NAS.i\ Contractor Report 3966 

Jet Shielding of Jet Noise 

John C. Simonich, Roy K. Amiet, 

and Robert H. Schlinker 

CONTRACT NAS1-16689 

APRIL 1986 

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11111111111111111111111/111111111111111111111 

NF02277 

NASA Contractor Report 3966 

Jet Shielding of Jet Noise 

John C. Simonich, Roy K. Amiet, 

and Robert H. Schlinker 

United Technologies Research Center 

East Hartford, Connecticut 

Prepared for 

Langley Research Center 

under Contract NASl-16689 

NI\S/\ 

National Aeronautics 

and Space Administration 

Scientific and Technical 

Information Branch 

1986 

Jet Shielding of Jet Noise 

TABLE OF CONTENTS 

SUMMARY . • • 

INTRODUCTION 

LIST OF SYMBOLS AND NOMENCLATURE 

PREVIOUS INVESTIGATIONS • 

Experimental Studies 

Constraints of Previous Experimental Studies . 

Theoretical Studies .••.•...•. . . . 

PRESENT INVESTIGATION 

Objective ...•.. 

Experimental Approach 

Analytical Approach • . • • 

THEORETICAL DEVELOPMENT OF THE JET SHIELDING ANALYSIS 

Page 

1 

3 

5 

9 

9 

12 

12 

15 

15 

15 

16 

17 

The Shielding Mechanism and Selection of the Analytical Approach 17 

Review of Previous Analysis and Experimental Confirmation 15 

Analysis . • . . • . • 20 

Application of Theory • • . • 27 

DESCRIPTION OF EXPERIMENT . • 

Acoustic Research Tunnel • 

Experimental Arrangement . 

Instrumentation . . . • • 

Test Program ...• 

Acoustic and Aerodynamic Qualification Tests 

iii 

31 

31 

31 

33 

37 

39 
TABLE OF CONTENTS (Cont'd) 

AERODYNAMIC MEASUREMENTS 

Objective and Approach 

Mach Number Distributions 

Total Temperature Distributions 

Supersonic Flow 

DATA ACQUISITION AND DATA REDUCTION PROCEDURE • 

General Features of Noise Reduction Due to Jet Shielding . 

Quantitative Definition of Shielding Effect .. . • . 

Acoustic Data Acquisition and Data Reduction Procedure • 

EXPERIMENTAL ASSESSMENT OF DUAL JET SHIELDING 

Objective 

Spectrum Dependence on Isolated Parameters • 

Azimuthal and Polar Directivity 

Sound Pressure Level Contours 

Differential Power Spectrum 

CONCLUSIONS . . • 

APPENDIX A - REVIEW OF PREVIOUS EXPERIMENTAL RESEARCH 

APPENDIX B - CORRECTIONS TO ACOUSTIC DATA . . . . 

APPENDIX C - SYNTHESIZATION OF THE AVERAGE SINGLE JET 

RADIATION FIELD • • . . . . . . . . 

APPENDIX D - DIFFERENTIAL POWER SPECTRUM 

REFERENCES. 

FIGURES 

iv 

, . 

Page 

43 

43 

43 

45 

45 

47 

47 

49 

50 

53 

53 

53 

58 

73 

74 

77 

81 

85 

87 

89 

91 
SUMMARY 

An experimental and theoretical study was conducted to develop a 

validated first principle analysis for predicting the jet noise reduction 

achieved by shielding one jet exhaust flow with a second, closely spaced, 

identical jet flow. A generalized dual jet noise analytical model was formulated in which the acoustic radiation from a source jet propagates through the 

velocity and temperature discontinuity of the adjacent shielding jet. Input 

variables to the prediction procedure include jet Mach number, spacing, temperature, diameter, and source frequency. Refraction, diffraction, and reflection effects, which control the dual jet directivity pattern, are incorporated 

in the theory. The analysis calculates the difference in sound pressure level 

between the dual jet configuration and the radiation field based on superimposing two independent jet noise directivity patterns. 

Assessment of the theory involved conducting dual jet noise and single 

jet noise experiments to establish the difference in directivity pattern due 

to jet shielding. The experiments were conducted with two 4.45 cm diameter 

parallel jets installed on the centerline of the United Technologies open jet 

Acoustic Research Tunnel. Microphones located in a fixed polar array measured 

the radiated noise as the source jet slowly rotated about the shielding jet, 

thereby, providing a complete directivity pattern measurement on a hemispherical surface surrounding the dual jet system. Converging and converging/ 

diverging nozzle sets were used to provide subsonic and supersonic shock-free 

flows. Finally, detailed Mach number and temperature surveys were conducted 

to determine which jet spacing conditions altered the individual acoustic 

source regions due to aerodynamic interference of the jet flows. 

Jet shielding was found experimentally to reduce noise levels in the 

common plane of the dual jet system relative to the noise generated by two 

independent jets. The shielded region extends to observer angles on either 

side of the dual jet common plane. Outside of this region an increase of 

noise occurs due to the redirection of sound rays from the shielded region in 

addition to acoustic reflections between the adjacent flow fields. A balance 

exists between the noise reduction and noise increase existing over a 

hypothetical sphere surrounding the dual jet system. This balance confirms 

that acoustic energy is conserved by the acoustic wavefront-flow field 

interaction phenomena which control the dual jet directivity pattern. It also 

demonstrates that a beneficial noise reduction at one observer angle is 

negated by a noise penalty at other observer angles. 

Jet shielding effectiveness increases with increasing Helmholtz number. 

Shielding is most effective for Strouhal numbers above the jet noise spectrum 

peak. Increasing subsonic Mach number enhances shielding and shifts the onset 

of shielding to Strouhal numbers below the spectrum peak. Further increases 
2 

to supersonic Mach number provide little improvement in shielding. For noninterfering dual jet flows, jet spacing has little affect on noise radiation 

in the common plane of the jet system. However, for small jet spacing 

resulting in the aerodynamic merger of the jet flows, sound pressure levels 

increase due to changes in the acoustic source region downstream of the jet 

merger. Changes of jet temperature were found to have a minimal effect on the 

dual jet directivity pattern. The maximum attainable noise reduction for two 

adjacent non-interfering jets with identical operating conditions is 3 dB. 

This limit is based on complete masking of one jet when the observer is in the 

common plane of the dual jet system. 

Measured dual jet shielding effects were successfully modelled by the 

first principles theoretical model. Jet noise reduction in the common plane 

of the dual jet system was well predicted while directivity patterns outside 

the common plane were also calculated. Predicted dependence on Mach number, 

jet spacing, temperature, and source frequency were verified experimentally. 

The analysis, therefore, successfully models changes in the acoustic 

directivity pattern generated by two adjacent, random-noise, distributedsource jets. 
INTRODUCTION 

Although current jet aircraft are considerably quieter than their 

predecessors, the environmental impact of aircraft noise near airports continues to be a problem. Many novel techniques have been proposed to reduce 

the various components of aircraft noise. A recently proposed technique for 

reducing turbo-fan jet exhaust noise is to use one jet, of a closely spaced 

dual jet arrangement, to shield the sound produced by the second jet exhaust. 

Noise reductions of from 3 to 6 dB appear to be possible with this arrangement 

based on previous experimental and theoretical studies. 

The dual jet shielding concept is illustrated in Figure 1. The sound 

radiated from the source jet is modified by interacting with the fluid discontinuity of the adjacent shielding jet through which the sound is transmitted. 

The shielding jet serves to refract, reflect, diffract, scatter, and attentuate the source jet noise radiation. These effects can alter the acoustic 

source directivity pattern with the final perceived directivity no longer 

being the superposition of the two independent jet noise radiation fields. 

The lack of a firm understanding of the potential noise reduction at a fixed 

radiation angle due to these propagation effects created a clear need for a 

fundamental study of the jet-by-jet shielding effect. 

An understanding of the jet shielding phenomenon is also critical to the 

use of aircraft noise contours for evaluating and controlling airport noise 

levels. Presently, noise predictions superimpose the sound field of each 

engine to obtain the total turbo-fan engine noise level at the sideline 

observer station shown in Figure 2. However, several factors involving both 

propagation path modifications and noise redirection influence the sound pressure level sensed by the observer. One of the postulated mechanisms is the 

jet shielding phenomenon. Thus, failure to adequately account for the potential noise reduction due to jet shielding on current side-by-side engine 

geometries could result in erroneous noise contour predictions. The jet 

shielding mechanism addressed here is therefore considered to be potentially 

important for aircraft noise control. 

An investigation of the potential noise reduction from dual jet shielding 

also contributes to the understanding and improvement of the jet noise 

suppression available from multitube nozzles. In this case, the dual jet 

geometry provides a fundamental approach for isolating the noise reduction 

achieved by two adjacent multitube nozzles. Once the noise reduction mechanism is quantified, the most promising multinozzle geometry and operating 

conditions can be optimally combined into a new suppressor design. 

The present study was also stimulated by the need to optimize engine 

locations on future aircraft for the purpose of reducing jet exhaust noise. 

Based on the success of the shielding concept, optimal mounting geometries 

3 
4 

could be selected to provide the greatest noise reduction below the flight 

path. In addition, current supersonic cruise vehicle technology evaluation 

studies with over/under the wing engine configurations would benefit from an 

understanding of the shielding phenomenon. 

In summary, a need existed for the development of an experimentally 

validated jet shielding analyses in which the jet velocity, temperature, 

diameter, and spacing were input parameters. The present study was directed 

towards these needs. 

The authors wish to acknowledge helpful discussions with J. C. Yu (NASA) 

and R. W. Paterson (UTRC) relative to interpretation and assessment of the 

experimental and analytical results. 
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LIST OF SYMBOLS AND NOMENCLATURE 

Radius of shielding jet 

Amplitudes of waves reflected from and transmitted through shear 

layer 

Sound speeds outside and inside shielding jet 

Jet diameter 

Frequency, Hz 

Fourier transform of solution; see Eq. (21) 

Hankel function of the second kind of order m 

Bessel function of first kind of order m 

Wavenumber (oo/c o) outside shielding jet, see Eq. (7) 

Wavenumber (oo/c l ) inside shielding jet, see Eq. (7) 

Wavenumber along z direction 

Stationary phase point; see Eq. (26) 

Wavenumbers defined in Eq. (7) 

Wavenumbes Ko and Kl evaluated at stationary phase point 

Helmholtz number 

Jet core length, jet merging length 

Local Mach number, also jet exit Mach number 

Eddy convection Mach Number 

Acoustic perturbation pressure 

Ambient pressure 

Total power spectral density with shielding operative. 

5 
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Mean static pressure 

Total power spectral density for two independent jets 

Distance of far-field observer from origin; see Fig. 5 

Also, radial displacement in aerodynamic measurements 

Distances of source and observer from jet axis, respectively; See 

Fig. 5 

Lateral jet separation distance 

Strouhal Number = fD/Vj 

Sound Pressue Level 

Parameter defined by Eq. (19) 

Ambient temperature 

Total temperature 

Static temperature 

Local streamwise jet velocity component 

Fluid velocity outside and inside shielding jet respectively for 

observer moving with trace speed 

Jet exit velocity 

Trace velocity of wave along shear layer 

Cartesian coordinate system defined in Fig. 5 

Axial displacement 

Source location on x axis 

Amplitude factor defined in Eq. (9), also weighting factor in 

expression for OASPL in Eq. (B-1) 

Jet expansion ratio = 1M2-1 

Dirac delta function 

1 if m = 0; 2 if m '" 0 
e 

6 

Po, Pl 

<P 

1/1 

1/1 

III 

Theoretical azimuthal angle of far-field observer; 6 = 0° for 

observer in same plane as source and axis of shielding jet (See 

Fig. 5) 

Experimental azimuthal angle of far field observer; 6 = 90° for 

observer in same plane as source and axis of shielding jet (See 

Fig. 7) 

Densities outside and inside shielding jet respectively 

Velocity potential function 

Theoretical polar angle of far field observer, measured from a 

line through the source and parallel to jet axis (See Fig. 5) 

Experimental polar angle measured from shielding jet axis to 

observer or microphone (See Fig. 7) 

Circular frequency, radians 

7 

PREVIOUS INVESTIGATIONS 

Previous studies demonstrated that an adjacent jet can provide an 

acoustic shield to suppress the noise from a source jet. The following 

discussion presents the relevant experimental and analytical state-of-the-art 

which formed the basis for development of the current program. 

