14.75

x/De=15.75

x/De=16.75

M= 0.8

AR 2 minor plane

Figure 6..Near and far field cross correlation coefficient for AR2 elliptical nozzle minor plane with far field

microphone at 30o and 90

o.

, ms

Rnf

0 1 2 3

-0.2

-0.1

0

0.1

0.2

x/De=0.25

x/De=1.75

x/De=2.75

x/De=3.75

x/De=4.75

x/De=5.75

x/De=6.75

x/De=7.75

x/De=8.75

x/De=9.75

x/De=10.75

x/De=11.75

x/De=12.75

x/De=13.75

x/De=14.75

x/De=15.75

x/De=16.75

M= 0.8

AR 3 major plane

, ms

Rnf

0 1 2 3

-0.2

-0.1

0

0.1

0.2

x/De=0.25

x/De=1.75

x/De=2.75

x/De=3.75

x/De=4.75

x/De=5.75

x/De=6.75

x/De=7.75

x/De=8.75

x/De=9.75

x/De=10.75

x/De=11.75

x/De=12.75

x/De=13.75

x/De=14.75

x/De=15.75

x/De=16.75

M= 0.8

AR 3 major plane

Figure 7. Near and far field cross correlation coefficient for AR3 elliptical nozzle major plane with far field

microphone at 30o and 90

o.

, ms

Rnf

0 1 2 3

-0.2

-0.1

0

0.1

0.2

x/De=0.25

x/De=1.75

x/De=2.75

x/De=3.75

x/De=4.75

x/De=5.75

x/De=6.75

x/De=7.75

x/De=8.75

x/De=9.75

x/De=10.75

x/De=11.75

x/De=12.75

x/De=13.75

x/De=14.75

x/De=15.75

x/De=16.75

M= 0.8

AR 3 minor plane

, ms

Rnf

0 1 2 3

-0.2

-0.1

0

0.1

0.2

x/De=0.25

x/De=1.75

x/De=2.75

x/De=3.75

x/De=4.75

x/De=5.75

x/De=6.75

x/De=7.75

x/De=8.75

x/De=9.75

x/De=10.75

x/De=11.75

x/De=12.75

x/De=13.75

x/De=14.75

x/De=15.75

x/De=16.75

M= 0.8

AR 3 minor plane

Figure 8.Near and far field cross correlation coefficient for AR3 elliptical nozzle minor plane with far field

microphone at 30o and 90

o.

, ms

Rnf

0 1 2 3

-0.2

-0.1

0

0.1

0.2

x/De=0.25

x/De=1.75

x/De=2.75

x/De=3.75

x/De=4.75

x/De=5.75

x/De=6.75

x/De=7.75

x/De=8.75

x/De=9.75

x/De=10.75

x/De=11.75

x/De=12.75

x/De=13.75

x/De=14.75

x/De=15.75

x/De=16.75

M= 0.8

AR 3 V notch major plane

, ms

Rnf

0 1 2 3

-0.2

-0.1

0

0.1

0.2

x/De=0.25

x/De=1.75

x/De=2.75

x/De=3.75

x/De=4.75

x/De=5.75

x/De=6.75

x/De=7.75

x/De=8.75

x/De=9.75

x/De=10.75

x/De=11.75

x/De=12.75

x/De=13.75

x/De=14.75

x/De=15.75

x/De=16.75

M= 0.8

AR 3 Vnotch major plane

Figure 9.Near and far field cross correlation coefficient for AR3 elliptical nozzle with notch along major

plane with far field microphone at 30o and 90

o.

, ms

Rnf

0 1 2 3

-0.2

-0.1

0

0.1

0.2

x/De=0.25

x/De=1.75

x/De=2.75

x/De=3.75

x/De=4.75

x/De=5.75

x/De=6.75

x/De=7.75

x/De=8.75

x/De=9.75

x/De=10.75

x/De=11.75

x/De=12.75

x/De=13.75

x/De=14.75

x/De=15.75

x/De=16.75

M= 0.8

AR 3 V notch minor plane

, ms

Rnf

0 1 2 3

-0.2

-0.1

0

0.1

0.2

x/De=0.25

x/De=1.75

x/De=2.75

x/De=3.75

x/De=4.75

x/De=5.75

x/De=6.75

x/De=7.75

x/De=8.75

x/De=9.75

x/De=10.75

x/De=11.75

x/De=12.75

x/De=13.75

x/De=14.75

x/De=15.75

x/De=16.75

M= 0.8

AR 3 V notchminor plane

Figure 10.Near and far field cross correlation coefficient for AR3 elliptical nozzle with notch along minor

plane with far field microphone at 30o and 90

o.

x/De

0 5 10 15 20

Circular Nozzle

AR3 V notch minor

AR3 V notch major

AR 3 minor

AR 3 major

AR2 minor

AR2 major

M = 0.5

x/De

Max

.C

ross

Co

rrel

atio

n

0 5 10 15 200

0.1

0.2

M = 0.8

(a)

x/De

0 5 10 15 20

Circular Nozzle

AR3 V notch minor

AR3 V notch major

AR 3 minor

AR 3 major

AR2 minor

AR2 major

M = 0.5

x/De

Max

.C

ross

Co

rrel

atio

n

0 5 10 15 200

0.1

0.2

M = 0.8

(b)

x/De

0 5 10 15 20

Circular Nozzle

AR3 V notch minor

AR3 V notch major

AR 3 minor

AR 3 major

AR2 minor

AR2 major

M = 0.5

x/De

Max

.C

ross

Co

rrel

atio

n

0 5 10 15 200

0.1

0.2

0.3

0.4M = 0.8

(c)

Figure 11. Comparison of peak cross-correlation between near and far field pressure fluctuations: a) far

field reference microphone at 30o. b) Far field microphone at and 90

o c) reference microphone at x/De=0.25.