Experimental Studies 

Early work on noise reduction of jet engines involved designing noise 

suppression nozzles. A multitube nozzle arrangement was used to break one 

large jet into multiple small jets. The observed noise reduction of this 

arrangement was initially thought to be due to such effects as rapid mixing, 

reduced shear, shifts of peak noise to higher frequencies and shock interactions. Progressively, researchers postulated that jet shielding might be 

partially responsible for noise reduction in this multi-element nozzle 

arrangement. 

In an effort to define the noise reduction, the simplest combination was 

selected, namely two parallel jets. The earliest example is the study by 

Greatrex and Brown in 1958 (ref. 1). Although their data show approximately a 

3 to 4 dB difference in noise between ASPL (9 = 90°) and ASPL (9 = 180°) the 

authors indicate an uncertainty in the reliability of the measurements. The 

noise reduction benefit appeared to decrease with increasing spacing as SiD 

increased from 1.2 to 1.4. 

A study of the effects of jet shielding on two jets of unequal S1ze was 

carried out by Morris, Richarz and Ribner in 1973 (ref. 2). A small secondary 

jet was mounted at an angle to the main jet so as to eliminate any aerodynamic 

interference and hence avoid degradation of the main jet performance. The 

objective was to alter the directivity pattern of the main jet by refracting, 

reflecting, and diffracting the sound field using the secondary jet. They 

found a maximum reduction of 5 dB. The attenuation increased for both 

increasing secondary jet velocities and temperatures. 

A study of the shielding effect of multi-tube nozzles was done by Gray, 

Gutierrez and Walker in 1973 (ref. 3). They measured the noise produced from 

37 tube nozzles and single tube nozzles using both 1/4 scale and full scale 

configurations. At low velocities, no shielding was detected. However, at 

transonic velocities and above, a nearly complete shielding was observed. 

As part of a larger study on jet noise reduction from shrouded multinozzles, Goethert and Borchers (ref. 4) reported on twin jet experiments 

9 
10 

conducted in 1974. For spacing to diameter ratios between 1.2 to 2.0, they 

found that the total sound power was approximately 1 dB lower than the noise 

produced by two independent jets. At larger spacings, however, only a .1 to 

.2 dB reduction was noted. 

A study of acoustic shielding in annular jets was performed by Ahuja and 

Dosanjh in 1977 (ref. 6). They examined the effect of shielding a noisy, 

circular inner jet with an annular outer jet. With the outer jet at the same 

temperature as the inner jet, little shielding benefit was observed. However, 

by heating the outer jet a 10 dB reduction could be obtained. A true 

reduction in acoustic power levels was observed, as opposed to a redistribution of acoustic energy by refraction. The shielding effect was seen at 

all angles, but was stronger at higher frequencies. 

A study of the acoustic shielding from twin, round heated jets was 

presented in 1977 by Bhat (ref. 7). In his test, the effects of spacing, 

dissimilar velocity, dissimilar jet size, and longitudinal stagger on acoustic 

shielding were examined. Sound pressure measurements were made about an arc 

only in the common plane of the dual jet system. For equal size jets with no 

longitudinal stagger, up to a 5 dB difference between the twin jets and a 

single jet incremented by 3 dB was noted at 40° from the jet axis. At 90° 

from the jet axis, no effect was observed. Although the range of lateral jet 

spacing tested was small (from SID = 1.12 to 2.0) an increase in shielding 

effect was observed at the closest spacing. The importance of acoustic source 

changes due to aerodynamic interactions at these close spacings was not 

evaluated. An increase in shielding effect was also noted for an increase in 

streamwise stagger. 

An acoustic study of heated twin jets was performed by Kantola in 1977 

(refs. 7, 8). Sound pressure measurements were made in an arc around the jet 

nozzle exit at only 3 polar angles, 0°,45°, and 90° from the dual jet plane. 

Lateral jet spacing, velocity and temperature were varied. Kantola found that 

as the spacing increased from SID = 1.33 to 3.0, the measured overall power 

level (OAPWL) decreased in the plane of the jets. No additional effect was 

noted for larger spacings. In the loud plane, 90° from the plane of the jets, 

OAPWL varied from less than the single jet noise level incremented by 3 dB 

level to greater than the single jet level incremented by 3 dB. Kantola 

interpreted this to indicate mixing suppression and additional noise 

generation respectively. At frequencies below about 2 kHz, little difference 

was noted between the load and the quiet measurements planes. At higher 

frequencies, however, over 8 dB of difference was noted for a microphone at 

30° from the jet axis. Even for the 90° off axis microphone, up to 2 dB 

difference was seen. The frequency at the onset of shielding was seen to 

decrease as the spacing increased. Kantola attributed this to an internozzle 

layer of cold fluid which exists between the jets and extends further 

downstream as the spacing increases. As the layer extends further downstream, 
the lower frequency jet noise sources are shielded. It was also noted that 

the shielding. It was also noted that the shielding effect increased with jet 

velocity up to sonic conditions. 

Several other model scale and full scale experimental studies have been 

conducted to confirm the shielding phenomena although the geometries involved 

did not correspond to the engineering problem addressed here. Two specific 

investigations are important to the present investigation. 

First, Shivashankara and Bhat (ref. 10) conducted a study of the noise 

reduction by two parallel jets with significantly unequal flows. It was 

observed that the sound of the high velocity (loud) jet could be shielded by 

the low velocity (quiet) jet by as much as 7.5 dB OASPL. No benefit was 

perceived at azimuthal angles greater than 75 0 from the plane of the jets. 

Since these effects occurred at small jet spacings (lateral spacing to 

diameter ratio of 1.5 to 1.6) it was necessary to evaluate the acoustic source 

changes due to aerodynamic interaction of the jet flows. By comparing velocity profiles obtained with single jet versus the dual jet configuration at a 

streamwise station of X/D = 5, it was reported that no significant mean flow 

interaction occurred. However, the present authors believe that more sensitive criteria are needed to determine jet interference effects. In addition 

acoustic source regions upstream of X/D = 5 contribute primarily to the high 

frequency content of the jet noise spectrum. In contrast, the spectrum peak 

is controlled by acoustic source regions downstream of X/D = 5 where the 

present authors feel aerodynamic interactions can occur. 

While the general results of reference 10 suggest that dissimilar jets 

should also be investigated, current and future aircraft engine operations 

continue to be based on similar flows with equal thrust from each engine. 

Thus, the present study concentrated on the dual jet shielding by similar 

flows. However, the dissimilar jet concept represents a further improvement 

in jet shielding noise reduction technology. 

A second important experimental st"udy was conducted by Yu and Fratello 

(ref. 11) to isolate the acoustic effect of the jet-by-jet shielding phenomenon from potential source changes due to the dual jet flow field interaction. 

This was accomplished by using a point source of sound in conjunction with the 

shielding jet. Different discrete tones and also 1/3 octave band random noise 

were emitted from a small acoustic source. Room temperature air and helium 

were used as the working fluids for the jet. The helium was used to simulate 

heating at a high temperature ratio. Since there was only one jet, no aerodynamic interaction was present, and the effect of acoustic shielding alone 

could be studied. Yu and Fratello found that the peak value of shielding, as 

measured by the differential power level between acoustic source only and both 

acoustic source and jet, increased with frequency, jet velocity, jet heating, 

and longitudinal source position. No trends were identified for the effect of 

11 
12 

lateral spacing on acoustic shielding Helmholtz number greater than 2. Qualitative comparisons with Kantola (ref. 8) and Bhat (ref. 7) confirmed the 

trends reported in previous dual jet studies in addition to the present 

study. 

The following general observations were presented in various combinations 

1n the above described investigations: 1) as much as a 5 dB decrease in noise 

is possible at a given operating condition; 2) the shielding effect generally 

decreases as the lateral spacing between the twin jets increases; 3) little 

shielding benefit is provided at low jet velocities and the effect increases 

with velocity; 4) no shielding benefit is present at low frequencies; 5) a 

larger shielding effect occurs when the jets are heated. 

Constraints of Previous Experimental Studies 

Although general conclusions obtained from earlier studies demonstrated 

the feasibility of the shielding concept, there were limitations in the scope 

and details of the experimental assessment. For example, measurements were 

often confined to one or two azimuthal angles, e (see Fig. 2), near the common 

plane of the dual jet system where the noise reduction was most effective. 

Consequently, noise penalties due to redirection of sound into other azimuthal 

planes was not determined. In addition, it is possible that for the close jet 

spacings used in many of the studies the acoustic source field was modified by 

premature merging of the jets. In this case, the two jets no longer functioned as independent source regions at large downstream distances where the 

low frequency jet noise sources are located. Finally, previous experiments 

were often restricted to cold flows while in other cases only a single jet 

velocity was tested. 

A final constraint of previous studies was the use of convergent nozzles 

employed in subsonic experiments to extend the velocity dependence measurements into the supersonic operating regime. The generation of shock noise and 

screech by the convergent nozzles introduces new noise mechanisms which 

presumably alter the relative acoustic source distribution on the jet axis. 

Furthermore, the rapid expansion of the jet plumes due to the shock structure 

at the jet exit planes possibly results in premature merging of the jets and 

consequent alteration of the jet noise source region. These acoustic source 

changes complicate the interpretation of the acoustic shielding effect as the 

jet velocity becomes supersonic. 

Theoretical Studies 

The jet shielding analytical model is based on calculating the sound 

transmission across a shear layer. Early studies of the phenomenon utilized 
simplified geometries in their analytical models to facilitate assessment of 

the concept. For exrunple, the studies by Cowan and Crouch (ref. 12) and 

Kantola (ref. 9) employ the theoretical model of Yeh (ref. 13) for sound 

transmission through two parallel shear layers. The work of Yeh is a minor 

extension of the work of Miles (ref. 14) and Ribner (ref. 15) since it uses 

two shear layers in place of the single shear layer model in references 14 and 

15. The model developed by Yeh is highly simplified and restricted when 

applied to the present problem since it treats both shear layers as plane and 

parallel. It also considers only rays contained in the plane which is normal 

to the shear layers and aligned with the jet velocity vector. Another limitation is that the transmitted ray propagates in the same direction as the 

original ray, eliminating any focusing effects which might occur in the cylindrical jet geometry addressed in the present study. Finally, the plane shear 

layer model of Yeh assumes that the wavelength of the incident ray is much 

smaller than the jet diameter. 

The analysis of Parthasarathy, Cuffel and Massier (ref. 16) uses the 

plane shear layer analysis of Ribner which they apply at the crossing point of 

each shear layer. In this analysis, multiple reflections inside the shielding 

jet are assumed not to occur; that is, once a ray is reflected, it is assumed 

to propagate outwards and the acoustic energy is lost. This model is accurate 

only if the reflection coefficient is small. For example, if the furthest 

shear layer (of the shielding jet) from the noise source reflected 90 percent 

of the energy incident on it, 90 percent of this reflected energy or 81 percent of the original incident energy would again be reflected in the direction 

of the sideline observer. Neglecting these multiple reflections could easily 

lead to an overestimate of the jet noise shielding effect. 

One of the first calculations specifically directed toward the jet 

shielding geometry was developed by Gerhold (refs. 17, 18). The boundary conditions of the continuity of pressure and displacement are identical to those 

used in earlier shear layer refraction studies. (A detailed review of the 

impact of the earlier shear layer refraction studies is given in the section 

titled "Theoretical Development of the Jet Shielding Analysis"). The source 

field modeled by Gerhold was expressed in terms of plane waves incident on a 

cylindrical shear layer. Qualitative confirmation of the analysis was presented in the study of Yu and Fratello (ref. 11) which duplicated the point 

source/single shielding jet geometry of the theoretical model. 

13 

PRESENT INVESTIGATION 

Objective 

The primary objective of the present program was to conduct an experimental study of the effect of flow from a jet on the radiated sound field of a 

neighboring jet with the same operating condition. Although previous investigators have conducted similar studies, the present experiment represents a 

definitive program in which the following comprehensive set of parameters were 

varied: a) jet Mach number, b) jet temperature, and c) jet spacing. The 

program was structured to vary only one parameter at a time thereby isolating 

the effect of the selected variable. By using small microphone intervals the 

experiment also provided the improved directivity information needed to identify possible redirection of sound. Also by using a shock-free convergingdiverging nozzle system for the supersonic tests, potential source changes 

existing in previous converging nozzle experiments were avoided. Finally, 

detailed Mach number and temperature surveys were conducted to determine if 

the small jet spacings created jet flow interaction. This permitted the identification of changes in the radiated sound field due to alterations in the 

downstream acoustic source region. 

A secondary effort was directed towards development of an analytical 

model to predict the shielding dependence on the experimental parameters. The 

theory models the shielding of discrete tones from a point source of sound by 

a nonspreading cylindrical jet with a uniform velocity profile. Although the 

present analysis is similar to the formulation by Gerhold, this separate 

theoretical effort was implemented to provide an independent check on the 

existing method for prediction of jet noise shielding. In addition, the 

availability of the analysis facilitated the present closely coupled theoretical and experimental program. This was critical to determining the conditions 

for which the discrete source/single jet combination adequately models the 

dual jet random noise distributed source configuration. 

Experimental Approach 

The dual jet and anechoic chamber experimental arrangement used in the 

present study is shown in Figures 3 and 4. Each of the 4.45 cm nozzles in the 

side-by-side jet configuration was supplied from a common plenum with heated 

high pressure air. Microphones located in a fixed polar array were used to 

measure the radiated noise as the source jet slowly rotated, thereby providing 

a fine azimuthal directivity measurement as e varied from 0 0 to 180 0

• Both 

converging (for subsonic flows) and converging/diverging (for supersonic shock 

free flows) nozzle sets were used. Flow visualization by the Schlieren technique in addition to a unique static pressure probe were used to set the 

shock-free supersonic operating conditions of the converging/diverging 

15 
16 

nozzles. Finally, extensive aerodynamic measurements were conducted to identify the jet spacings conditions for which aerodynamic merging and interference altered the acoustic shielding measurements. 

Analytical Approach 

A theory was developed to predict changes in the jet noise directivity 

patterns due to the presence of an adjacent shielding jet. The analysis 

models the dual jet configuration in terms of a discrete tone radiation from a 

point source of sound interacting with the cylindrical zero thickness shear 

layer of a single shielding jet. The global effects of reflection, refraction 

and diffraction of sound rays by velocity and temperature discontinuities of 

the shielding jet are implicitly included in the analytical model. Multiple 

reflections and acoustic focusing are also incorporated in the model. The 

analysis applies for all ratios of acoustic wavelength to jet diameter and 

permits nonplanar wavefronts incidence at the shielding jet. 
THEORETICAL DEVELOPMENT OF THE JET SHIELDING ANALYSIS 

The Shielding Mechanism and Selection of the Analytical Approach 

The transmission of sound through an adjacent jet is controlled by the 

flow and temperature discontinuity. Under certain conditions, these discontinu~t~es partially or totally reflect sound since the shielding jet has a 

different impedance compared to the surrounding ambient air. In other cases, 

the sound wave penetrates the shielding fluid but is refracted by the flow 

field resulting in a change of the noise directivity pattern. Finally, the 

sound can be diffracted by the discontinuity at the jet interface or scattered 

by the turbulent flow regime of the shielding jet. The difference between the 

sound pressure level measured by an observer in the presence and in the 

absence of the fluid shield defines the noise reduction due to the phenomena 

of reflection, refraction, diffraction and scattering. 

The present analysis models the combined effects of the reflection, 

refraction, and diffraction mechanisms but does not treat the scattering 

mechanism. While the individual mechanisms incorporated in the analysis are 

easily described, the general theory implicitly predicts the global effects. 

Contributions from the individual mechanisms are, therefore, not separable due 

to the complex interaction of the resulting waves arriving at the far field 

observer location. For example, phasing between refracted and diffracted 

waves must be known if these mechanisms are to be isolated. In this case 

phasing between wavefronts can result in an increase or decrease of the sound 

pressure level relative to the non-shielded environment. 

The theory models the dual jet geometry as a single point source emitting 

a discrete tone which propagates through the adjacent shielding jet. Selection of the point source approach is based on the results of jet noise acoustic source distribution measurements which show that specific source frequencies are confined to a local axial region of the source jet. Selection of the 

discrete tone model was based on the need to model the random jet source in a 

tractable format. Also the analysis assumes a nonspreading shielding jet with 

a uniform velocity profile. The effects of finite shear layer thickness or 

potential aerodynamic merging which exist in realistic dual jet configurationa 

are not included. Finally, scattering of sound by the turbulent jet flow is 

not included because of the complexity of modeling this mechanism for the 

radially distributed axially varying turbulent shear flow. Considering the 

above analytical simplifications, the objective of the current study was to 

determine if the resulting model predicts the experimental results of the dual 

jet configuration. 

17 
18 

Review of Previous Analyses and Experimental Confirmation 

The analytical treatment of the jet shielding problem is based on 

calculating the sound transmission across a shear layer. Although many of the 

previous analyses in this field did not treat the specific jet shielding 

geometry, they are discussed here since they formed the theoretical basis for 

the present analysis. 

The first correct analysis of sound transmission across a shear layer was 

formulated by Miles (ref. 14) and independently by Ribner (ref. 15). Both 

investigators considered the case of a plane wave incident on a two-dimensional zero thickness shear layer. At the shear layer the incident wave gives 

rise to a transmitted and a reflected wave. The amplitudes of these waves are 

determined by matching pressure and fluid displacement across the shear layer. 

These boundary conditions at the shear layer interface correctly model the 

acoustic transmission process. Earlier studies had matched normal velocity 

across the shear layer. This was an incorrect boundary condition because of 

the difference in mean velocity across the shear layer. 

Gottlieb (ref. 19) considered the case of a point sound source near a 

plane shear layer. This replaced the assumption of an incident plane wave and 

allowed the calculation of the directivity pattern of point sources in the 

presence of a shear layer. His formulation differs from the present jet 

shielding analysis and the analysis of Gerhold only in the geometry of the 

shear layer. 

Graham and Graham (ref. 20) extended the analytical capability to shear 

layers of finite thickness. However, for finite shear layers, pressure and 

fluid displacement cannot be matched across the interface. Instead the finite 

thickness shear layer problem requires the numerical integration of an 

ordinary differential equation across the shear layer to determine the 

reflected and transmitted wave amplitudes. 

Howe (ref. 21) considered the time dependent problem of an impulse 

produced by a point source impinging on a plane zero-thickness shear layer. 

This approach allows the study of shear layer instabilities induced by the 

incident wave. In all the other studies, including the present one, the 

instabilities are suppressed by assuming a steady state. 

Shear layer refraction phenomena have also been included in jet noise 

analyses which model the effect of flow on the assumed quadrapole sources. In 

this case, the Lighthill approach, which distributes quadrupoles in a freestream, is modified by imbedding the quadrupoles in the jet shear flow and 

calculating the resulting radiation. This approach, used for example by 

Tester and Burrin (ref. 22) for jet noise calculations, is similar in many 

respects to the problem treated here. The primary difference is that 

reference 22 assumes the shear layer has a finite thickness whereas the 
present model assumes a zero thickness. Also, reference 22 imbeds the source 

in the refracting shear layer whereas the source is external to the shear 

layer in the present model. 

Several other studies relevant to the prediction of jet noise have been 

formulated using approaches similar to reference 22. These include the work 

of Mani (refs. 23, 24) and Goldstein (ref. 25). As in reference 22, these 

studies placed the sound source inside the jet whereas in the present problem 

the sound source is located outside the shielding jet. 

A different approach was developed by Amiet (refs. 26, 27) and Jacques 

(ref. 28). These investigators assumed that the acoustic wavelength of the 

incident wave is small compared to the jet diameter permitting the application 

of geometrical acoustics techniques to calculate an angle and an amplitude 

correction. This method is useful for subtracting out the effects of shear 

layer refraction when the source type is not known. The correction in angle 

and amplitude is not dependent on source type, making the technique useful for 

analyzing noise data obtained in an open jet acoustic wind tunnel. However, 

the method ignores multiple reflections such as might occur inside a jet, and 

also assumes the acoutic wavelength is much smaller than the jet diameter. 

Whereas this method has the advantage of being independent of source type, the 

high frequency limitation precludes its use for the present calculation. 

Methods for correcting acoustic data obtained in open jet wind tunnels 

have also been developed by Candel (ref. 29) and Tester and Morfey (ref. 30). 

Candel employed a ray tracing technique to obtain the angle and amplitude 

correction. Thus, realistic jet velocity profiles with finite thickness and 

axial velocity variations could be investigated. The use of ray tracing in 

this case, however, limits the analysis to high frequency. Tester and Morfey 

devised a simpler model by locating a source on the jet centerline and surrounding it with a finite thickness shear layer. While radial velocity variations were represented in this way, axial variations were not included. The 

resulting model was then used to calculate low frequency and high frequency 

shear layer transmission effects. The results at high frequency compare 

closely with those of Amiet (ref. 27) and Jacques (ref. 28) for the zero 

thickness shear layer case at moderate Mach numbers of the order of 0.5 or 

less. This indicates that for many problems the shear layer thickness may not 

be an important parameter, at least for angles outside the zone of silence. 

One of the first analyses specifically directed toward the jet shielding 

problem was that of Gerhold (refs. 17, 18). In his analysis the jet is 

modeled as a plug flow with a zero thickness shear layer. The boundary conditions of continuity of pressure and displacement at the shear layer are identical to those used in earlier studies which assumed a zero thickness shear 

layer. The source field modeled by Gerhold is expressed in terms of cylindrical harmonic incident on the cylindrical shear layer. Thus, the difference 

between his work and earlier studies is in the circular shear layer geometry. 

19 
20 

The geometry difference between the formulation of Gerhold and the 

earlier studies can be demonstrated by a comparison with the analysis of 

Gottlieb (ref. 19) which uses a plane zero thickness shear layer. The latter 

analysis expresses the source field in terms of plane waves incident on a zero 

thickness plane shear layer. Similarly expressing the incident sound field in 

terms of plane waves in the analysis of Gerhold would result in difficulties 

in applying the boundary conditions at the shear layer interface. Instead 

Gerhold expresses the incident sound field in terms of cylindrical harmonics 

which conform to the cylindrical boundary of the shear layer. Similar methods 

were employed by Tester and Burrin (ref. 22) for a finite thickness cylindrical shear layer, and by Mani (ref. 23) for a cylindrical zero thickness shear 

layer. 

Verification of the above described fundamental shear layer transmission 

theories and boundary conditions applicable to the present problem have been 

provided by several investigators. A preliminary experiment by Amiet 

(ref. 26) showed agreement between theory and experiment for the angle correction. More detailed testing by Schlinker and Amiet (refs. 31, 32) provided 

further confirmation of both angle and amplitude corrections. Experimental 

studies with a sound source inside a jet were also performed by Candel, et. 

al. (ref. 33) and Ahuja et. al. (refs. 34, 35). The latter experiments 

provided similar confirmation of the fundamental theory used in the analysis 

of sound propagation through a shear layer. 

Analysis 

Formulation of the Approach - The analytical model permits a pure tone 

point source and an observer to be located at arbitrary points outside the 

shielding jet flow field (see Fig. 5). The cylindrical shear layer of the 

shielding jet has zero thickness; i.e., plug flow of diameter, 2a, and velocity V. The Z axis is aligned with the jet axis and the X axis passes through 

the source. The azimuthal angle, 8, is defined to be the angle between the XZ plane and the plane containing the jet axis and the observer. (Note that in 

the experiment, the point where 8 = 0° is rotated by 90° compared to that 

point in the theory). The polar angle W is the angle between a line parallel 

to the jet axis and the line joining the source and observer. The jet 

interior has density PI and sound speed cl, while the values in the 

exterior region are Po and co. The sound source is at a distance 

Ro = Xo > a from the axis and the observer is at a distance R > a from the 

axis. The z component of the distance between the source and observer is 

ZOo 

Summary of the Approach - The analytical approach used in the present 

report and in the studies of Gerhold (refs. 17, 18) employs a standard 

formulation used by previous authors (e.g., Mani (ref. 23) in the study of 

shear layer refraction. The method begins with the wave equation for the 
velocity potential inside and outside the shielding jet. Since the jet flow 

field conditions in the z direction are constant the wave equation can be 

easily Fourier transformed. This simplifies the analysis by eliminating the z 

variable until the inverse transform is performed. Assuming a sinusoidal 

dependence for the acoustic source and identifying a separation of variables 

results in a Helmholtz equation in terms of the variables R, e and w. The 

source field in these variables is given by Equation 8, below. This source 

field impinges on the shear layer leading to transmitted and reflected waves 

given by Equations 10 and 11. The unknown amplitudes of the transmitted and 

reflected waves are determined by matching pressure and fluid displacement at 

the jet boundary. A Fourier inversion is then performed on kz to obtain the 

final acoustic pressure result. 

To avoid performing the inversion numerically, the observer is assumed to 

be located in the far field allowing the integral to be approximated analytically. This approximation is based on the method of stationary phase which is 

commonly used to make such far-field approximations. The details of the 

analysis are given below. 

General Expression for the Far Field Sound - The wave equation for the 

velocity potential ~ outside and inside the jet flow field is 

'\J2 4> + \(~ Q 

a) Outside ci> : + 8 (x - X 0) 8 (y) 8 (z) 

0 

(1) 

b) Inside 2 . M ¢ 2 cp w2 cp 'V c:p - 2 I W C Z - M Zi + CZ : 0 

I I 

(2) 

The velocity potential is related to the pressure field by the linearized 

momentum equation 

p: - Po 

where ko = w/co and a time dependence 

above three equations. (Gerhold uses 

are complex conjugates of the results 

Ocp 

Ot 

exp (iwt) has 

exp (-iwt) so 

found here.) 

(3) 

been assumed in the 

that many of his results 

If the velocity potentials in Equations 1 and 2 are decomposed into their 

spatial Fourier components 

21 
22 

CD--'-

cp = J cP (kZ)eikzZ dk

z 

-CD 

these equations then become 

a) Outside 

b) Inside 

where 

(\72

2 

+ K02) 4> - = QO 

21TPO 

8 (x-Xo ) 8 (y) 

2 2"" 

('\72 + K I) cP : 0 

2 02 02 

\72 == o X2 + Oy2 

k,= ( ~I + Mk z) 

Ko == .j k 2 _ k 2 

o z 

K= /k 2 _k 2 

I 'V I Z 

(4) 

(5) 

(6 ) 

(7) 

It should be noted that kz in Equation 7 employs a plus sign in the definition of kl whereas Gerhold uses a minus sign. This difference in the definition of the Fourier transform results in k

z 

in Equation 26 being negative 

while Gerhold defines it to be positive. 

The solution of these equations can be written as a combination of 1nC1-

dent, transmitted and reflected waves. The source given in Equation 1 

produces an incident wave which can be represented as 

~n= 

where 

Q ~ Em COS m 8 { m=O 

Em = 1m: 0 

:2 m;tO 

(2) J m (Ko R) H m (Ko Ro) 

(2) Hm (Ko R) J m (Ko Ro) 

Q1Qo 

Ro: Xo 87TPO 

R < Ro 

R > Ro 

(8 ) 

(9) 
Here Ro is the distance of the source from the jet axis and R the distance 

of the observer from the jet axis; i.e., the field point. (See Equation 

7.3.18 of reference 36). The reflected and transmitted waves can now be 

written as 

~R 

ro 

= L 

m=o 

(2) Am Hm (KoR) cos m e (IO) 

'"" ro 

CPr = m~o 8m J m (K ,R) cos m 8 (I 1) 

Boundary Conditions - The constants Am and Bm in Equation 10 and 11 

are determined by matching boundary conditions at the jet interface R = a. 

First, the pressure must be continuous at R = a. From Equations 3 and 4, 

pressure is related to ~ by 

p= - ip,C, k, 4> R < 0 

(12 ) 

= - i Po c 0 k 0 4> R>O 

From Equations 9-11, 

Po Co ko 1 m ~ 0 [a < m cos m e J m (K 0 0 I H ,,\2) ( Ko R 0 I + Am H.i2) (K 0 0 I COS m eli 

ro 

=p, c, k, L 8m J m (K,o) cos me 

m= 0 

(13) 

Because e is a variable, this equation must match on a term by term basis, or 

(2) (2) 

a Em Jm{KoO) Hm (KoRo) + Am Hm (Ko 0) = 

C, kl p! 

Co ko Po 

8 m Jm (K, 0) (4) 

Also, there must be continuity of shear layer displacement at R = a. 

Note that this condition is not the same as continuity of radial velocity, an 

error that appeared in analyses prior to the works of Miles (ref. 14) and 

Ribner (ref. 15) (The continuity of displacement and velocity are not the same 

because there is a zero order velocity jump across the shear layer). Satisfying continuity of displacement for the interface requires determining the 

23 
speed at which the disturbance travels along the jet shear layer. The Fourier 

component, exp (i wt + i kz z), of the potential function is a wave which 

travels with velocity given by 

V : - w/k 

z Z (5) 

In a coordinate system moving with the wave this wave component remains 

steady in time. In this coordinate system the fluid velocity inside the jet 

1S 

Vi: V+ w/k z (6) 

while the fluid velocity outside the jet is 

Vo = w/kz on 

Continuity of shear layer displacement is insured by equating the slopes of 

the flow vectors across the shear layer, i.e., the perturbation radial 

velocities divided by Vi or Vo respectively. Thus, from Equations 9-

11. 

,(2) (2)' PI C I k I , a Em Jm (Ko 0 l Hm (KoRo' + Am Hm (Kool: Bm T k J m (K I 0) (8) Po Co 0 

where 

2 2 ko Po Co K, 

T= 

k ,2 PI C 12 Ko 09 ) 

Equations 14 and 18 are two equations for the two unknowns Am and Bm· 

Elimination of Bm gives 

(2) [I , ] _ a Em Hm (K o Ro) - TJ m (K, 0) Jm (Koa) + J m (Koa) Jm (Kia) 

Am - (2)' (2), -Hm (Koa) Jm(K, 0) + Hm (Koa) J m (K,a) T 

(20) 

24 
where the primes denote differentiation of the Bessel functions with respect 

to the argument. 

The potential field for R > Ro is the sum of ~in and ~R which, after 

inverting the Fourier transform, gives 

where 

co 

cp : a L €m COS 

m=Q 

co 

8J (2) ikzZ 

m Hm (KoR Fm(Ko,KI)e dk z (21 ) 

-co 

F m ( Ko , K I ) == J m (Ko Ro) + H~)(KORO) [Jm (Kia) J~ (Koe) - TJm (Koa) J~ (Kia)] 

T H ~ (K 0 a) J m' (K I a ) - J m (K I a) H ~ ( K 0 a ) 

(22) 

This is the complex conjugate of the result derived by Gerhold. 

The Stationary Phase Method - The summation and integration in Equation 

21 can be performed numerically. However, since the far-field solution will 

be of the greatest interest, the method of stationary phase can be used to 

analytically perform the integration for wR/co »1. For the case of large 

R, 

(2) (K R) - / -K2R Hm 0 V 1T 0 

e-i(KOR- ; m - ;;) (23) 

The method of stationary phase applies to the integrals with a rapidly 

varying phase; this gives a cancelling effect except at the point of stationary phase where the phase varies the slowest. Introducing Equation 23 into 

Equation 21 gives a phase 

'it : - Ko R + k z Z (24) 

25 
The point of stationary phase is now determined by setting the derivative of 

the phase equal to zero. Thus, 

dlJ! : 0: k z R 

+ z (25) 

d k z Ko 

giving 

k z = kz I : - ~ (26) dlJl f 

- =0 

dkz 

Ko == Ko L : R ko/r (27) 

k z 

1<, : K'I (28) 

kz 

d

2 

'" I = 

,3 

Also, (29) dk 2 k R2 z - 0 kz 

Note that kz in Equation 26 is negative whereas Gerhold defines it to be 

positive. The difference lies in the definition of the Fourier transform. In 

Equation 7 kz appears with a plus sign in the definition of k, whereas Gerhold 

employs a minus sign. 

The method of stationary phase indicates that all quantities, except for 

the phase factor, can be evaluated at the point of stationary phase kz and 

taken outside the integral. The phase is evaluated in a Taylor series so that 

the integration can be performed analytically. Thus, the integral in Equation 

21 becomes 

a:> 

Lm : Fm (Ko' I«) ../ 11' K! R e i (m + 1/2) 17'/2 - i kof J e

i 

r3 k 2 

z 

2 ko R 

(30) 

dk z 

-a:> 

26 
Using the relation from page 395 of reference 37, the integral remaining ~n 

Equation 30 is 

co 

I ,= 2 J 

o 

2 

( r 3 kz ) dk 

COS 2 ko R Z = ~ 7T ko R2/ r 3 

The final result for the velocity potential is then 

cp = a 

J2 

r 

i ('77"/4 - ko r) e 

co 

L €mFmCKo,K,)jm COS m e 

m=O 

(31) 

(32) 

Introducing this result in Equation 3 then gives the following expression 

for the pressure 

p = - i Po w cp (33 ) 

There remains an infinite summation to be performed in Equation 33. This 

in general must be performed numerically. However, the summation over the 

first term in Fm can be carried out to give the result for a free field 

source for an observer in the far field; i.e., 

co Jo Em Jm rKo Ro) i m COS m 8 = eikoRo cos Blr (34) 

This result follows from Equation 8.511.1 of reference 37 after making the 

substitution t = iei6 . 

Application of Theory 

Procedure - The solution for the far-field acoustic pressure, created by 

the point source/single jet combination illustrated in Figure 5 is given by 

Equation 33. Here the velocity potential is obtained from Equation 32 with 

the particular values of Ko and Kl given by Equations 27 and 28. As noted 

earlier, the first term in the expression for the parameter, Fm, in Equation 

32, can be evaluated directly using the closed form expression given in 

27 
28 

Equation 34. This closed form approach avoids long computation times, especially if KoRo is large, since numerical solutions for this term generally give 

significantly slower convergence compared to the remaining term in the expression for Fm' 

To quantify the change in the source noise level at the observer station 

when the shielding jet is present, the far field pressure, given by Equation 

33, is normalized by the incident pressure. The incident pressure is determined from the far field equation CEq. 33) except that the incident velocity 

potential ~in CEq. 8) is employed. Thus, the ratio of free-field-to-shielded 

acoustic pressures, is given by the ratio of ~/~in' In terms of the decibels, 

the change in pressure is defined by ~SPL = 10 10glO C~/~in)2. 

Comparison with Previous Investigations and Numerical Test Cases - The 

analytical results presented here agree with the corresponding results of 

Gerhold. As a check on the numerical predictions generated by the Gerhold 

analyses, an independent computer code was developed during the present study 

to calculate the sound pressure level changes associated with jet sheilding. 

The program predicts the parameter ~SPL for specific values of Ro ' R, ~, ~, 

a and 00. 

Input conditions employed in the comparison of the two computer codes 

corresponded to the values reported by Gerhold in reference 18. Calculated 

values obtained from the UTRC code were compared with values generated independently at NASA Langley where the computer model of the Gerhold analysis was 

available. Comparison of the separate predictions confirmed that the computer 

codes provided the identical numerical values, to within four decimal places, 

for the acoustic pressure ratio determined from ~/~in' 

Based on the above described evaluation of the generalized sheidling 

analyses and the associated computer code the theory was applied during the 

present closely coupled theoretical and experimental program. The objective 

was to determine the conditions for which the discrete source/single jet combination adequately models the dual jet random noise distributed source configuration. Without the on-site jet shielding prediction capability developed 

in the present study, such direct assessments would not be possible. This is 

evident in the section titled "Experimental Assessment of Dual Jet Shielding" 

where the critical selection of the single jet/point source geometry for simulation of the dual jet experiment is discussed. 

As a further check on the numerical solution, an energy balance calculation was performed for the geometry shown in Figure 5. Analytically, there is 

no mechanism for the interchange of energy between the mean flow and the 

acoustic field. For the experiment it is possible for the shielding jet to 

modify the acoustic impedance seen by the source if the source is less than an 

acoustic wavelength from the jet. However, for the analytical model, the 
far-field assumption should ensure that the acoustic impedance is the same 

with and without the shielding jet. Thus, the energy radiated to the far 

field should be invariant with the addition of the shielding jet. 

The energy calculation was obtained by numerically integrating the farfield intensity over a spherical surface surrounding the point source/shielding jet configuration shown in Figure 5. Within the numerical accuracy of the 

calculation the acoustic energy radiation was found to be the same with and 

without the shielding jet. 

29 

DESCRIPTION OF EXPERIMENT 

Acoustic Research Tunnel 

The experiment was conducted in the UTRC Acoustic Research Tunnel which 

is described in detail in reference 38. Figure 6 shows the open circuit open 

jet design of the acoustic tunnel and the air supply system used for model jet 

noise simulation studies. High pressure air, up to 27.5 bar (400 psi) at 4.5 

kg/sec (10 Ibm/sec), is supplied to a propane combustor which provides heated 

high speed air up to 538°C (lOOO°F). A muffler downstream of the combustor 

attenuates the combustion noise and valve noise before the air supply line 

enters the side of the acoustic tunnel inlet section. Beyond this point the 

air supply line is routed along the tunnel centerline terminating at the model 

nozzles which, in the present experiment, extended approximately 1.5 minto 

the anechoic chamber. The open jet test section surrounding the nozzles 

typically provides forward flight simulation although the present test was 

conducted under static operating conditions. 

The test section is surrounded by a sealed anechoic chamber 4.9 m high, 

5.5 m long (in the jet centerline direction), and 6.7 m wide. The chamber 

walls are lined with 0.5 ill high fiberglass wedges which provide an anechoic 

acoustic environment above 175 Hz. Downstream of the test section, the airflow enters a diffuser through a circular collector with acoustic treatment on 

its flow impingement surface. The diffuser is designed to operate unstalled 

and hence is not a major source of background noise. To avoid tunnel fan 

noise from propagating upstream into the anechoic chamber, a Z-shaped muffling 

section with two right angle bends and parallel treated baffles is located 

between the diffuser and the fan. The flow is exhausted to the atmosphere by 

a 1100 kW centrifugal fan. 

Experimental Arrangement 

Figure 7 shows the anechoic chamber experimental arrangement. A fixed 

array of 9 microphones on a 3.05 m (10 ft) radius arc was centered on the 

shielding jet exit plane. The microphones were located in a horizontal plane 

at 10° increments between 20° and 100° from the shielding jet centerline. 

Acoustic shielding effects were investigated by rotating the source jet on a 

fixed radius arc about the shielding jet. This technique of rotating one jet 

while fixing the microphone location was equivalent to the observer in 

Figure 2 being situated at different azimuthal angles relative to the aircraft. The multiple engine configuration in Figure 2 was, however, replaced 

by the present dual jet configuration. This simplified geometry isolated the 

side-by-side acoustic and aerodynamic interactions in addition to providing a 

fundamental experiment capable of assessing the present theory. 

31 
32 

Approximately a 200 0 source jet rotation range was obtained using the 

technique shown schematically in Figure 8. Here high pressure air from the 

upstream propane burner was supplied to a common plenum (located in the tunnel 

inlet) for the purpose of delivering equal pressure and temperature flows to 

each nozzle. The source jet was constrained to move in a circular arc by a 

bearing situated at a fixed radius in the rotating disk. A variable speed 

electric motor with a chain and sprocket arrangement was used to rotate the 

disk. The air supply line for the fixed shielding jet penetrated a hole in 

the rotating disk. A flexible stainless steel tube connected the rotating 

source jet and the fixed upstream plenum. Since the plenum and rotating disk 

obstructed the open jet test section the model nozzles could not be tested 

with forward flight simulation. 

Two matched sets of nozzles with an exit diameter of 4.45 cm (1.75 in.) 

were used in the experiment, a converging pair and a converging/diverging 

(G/D) pair. The converging nozzles were employed for subsonic tests (M = 0.6, 

0.94 and the G/D nozzle set was used for supersonic tests. The interior geometry of each G/D nozzle duplicated the contour used earlier by Laufer, 

Schlinker, and Kaplan (ref. 39) to study single flow shock free supersonic jet 

noise at M = 1.5. Although the nozzle profile in reference 39 was designed 

using an inviscid code shadowgraph measurements demonstrated the shock free 

operating point to be M = 1.47. Similar measurements, using Schlieren methods 

in addition to static pressure probe measurements, were performed in the 

present study to identify the shock free operation point. The improved sensitivity of the static pressure measurement, however, resulted in a slightly 

different operating point relative to reference 39 with M = 1.46. 

Jet spacing (S), relative to nozzle diameter (D), was varied by changing 

the initial radial displacement between the source jet and the shielding jet. 

This was accomplished by connecting to the source jet a supply pipe with an 

offset centerline. 

To m~n~m~ze the generation of upstream turbulence (which can alter the 

jet noise spectrum) large diameter (15 cm) supply lines were used between the 

plenum and the rotating disk. A liner was also installed on the interior wall 

of the flexible tube used on the source jet supply line. This provided a 

smooth wall for the purpose of minimizing the generation of turbulence. The 

maximum flow angle change in the offset section used to change jet spacing was 

limited to 15 degrees. This minimized the generation of secondary flows in 

the turning sections which could be another source of flow disturbance. In 

addition a 1.2 m length of the 10 cm diameter pipe was used downstream of the 

offset pipe on the source jet supply line (also on the shielding supply line) 

to permit the turbulence to decay before entering the source jet nozzle. 

Finally, a pipe-to-nozzle-area contraction-ratio of approximately 5 was 

employed to further reduce the initial turbulence level at exit plane of each 

jet. This ratio was limited by the upstream 10 cm diameter supply pipe and 

the smallest jet spacing ratio. 
The complicated equipment associated with rotating the source jet blocked 

the acoustic tunnel open jet flow surrounding the test nozzles. Consequently, 

forward flight effects were not tested and the study was limited to static jet 

noise directivity patterns. However, to avoid developing locally hot regions 

in the anechoic chamber when conducting the high temperature jet noise studies 

under these static conditions, the tunnel fan system was operated at approximately 3 m/sec. Ambient air in the anechoic chamber entrained in this process 

was replaced by air flow through large holes in the rotating disk (34 percent 

open area). Also, an access door to the chamber was partially opened to 

entrain cooler outdoor air. 

The above described rotating jet configuration was essential to defining 

the azimuthal directivity patterns for which limited documentation was 

obtained in previous experiments. Also, the decision to rotate the jet in 

place of rotating the microphones on an arc in the azimuthal direction was 

based on the requirement to minimize ambient air temperature gradients, in the 

anechoic chamber. Rotation of the microphone array to an azimuthal location 

above the nozzle would have placed the microphones near the ceiling of the 

chamber where the hot air from the heated jets could migrate. The temperature 

limit for microphone operation in addition to the potential thermal gradients 

through which the jet noise would propagate precluded using the rotating 

microphone approach. Instead, the nozzles were rotated while the microphones 

were located in a horizontal plane 1.6 m above the floor of the anechoic 

chamber. 

Instrumentation 

Acoustic Measurements - Measurements of the far field jet noise were made 

with 0.635 cm diameter microphones at normal incidence. Signals from the 

microphone preamplifiers were high-pass filtered (at 200 Hz), amplified and 

finally recorded on magnetic tape, using a 15 track, FM tape recorder system. 

Acoustic data was reduced to 1/3 octave band levels on an analyzer with 0.1 dB 

resolution. The analyzer generated absolute sound pressure levels for the 31 

bands between 50 Hz and 50 kHz. A narrow band spectrum analyzer was also 

used, mainly for diagnostic purposes. 

Frequency response of the above described data acquisition system was 

calibrated prior to performing the test program. Microphone cartridge calibrations conducted according to National Bureau of Standards procedures indicated a maximum variation of ±l dB over the 200 Hz to 50 kHz range of the 

present study. The frequency response of the microphone preamplifer-to-tape 

recorder section of the data acquisition system was also calibrated. In this 

case, a white noise signal was injected into the preamplifier and recorded on 

analog tape. Playback of the signal from each recording channel was compared 

on a spectrum analyzer with the initial white noise input signal. The 

33 
34 

frequency response was observed to be flat within ±l dB for all microphones 

from 200 Hz to 50 kHz. 

Frequency response variations of the above described data system suggest 

potential uncertainties in the experimental results since changes in the 

radiated source jet directivity due to shielding were of comparable magnitude. 

However, the shielding phenomenon is defined by the difference between the 

dual jet and a corresponding single jet sound pressure level measurement. 

Since the same microphones and instrumentation channels were used for each 

data set, the previously described variations in response with frequency do 

not impact the results of the present study. In essence, the shielding 

phenomenon addressed here is not a function of absolute sound pressure level, 

but instead is represented by a relative level change. 

Velocity and Pressure Measurements - Mean Mach number profiles of the 

developing region of the subsonic merging jets were obtained with pitot 

probes. A 1.58 mm (1/16 in) tip diameter tube and support was used to survey 

the total pressure field in radial and axial directions. 

To determine the shock free operating point for the supersonic nozzle 

set, measurements of both total and static pressure were obtained on the 

centerline of each jet. A square edged, round pitot tube measured the total 

pressure. The probe generated a detached normal shock which was accounted for 

in the data reduction. Total pressure measurements were corrected by the 

Rayleigh equation to give local Mach number. A separate probe, similar to one 

used by Pinckney (ref. 40), measured the static pressure in the supersonic 

region of the jet flow. The same probe configuration was employed by Seiner 

in an earlier supersonic jet noise study (ref. 41). A 5.08 cm (2 inch) spanwise separation of the total and static pressure probes eliminated probe 

interference during flow traverses. 

The pressure sensing probes were mounted on a double wedge wing support 

(diamond shaped cross-section) with a wedge half angle of 7°. A small wedge 

angle was selected to ensure an attached shock wave on the support strut. A 

detached shock wave could interfere with the pressure field sensed at the 

pressure sensing probe location 3.8 cm (1.5 inches) forward of the support. 

Both the subsonic and supersonic probes were traversed across the twin 

jet flow field using a 3 axis traverse system. Stepping motors moved the 

probes in two orthogonal directions within a plane normal to the jet axis. 

Traverse increments of 0.0127 mm (0.0005 in) were used. Axial traverses were 

obtained with a DC motor and a controller providing a resolution of approximately 2.5 mm (0.1 in). The traverse system, shown in Figure 9, was moved 

continuously. Voltages from the pressure and temperature sensing transducers, 

in addition to the encoder positions, were stored on the computer data acquisition system (discussed in detail in the subsection titled Computer Data 

Acquisition and Data Reduction System). 
In addition to the downstream jet profile measurements, static and total 

pressure measurements were obtained at a reference station in the 10 cm pipe 

upstream of each nozzle. These upstream pressures were used to set the jet 

Mach number during the acoustic study when the flow traversing system was 

removed from the anechoic chamber. In the case of subsonic flows, the upstream pressures were calibrated relative to the desired nozzle exit conditions determined during the jet flow surveys. For the supersonic converging/ 

diverging nozzles, a three step process was used to identify the upstream 

pressure required for shock free operation. Details are presented in the 

subsection titled Shock Free Operating Conditions. 

During the above calibration process, a small difference was observed 

between the dual jet nozzle exit Mach numbers. This was attributed to the 

different flow losses in the piping sections linking the upstream plenum and 

each nozzle. Jet operating conditions were, therefore, based on the upstream 

pressure in the source jet air supply line. Differences between the source 

and shielding jet exit Mach numbers were not considered to have an impact on 

the present jet shielding acoustic study as discussed in the section titled 

Aerodynamic Measurements. 

Temperature Measurements - Total temperature profiles of the heated 

merged jet flow field were obtained with a specially designed double shielded 

thermocouple probe. Design criteria, based on the earlier work of Moffat 

(ref. 42), limited errors from velocity, radiation, and conduction to less 

than 5°C over the entire range of Mach numbers and temperatures tested. An 

outer shield with a 6.35 mm (0.25 inch) diameter provided a smaller sensing 

area and less flow blockage than commercially available units. An independent 

check on the probe calibration was obtained by comparing measurements taken 

with a larger commercially available 9.53 mm (3/8 inch) diameter triple 

shielded thermocouple probe. Temperature readings from the two units were 

within 5°C of each other. During the temperature flow surveys the UTRC 

designed unit was mounted on the traverse unit along with the total pressure 

probe and separated by a distance of 3.8 cm (1.5 inches). 

Jet total temperature operating conditions were set using temperature 

readouts from thermocouples mounted upstream of each nozzle. The sensors were 

located at the same reference station where total and static pressure 

measurements were obtained when setting the jet flow Mach number. Similar to 

the calibration of the upstream pressure sensors, the upstream thermocouples 

were calibrated relative to the specially designed UTRC probe situated at the 

jet exit. 

Flow Visualization - Figure 10 shows the Schlieren system used to determlne the shock free operating condition for the M = 1.5 converging diverging 

supersonic nozzles. This technique was also helpful when documenting the 

onset of jet merging as the dual jet spacing was decreased. 

35 
36 

The Schlieren system used 25.4 cm (10 in) diameter mirrors which were 

fixed at the nozzle exit. A video camera permitted viewing the resulting 

optical image from the control room. Photographic records were obtained using 

a 35 mm single lens reflex camera with a strobe light (nano-second pulse duration) to capture the jet structure. A sample photo obtained for an off design 

pressure setting on the supersonic converging diverging nozzle system is shown 

in Figure 11. 

Source Jet Rotation Position and Rotation Rate - A digital encoder was 

employed to sense the rotating source jet position. By using a 12 to 1 

gearing ratio between the encoder and the chain driven rotation system, a 0.10 

angular resolution was provided. Rotation rate was adjusted to produce a 90 0 

azimuthal change in approximately 8 minutes. This slow rotation, which 

created an 8 minute tape record for the microphone signals, was experimentally 

determined to provide a pseudo steady state during the 1 second data processing time used for the repetitive spectrum analyses (described further in 

following subsection). 

Computer Data Acquisition and Data Reduction System - Acquisition and 

processing of the large acoustic data base obtained in the present study was 

performed by a computer controlled system. A schematic of the automated 

system is shown in Figure 12. 

Data acquisition proceeded in the following sequence. After the desired 

Mach number and total temperature were established, the jet rotation and computerized data acquisition system were activated. The computer controlled the 

tape recorder, which recorded the signals from the 9 far field microphones, 

the time code generator, and the upstream reference station pressure and temperature sensors. (Temperature and pressure data was later used to correct 

the acoustic sound pressure levels for small changes in jet velocity as the 

source jet rotated). In addition the angular position encoder output was 

stored on the computer hard disk along with the time code. Both signals were 

sampled once per second during the jet rotation. 

Data reduction involved playback from the tape recorder to the 1/3 octave 

band spectrum analyzer. The desired data record was located by searching the 

analog tape for the associated time code signal. Processing by the spectrum 

analyzer was computer activated 15 seconds after identifying the start of the 

record. A time delay was introduced to permit setting (remotely by the computer) the maximum input amplifier sensitivity on the analyzer without overloading the circuitry. A 1 second repetitive averaging time was selected on 

the analyzer with the computer sampling the output from the 31 frequency bands 

(stored in a digital buffer) every 2 seconds, or, approximately every 0.5 0 of 

source jet rotation. The sampled spectrum was stored on the computer mass 

storage disk. During playback, the pressure and temperature data from the 

tape record was also digitized every 2 seconds, converted to engineering 

units, and stored on disk. 
Since the acoustic signals and jet rotation position were initially 

stored on separate systems (FM tape for acoustic signals, disk storage for jet 

position) it was necessary to merge these records to create sound pressure 

level versus azimuthal position information. This was achieved by using the 

time code generator signal. During playback of acoustic data each digitally 

sampled record from the 1/3 active band analyzer was linked with the appropriate time code which was simultaneously sampled at the tape recorder output by 

the computer. A similar set of jet position versus time code files was also 

available on the computer disk storage system. Merging of these files 

provided the required sound pressure level versus azimuthal angle information. 

The same technique was used to determine the jet operating pressure (used to 

calculate Mach number) and total temperature at each azimuthal station. This 

permitted correcting the dual jet noise for small changes in the upstream 

operating pressure. 

Test Program 

Selection of Acoustic Test Conditions - To provide a broad data base for 

current and future turbo-fan engine aircraft, a wide range of test conditions 

was selected. To assess the affect of Mach number on the jet noise shielding 

mechanism, both subsonic (M = 0.6 and 0.94) and supersonic (M = 1.46) jet exit 

Mach numbers were used. The subsonic operating conditions are typical of 

current commercial aircraft jet engines. The supersonic test condition 

simulated the pressure ratio of previously proposed engines for supersonic 

cruise vehicles. 

To assess the effect of thermal discontinuties, the above defined Mach 

numbers were investigated over a range of total temperatures. One series of 

tests was conducted without heat addition to the flows such that the jet exit 

static temperature was approximately equal to the ambient air temperature 

(nominally 25°C). This operating condition minimizes the temperature effect, 

thereby isolating the Mach number discontinuity dependence. Three additional 

temperatures of nominally 316°C (600°F), 427°C (800°F), and 538°C (lOOO°F) 

were selected to simulate current engine operating conditions. These temperatures span the range from the fully mixed temperature downstream of a highbypass ratio turbofan to typical turbojet operating conditions. 

Engine spacing effect on current full scale aircraft was investigated 

using three lateral separation distances, SiD = 3.1 (nominal), 5.5, and 8.1. 

The smallest distance simulates present Boeing 727 (SiD ~ 2.5) aircraft and 

earlier Boeing 707 (SID ~ 4) aircraft. The largest spacing corresponds to the 

distance between the opposing inboard engines on under-the-wing mounted airframe designs. For example, for the Boeing 737 SiD ~ 7 while SiD ~ 8 on the 

Boeing 747. The intermediate value of SiD = 5.5 was selected to establish the 

trend with increasing separation. 

37 
38 

The source jet azimuthal rotation range initially extended from e = 0 to 

200°. (See Fig. 7). To shorten the 16 minute tape record created by the slow 

rotation rate through this large azimuthal range, e was confined to rotate 

from 80° to 200°. This was possible since both jets in the dual jet system 

operated at the same Mach number and total temperature. Under this condition, 

the radiated acoustic directivity pattern was symmetric about e = 90° permitting a significant reduction in the rotation range. Verification of the 

symmetry properties is given in the Section titled Experimental Assessment of 

Dual Jet Shielding. 

It is important to recognize that the laboratory coordinate system is 

rotated 90° compared to the coordinate system used in the theoretical development section. For the laboratory coordinate system, e = 90° occurs when the 

$ = 90° microphone, the shielding jet, and the source jet are in line. In the 

theoretical coordinate system, this condition corresponds to e = 0°. These 

differences in e are evident when comparing Figures 5 and 7. 

For the supersonic test points, azimuthal measurements were limited to 

two fixed angles given by e = 90° and 180° in the laboratory coordinate 

system. This limitation occurred because of the difficulty of controlling the 

supersonic jet operating pressure. Tight tolerances for shock free operation 

could not be satisfied during the approximately 8 minutes required for the 

azimuthal rotation. Instead acoustic data was obtained at the two fixed 

angles which, after comparison of the sound pressure levels, were expected to 

show the largest effect of jet shielding. 

The above described difficulty in controlling the total pressure did not 

represent a problem for the subsonic test cases. For subsonic test conditions, small variations in the upstream plenum chamber pressure were corrected 

using jet noise scaling laws (see section titled Data Acquisition and Data 

Reduction and Appendix B). Most corrections were smaller than 0.3 dB with the 

maximum correction during the test program being 0.75 dB. 

Aerodynamic Study - The extensive range of separation distances defined 

above delineates the effect of engine separation on the magnitude of jet noise 

shielding for current airframe configurations. The smallest separation distance also permits evaluating the acoustic effects created by aerodynamic 

interference or merging. In this case, noise reduction or additional noise 

generation can occur due to alteration of the acoustic source regions. The 

potential acoustic impact of the aerodynamic merging at small SiD necessitated 

conducting detailed aerodynamic measurements to document the merging process 

of the dual jet configuration. 

Aerodynamic measurements were conducted for SID = 2.7, 3.1, 3.8, 5.5, and 

7.9. In comparison to the acoustic measurements, acquisition of aerodynamic 

data was possible at smaller spacings due to a mechanical equipment simplification. For the acoustic study with rotation of the source jet around the 

shielding jet, a spacing plate was required to maintain the jets at a fixed 
separation distance. This plate was not required for the aerodyamic phase of 

the experiment where the nozzles were stationary. 

Aerodynamic measurements involved mean total pressure and mean total 

temperature surveys. With the dual jet system oriented in a fixed vertical 

plane (see Fig. 7) probe traverses were conducted along horizontal lines 

surveys at different heights, relative to each jet centerline. This approach 

provided sufficient data to generate a contour plot of total pressure and 

total temperature in the plane normal to the jet axis. Measurements were 

repeated at selected downstream stations to trace the development of the jet 

flow field. 

In addition to the planar surveys at selected axial stations, continuous 

axial traverses were conducted to identify the location at which the independent jets merged aerodynamically. This was achieved by traversing in the 

axial direction on a line midway between the two jet centerlines. 

Acoustic and Aerodynamic Qualification Tests 

Background Noise - Several preliminary acoustic measurements were conducted to establish the quality and limitations of the acoustic data. To 

demonstrate that the jet noise phenomena investigated in the present study 

were not masked by facility noise, background noise levels were compared to 

the jet noise levels at selected operating points. 

Background noise tests were performed by removing both jet nozzles from 

their upstream 10 cm diameter air supply lines. Mass flow rate and total 

temperature in the air supply lines duplicated the operating conditions with 

the nozzles attached. The resulting jet velocity and, hence, the jet noise 

were significantly reduced at the exit of the 10 cm diameter pipe, thereby, 

providing a calibration of the noise generated in the upstream piping. Both 

cold and hot tests, with combustion noise present, were performed. The mass 

flow was measured using ASME procedures for standard sharp edged orifice 

plates installed upstream of the combustor. 

Background noise measurements, obtained with flow in both air supply 

lines, were compared to the noise from a single jet in the dual jet shielding 

configuration. The single jet comparison, instead of a dual jet comparison, 

was selected since it represented the maximum background noise source for 

which an adequate signal-to-noise ratio was critical. In the limit, total 

masking of the source jet by the shielding jet would result in only the 

shielding jet radiation arriving at the far field microphone location. 

Comparisons between background noise levels and noise from a single jet 

are shown in Figure 13. To assess the effect of flow rate on the upstream 

piping and combustor noise, the lowest (M = 0.6) and highest (M = 1.46) exit 

39 
40 

Mach numbers are presented. In both cases, the highest jet exit temperature 

~700 K) is shown since this condition was expected to generate the maximum 

noise in the upstream propane heater. 

The comparison for the subsonic test case in Figure l3a shows a m~n~mum 

of 6 dB signal-to-noise ratio at all polar radiation angles when the acoustic 

source frequency is approximately 400 Hz. At frequencies above 1 kHz, where 

the jet shielding phenomenon dominated, large signal to noise ratios occurred 

with values ranging from 15 dB to 40 dB. Similar results were observed for 

the supersonic test conditions shown in Figure l3b. These examples illustrate 

that over the spectrum range where the jet shielding mechanism was operative, 

an adequate signal-to-noise ratio existed permitting conclusions to be drawn 

directly from the data. 

Comparison of Jet Noise Spectra with Previous Investigations - To further 

establish that the present facility provides clean jet noise data, single jet 

noise measurements were compared with previously published data. For this 

purpose, 1/3 octave band sound pressure levels from the shielding jet were 

compared with measurements reported by Plumblee et al (ref. 43). The results 

for three polar angles are shown in Figure 14 for a common M = 0.6 operating 

condition. The data are presented in terms of Strouhal number since the jet 

exit diameters differed. Absolute sound pressure levels are referenced to the 

present jet exit diameter by using the standard area scaling relationship. 

Finally, a 0.3 m difference in the microphone array radius was compensated for 

by using the inverse square law decay relationship to convert the data in 

reference 43 to the equivalent radius used in the present study. 

A comparison of the spectra in Figure 14 indicates the spectrum shapes 

are similar demonstrating that the present jet noise study is typical of other 

jet noise experiments. The absolute sound pressure levels are, however, 

different between the two experiments. While the source of the difference was 

not clear, conclusions of the present study were not impacted. This is 

because the jet noise shielding phenomenon is independent of the specific 

spectrum shape or amplitude and instead represents a relative level change due 

to propagation through the adjacent jet. 

An evaluation of the spectra shown in Figure 14 also indicates an anomoly 

at high frequency in the present experiment. Absolute sound pressure levels 

in the 31.5 kHz and 40 kHz bands fall outside the general spectrum shape 

suggested by the dashed line. Since this exception occurred in a frequency 

range with a large signal-to-facility-background-noise ratio, the source of 

this deviation was considered to be the jet itself. While the precise origin 

of this noise was not identified, it did not impact the present study since 

data at frequencies above 20 kHz was not used to develop conclusions. 

Humidity effects at these high frequencies were significant relative to the 

procedure used for experimentally isolating the jet shielding effect (see 
Appendix B). Consequently, data above 20 kHz could not be used for quantitative interpretations of the jet shielding phenomenon. 

Shock Free Operating Conditions - The supersonic shock-free jet operating 

pressure was determined by minimizing the strength of the potential core shock 

cells. A three step process was used to identify the correct operating pressure. First, Schlierern visualization was used to define the pressure range 

where the strong shock cells associated with over-expanded or under-expanded 

flow disappeared. Second, static pressure surveys along the jet centerline 

were used to further isolate the shock free operating point. In this case the 

upstream total pressure was adjusted to minimize the small static pressur~ 

changes associated with weak shocks and expansion fans which occur at slightly 

off-design operating conditions. Finally acoustic measurements were conducted 

at ~ = 900 to the jet to check for shock associated noise. 

Relative to the acoustic measurements narrowband spectra were used to 

confirm the absence of shock associated discrete tones. Figure 15 shows a 

typical spectrum for the shielding jet nozzle operating at M = 1.46 with 

To = 300 0K. The measurement was obtained at a polar angle of ~ = 90 0 where 

screech is easily detected in comparison to angles close to the jet axis. No 

evidence of screech was observed in this spectrum or any of the supersonic 

spectra examined. 

One third octave band measurements were also used to search for increased 

broadband noise due to accelerated mixing of the jet flows by the shock cells. 

Although the 1/3 octave band levels indicated a minimum noise level as a function of upstream nozzle pressure, the acoustic sensitivity to operating pressure adjustments was weak compared to changes in the jet centerline static 

pressure. Consequently, the final criterion used to select the upstream shock 

free operating pressure was based on minimizing the jet centerline static 

pressure variations (an example is provided in the section titled Aerodynamic 

Measurements). 

41 

AERODYNAMIC MEASUREMENTS 

Objective and Approach 

The objective of the aerodynamic measurements was to define the axial 

location at which the dual jet merging occurred. A knowledge of this merging 

distance was required to assist interpretation of acoustic results. Close to 

the nozzles, the jets were expected to develop independently. Further downstream merging was expected with the location of merging depending on jet 

spacing, and possibly Mach number or temperature. 

A secondary objective of the aerodynamic measurements was to establish 

that the jet flow fields exiting from the model nozzles initially developed as 

standard turbulent jets. In most previous acoustic studies of jet shielding, 

such flow documentation was not provided. The present qualification tests 

were particularly important for the supersonic test conditions where a shock 

free flow was required from the converging-diverging nozzles. 

Mach Number Distributions 

Radial Profiles - Jet Mach number radial surveys at sequential downstream 

axial locations are shown in Figure 16 for a typical test condition. This 

figure corresponds to a cold (To = 300 K), M = 0.6 jet operating condition 

with the two jets at close spacing (SiD = 2.7). Plotted in Figure 16 is jet 

Mach number, calculated from total pressure measurements, as a function of 

normalized radial position (riD) for various axial locations ranging from 

the nozzle exit (X = 0) to forty-one diameters downstream. From the figure, 

merging of Mach number profiles in the gap between the jet centerlines is 

observed to occur at a position between 4.6 and 9.1 diameters downstream of 

the exit plane. A more precise definition of the merging location is given 

subsequently. 

Measurements at the same M = 0.6 nozzle exit Mach number but with elevated temperature (To = 811 K) show similar trends in Mach number profile 

development. These results are given in Figure 17. In this case, the jet 

spacing was smaller (SiD = 2.3) due to differential thermal expansion in the 

two pipes supplying the nozzles. This difference in spacing is believed 

responsible for the fuller mid-gap profiles obtained in the hot test at 

X/D = 9.1. Further downstream (X/D = 18.3), where initial spacing effects 

would be expected to have less influence, the cold and hot profiles are similar. Results suggest that stagnation temperature changes at constant Mach 

number conditions do not affect jet merging length. 

Figures 18 and 19 show that isothermal and hot jet Mach number distributions at a supersonic exit condition (M = 1.46) were similar, as observed in 

43 
44 

subsonic tests. Differences between profiles in Figures 18 and 19 tend to be 

within several percent of exit Mach number except for station X/D = 18.3 where 

a ten percent difference occurs. The reason for the change in profile shape 

at this station is not known. The location of jet merging is observed to 

occur between 4.6 and 9.1 diameters downstream of the exit as in the previously discussed subsonic 0.6 Mach number case. 

Potential Core Length - In addition to the radial profile measurements, 

jet centerline surveys were performed to document the aerodynamic behavior of 

the jets. A typical centerline Mach number distribution is given in Figure 

20a, with an enlargement of the potential core region provided in Figure 20b. 

For this subsonic test case, the potential core length, where the flow is 

basically inviscid, is observed to extend to approximately five nozzle diameters. Figure 21 shows this length increased monotonically with increasing 

Mach number as would be expected. As in the case of the radial profiles, the 

data show that a change in jet temperature ratio from unity to 2.7 had no 

measurable effect. 

Jet Merging Length - The distance from the nozzle exit plane at which 

jet interaction occurs, termed the jet merging length, can be defined based on 

Mach number or temperature measurements. Since the thermal spreading rate of 

jets exceeds the momentum spreading rate, this length varies with the definition employed. Here, merging length will be taken as the distance from the 

nozzle exit plane to the axial station at which a measureable Mach number is 

obtained. For this measurement, a traverse is performed along a line parallel 

to and midway between the two jet centerlines. Typical traverse results are 

shown in Figure 22 for unheated, 0.6 Mach number jet with various initial jet 

spacings. As shown in the figure, an abrupt increase in Mach number from zero 

occurs at various distances depending on jet spacing, thereby allowing merging 

length to be determined accurately. Based on the summary plot in Figure 23, 

the merging length for isothermal jets was found to be relatively independent 

of jet exit Mach number and to increase linearly with jet spacing. Heated jet 

measurements were not obtained although results presented above suggest that 

temperature effects would be small. Based on the data of Figure 23, the 

merging length can be taken as approximately three times the lateral jet 

spacing. 

The above described use of Mach number profiles to determine the jet 

merging length may appear inappropriate when compared to using absolute 

velocity profiles. Admittedly, the hot jet will have a higher local velocity 

than the cold jet at corresponding radial locations for the same Mach number. 

However, the procedure for determining merging location is not based on 

absolute velocity but on the asymptotic extrapolation of the data points 

presented in the profiles of Figure 22. The axial intersection of the extrapolated points is expected to be the same whether Mach number or velocity 
profiles are employed. Mach number profiles, which require only total 

pressure surveys, were selected to simplify the experimental determination of 

the merging location. In comparison, velocity profiles require both total 

pressure and total temperature surveys to deduce local velocities. 

Total Temperature Distributions 

Jet total temperature distributions were measured to establish that normal heated jet conditions had been achieved. Radial and jet centerline distributions were measured for an exit stagnation temperature conditon of 8ll o

K 

at exit Mach numbers of 0.6, 0.94 and 1.5. Typical radial profiles are given 

in Figure 24 for a Me = 0.6 condition. Based on temperature, jet merging is 

observed to occur between the nozzle exit and axial station X/D = 4.6. Comparison of these profiles with the results of Figure 23 indicates that the 

merging length based on thermal spreading is shorter than that derived from 

the Mach number distributions, as would be expected. 

Supersonic Flow 

Static Pressure and Mach Number Distributions - For supersonic exit conditions, jet centerline static pressures were measured since they provide a 

more precise means of establishing shock-free operation than Schlieren flow 

visualization. Fig~re 25 shows the axial static pressure distribution on the 

jet centerline for a cold, M = 1.46 operating condition, the Mach number which 

minimized the axial pressure fluctuations of the M = 1.5 shock free nozzle 

design. The shock cell pressure fluctuations observed at this operating point 

were very small (on the order of 8 percent of reference static pressure) and 

of the same magnitude as those measured by Sein~r and Norum (ref. 41) in 

similar "shock-free" experiments. Spacing between shock cells varied from 

about 1.4 diameters near the jet exit plane to 0.9 diameters at X/D = 10. 

Variations of Mach number on the jet centerline are shown in Figure 26 

for the shock free operating point. Parts band c of this figure represent 

enlargements of Part a. Mach number oscillates in the potential core region, 

similar to the static pressure variations, due to the weak shock cell structure. 

Flow Visualization - Figure 27 shows a series of 7 Schlieren photographs 

obtained at To = 300 K and SID = 2.7 for the converging diverging nozzle set 

at different operating conditions. The first photograph shows the dual jet 

system with an underexpanded operating condition. The subsequent photographs 

show the effect of increasing the upsteam stagnation pressure until the flow 

becomes overexpanded. The data is presented as a function of e = (M2-l)1/2. 

45 
46 

Near the optimal shock free operating point. S = 1.06. the flow exits the 

nozzle with a very small jet divergence angle. As the pressure is lowered the 

divergence increases and diamond shaped shock cells appear in the jet. Even 

at the smallest jet spacing there appears to be no shock wave interaction 

between the two jets. 
DATA ACQUISITION AND DATA REDUCTION PROCEDURE 

The experimental technique for investigating the jet shielding phenomenon 

involved continuous rotation of the source jet about the shielding jet. This 

approach documented the directivity pattern changes close to the plane of the 

two jets, corresponding to the sideline observer in Figure 2. In addition, 

this method defined the changes at angles corresponding to the observer 

directly below the aircraft flight path in Figure 2. To quantify the experimental results, the present chapter begins with a summary of the general features of the jet shielding noise reduction mechanism. Based on this discussion a quantitative definition of the shielding phenomenon is formulated. 

This is followed by a description of the data acquisition and data reduction 

procedures which were used to assign numerical values to the shielding mechanism. 

General Features of Noise Reduction Due to Jet Shielding 

The jet shielding phenemonon is represented in a simplified form in 

Figure 28. The jet closest to the observer is referred to as the shielding 

jet since it potentially masks the second jet which is referred to as the 

source jet. To understand the resulting changes in the far field directivity 

pattern, each jet is considered to be an isolated independent acoustic source 

operating in the presence of an adjacent flow field. The following discussion, which begins with the source jet, uses the schematic in Figure 28 to 

illustrate the acoustic wave interactions between two adjacent jets. 

Radiation from the source jet impinges on the shielding jet as it propagates towards the observer at a specific sideline angle (Fig. 28a). During 

the acoustic wavefront interaction with the shielding jet several mechanisms 

can conceptually result in a noise reduction. First, refraction, reflection, 

and turbulence scattering of sound to other sideline angles can decrease the 

noise level sensed at the fixed observer station. It should be noted, 

however, that since acoustic energy is conserved during these different 

interaction processes, noise levels must increase at other observer orientations. Benefits achieved at the fixed sideline observer station in Figure 2 

may, therefore, create acoustic penalties at other radiation angles. This 

observation represents the basis for the extensive azimuthal and polar 

acoustic survey in the present experiment. 

The second mechanism which potentially reduces source jet noise involves 

phasing of the acoustic waves after interaction with the shielding jet. In 

this case diffracted and/or scattered waves can combine with each other and 

with the transmitted (refracted) waves to cancel acoustic pressure waves at 

47 
48 

the observer station thereby, reducing the noise levels. However, this same 

phasing mechanism can also increase noise due to wavefront reinforcement. 

In summary, the source jet noise changes observed in the common plane of 

the two jets in Figure 2 are considered to be controlled by redirection of the 

source jet radiation to other observer angles and phasing of transmitted and 

diffracted waves. In the limit of total redirection of all acoustic radiation, the source jet would be completely masked and only the shielding jet 

noise would be sensed by the observer. 

With the discussion of the source jet completed, the shielding jet can 

now be considered (Fig. 28b). Here the radiation pattern is controlled by a) 

acoustic waves propagating directly from the shielding jet to the observer and 

b) waves initially radiated towards the source jet. In the latter case, the 

waves incident on the source jet are reflected and propagate towards the 

shielding jet where they again encounter the same transmission phenomena 

described above. Similar to the source jet case, a noise reduction can occur 

involving a) redirection of the reflected waves, and b) phasing between the 

direct acoustic radiation (from the shielding jet) and the reflected waves 

(after diffraction, turbulence scattering and transmission through the 

shielding jet). 

In the limit of total reflection of the shielding jet noise by the source 

jet and no redirection of this reflected sound, the observer hears a second 

source with the same strength as the shielding jet. This represents a 3 dB 

increase in noise relative to the two independent jets in the dual jet system 

(or a 6 dB difference relaiive to a single jet). In contrast if the reflection coefficient is zero or all reflected energy is redirected by the shielding jet to other sideline angles the observer senses only direct radiation 

from the shielding jet. 

It should be noted that larger noise reductions or n01se 1ncreases are 

possible if the two jets contain coherent noise source regions. In this case, 

phasing between the source regions results in cancellation or reinforcement of 

acoustic wavefronts, thereby, accentuating the effects of shielding. However, 

coherence between the jets requires the jet flows to be acoustically coupled, 

a condition which is not expected for the random noise distributed source 

regions of the present dual jet geometry. Acoustic coupling, is possible with 

a supersonic dual jet flow with screech present. Since this operating condition is outside the scope of the present study, noise reductions or increases 

due to phasing between coherent source regions of the two adjacent jets is not 

considered to be an operative physical phenomenon. 
Quantitative Definition of Shielding Effect 

A quantitative definition of the jet shielding phenomenon can now be 

formulated based on the fundamental noise reduction mechanisms described in 

the previous subsection. The formulation employs the under-the-wing engine 

configuration shown in Figure 2 although the results apply in general to sideby-side engine geometries. 

In the absence of shielding, the observer senses acoustic radiation from 

each jet exhaust flow. Considering the individual jet flows to be incoherent 

sources (no acoustic/flow coupling), the measured total power spectral density, P¥, considering adjacent engines is given by p¥ = Pf + PI· Here pt and P~ 

are the individual acoustic power spectral density contributions which are a 

function of f, R, e and ~. 

Simplifications, such as assuming a geometric far field condition for the 

observer, would replace the different engine-to-observer distances, Rl and R2 

in the expression for PI, with a common distance. However, such differences 

in distance are retained for the purpose of generality since aircraft may be 

in close proximity to sideline observers during ground operations where the 

assumption of Rl * R2 does not apply. ~lso, by retaining the specific 

distance dependence, the equation for Pf duplicates the present experimental 

test geometry. Experimentally, geometric far field conditions could not be 

achieved for the largest dual jet spacing corresponding to SiD = 8.1 or S = 36 

cm. (A further discussion is given in the next subsection.) 

with shielding operative, p¥ is replaced by P6. The resulting change 1n 

noise relative to two independent jets is then defined by the expression 

f,SPL = lOloglO 

2 

PD 

PI + P~ 

(35 ) 

The parameter f,SPL can also be defined relative to a single jet. In this 

case the denominator in Equation 35 is replaced by the mean-squared sound 

pressure level from a single jet. Ideally, for large jet-to-observer 

distances PI = P~ so that only a single measurement is needed for the denominator. However, due to the differences in jet-to-observer (microphone) 

distances in the present study, PI * PI. In this case the single jet 

49 
50 

reference level must be represented as the average of the dual independent 

jets, i.e., 1/2 CPt + PI). Relative to the single jet, Equation 35 becomes 

lISPL lOloglO 

2 

PD 

1 ( 2 2) '2 PI + P2 

(36 ) 

This single jet reference level was selected in the present study since it 

represents the minimum noise level possible when one jet in the incoherent 

dual jet system is totally shielded (assuming phasing is not operative). In 

this case, P~ = PI and lISPL = 0 so that relative to a single jet, the dual jet 

generates the same noise level. On the other hand, with shielding inoperative, lISPL = 3. The 3 dB change in sound pressure level now indicates that 

the dual jet system is perceived as two independent jets in comparison to the 

single jet. 

Acoustic Data Acquisition and Data Reduction Procedure 

Single Jet Reference Level - To determine the shielding parameter lISPL 

from the experimental data, each test condition was investigated with a) the 

dual jet configuration and b) a single jet operating at the same flow condition. The latter measurement was used to synthesize the dual independent jet 

configuration needed in the denomenator of Equation 36 (see Appendix C for 

details). Due to the axial symmetry of the single-jet directivity pattern, 

the acoustic survey was reduced to one data record. In this case the shielding jet was used in conjunction with the fixed microphone array. During this 

measurement the source jet air supply line was terminated with a cap confining 

the flow to the shielding jet. To avoid converting the test arrangement from 

single to dual jet configurations at each test condition, all single jet 

measurements were conducted after completion of the dual jet study. 

It should be noted that early efforts to change the operating configuration using a butterfly valve installed in the source jet air supply line downstream of the common plenum were not successful. Noise generated by the valve 

in addition to a small pressure loss across the valve resulted in background 

noise and a significantly dissimilar jet operating condition. The use of two 

separate air supply systems was also initially considered during the facility 

hardware design phase but the potential dissimilar operating conditions 

resulted in selection of the common plenum shown in Figure 8. 
Corrections to Acoustic Data - A jet noise velocity scaling law was also 

applied to the data to correct for small variations in jet exit pressure and 

temperature as the jet rotated. These minute changes occurred as the control 

valve supplying the common plenum responded to the gradual decrease in the upstream facility pressure during the approximately 8 minute data acquisition 

phase. Details of the correction procedure are discussed in Appendix B. Such 

corrections were not necessary for the supersonic data since the test time was 

short (continuous source jet rotation was not applied). Also the operating 

pressures were held to a tolerance of ±O.lS psi to avoid screech tones. 

Although relative humidity was monitored in the anechoic chamber during 

each test condition, corrections for humidity effects were not applied to the 

acoustic data. This decision was based on the detailed discussion presented 

in Appendix B. 

51 

EXPERIMENTAL ASSESSMENT OF DUAL JET SHIELDING 

Objective 

The objective of this phase of the study is to experimentally assess the 

acoustic shielding of jet exhaust noise by an adjacent jet flow field. The 

shielding mechanism is investigated using a dual jet system with variable 

spacing between the parallel jet flows. Tests performed over a range of jet 

Mach number, jet temperature, and jet spacing determine the shielding sensitivity to isolated changes of each parameter. 

Several evaluation procedures are employed in the assessment of the 

experimental data. First, changes in the dual jet noise spectrum shape, 

plotted as a function of Strouhal number, are examined at selected radiation 

angles as the test conditions vary. This approach provides a simple evaluation of the shielding effectiveness relative to the jet noise spectrum. In 

addition, changes in azimuthal or polar directivity shape are examined at 

fixed Helmholtz numbers. (The Helmholtz number, kD, is defined as the product 

of wavenumber and frequency). The objective in this case is to assess the jet 

noise reduction (due to shielding) and jet noise increase (due to reflections) 

over the azimuthal range 0 0 

( a ( 1800• Finally, the complex interdependence 

of jet noise source frequency and radiation angle is evaluated in a series of 

sound pressure level contours plotted as a function of Strouhal number versus 

azimuthal angle for various polar angles. These results provide guidelines 

for application of the shielding concept as a jet noise reduction technique. 

In each of the above evaluations, the effect of shielding is defined as 

the difference between the sound pressure levels generated by the dual jet 

configuration and a single jet operating at the same flow condition. The 

single jet is selected as a reference since it represents the minimum noise 

level when one jet in the dual jet system is totally shielded (See section 

titled Data Acquisition and Data Reduction Procedure for a discussion of the 

shielding mechanism and the minimum noise level). 

The experimental results described in the present section also form the 

basis for the critical evaluation of the jet noise shielding theory. However, 

prior to comparing experimental and predicted shielding effects, the point 

source/single jet combination which best models the dual jet geometry must be 

selected. Based on this selection, theoretical predictions are presented for 

comparison with the dual jet random noise distributed source field. 

It should be noted that evaluation of the shielding effect as a function 

of Strouhal number and Helmholtz number represents evaluating the phenomenon 

from two different, but important, viewpoints. The first approach identifies 

the frequency domain of the jet noise generation for which shielding provides 

53 
54 

a noise reduction. The second viewpoint addresses only the dependence of the 

propagation phenomenon on the acoustic source frequency and the shielding jet 

characteristics. This latter approach is necessary for theory-experiment 

comparisons and represents an assessment of the propagation phenomenon. 

Spectrum Dependence on Isolated Parameters 

The Shielding Effect - To show the general effects of introducing an 

adjacent shielding jet on the source jet radiation, results are presented for 

1/3 octave band spectra for four cases. Two of the conditions correspond to 

the dual jet at an observer azimuthal angle of e = 90° and 180°. For comparison purposes the two remaining conditions correspond to single jet measurements synthesized according to the denominator of Equation 36, at the same 

azimuthal angles. Here the e = 90° case represents the dual jet orientation 

associated with maximum possible noise reduction since the noise from the 

source jet is masked by the shielding jet. On the other hand, the e = 180° 

dual jet measurement conceptually represents the orientation for maximum noise 

radiation since the observer senses sound from both jets. (Note that with 

identical flows from each nozzle in the dual jet system, the acoustic radiation pattern is expected to be symmetric about e = 90°. Thus, either e = 0° 

or 180° can be used in this evaluation.) 

The noise radiation dependence on these different dual-jet orientations 

can now be illustrated using the spectra in Figure 29a. The test conditions 

associated with each spectrum in this figure correspond to M = 0.6, 

To = 300 0K, SiD = 8.1 and ~ = 40°. Sound pressure is presented in terms of 

1/3 octave band levels. Indicated values are obtained by averaging the 

azimuthal directivity data (to be described shortly) within a ±SO region 

centered at e = 90° or 180°. Frequency dependence is given in terms of 

Strouhal number to permit comparison with other jet operating conditions. 

The effectiveness of the shielding mechanisms in the common plane containing the two jets is determined from the parameter, 8SPL(e = 90°), which 

represents the difference between the dual jet e = 90° measurement and the 

single jet measurement in Figure 29a. The calculated values in Figure 29d 

show that near the spectrum peak, 8SPL is approximately 2.5 dB. Jet shielding 

appears, therefore, to be small. In contrast, at high Stouhal number, 

8SPL(e = 90°) ~ 1.5 dB indicating the shielding mechanism is operative. 

These results describe the effectiveness of masking one jet when the 

observer is in the common plane of the dual jet system. However, an observer 

at an orientation normal to this common plane (e = 180°) senses the degree to 

which the dual jet system operates as two independent source jets. This feature is determined from the parameter, 8SPL (e = 180°). Based on Figure 29d, 

this parameter is approximately 4 dB throughout the acoustic spectrum. Since 

two non-interacting jets would give 8SPL = 3 dB, it appears that excess noise 

is radiated at e = 180°. 
One potential source of the excess jet noise at e = 180° is the aerodynamic interaction of the two jets. In concept, such an interaction could 

alter the acoustic source distribution by creating a merged jet flow field. 

But, aerodynamic measurements for this test condition demonstrated (Fig. 23) 

that the dual jet merger is delayed until x/D = 23. Source alteration would, 

therefore, be controlled by acoustic source regions beyond this axial station. 

Based on directional microphone measurements (ref. 44) acoustic sources at 

x/D ~ 23 contribute primarily to the spectrum range St ~ 0.1. Since the 4 dB 

spectrum difference in Figure 29d occurs over the range 0.1 ~ St ~ 10 aerodynamic merging is not expected to be the origin of the observed excess noise. 

(For smaller jet spacing, source alteration was postulated to be an effective 

noise mechanism as described in the subsection titled Lateral Spacing 

Effects). 

In the absence of source alterations, a possible explanation for the 

excess noise at e = 180° is the reflection and turbulence scattering of sound 

from one jet by the flow field of the adjacent jet. Support for this postulated mechanism is provided by detailed azimuthal surveys which indicate a 

consistent trend of excess noise when the far field microphone array is 

approximately normal to the plane of the dual jet system (e = 0° or 180°). 

Furthermore, excess noise has been observed in previous experimental studies 

as will be described shortly. Finally, the present analytical model for the 

dual jet shielding mechanism predicts bSPL noise levels exceeding 3 dB at 

large azimuthal angles as described in theory-experiment comparisons in the 

following subsections. 

Mach Number Dependence - The sequence of differential spectra shown in 

Figure 29d, 2ge, and 29f can now be used to establish the effect of Mach 

number on the dual jet shielding process. Similar to the approach developed 

in the previous subsection, conclusions are drawn from comparison of single 

jet and dual jet spectra at e = 90° and 180°. In each case the polar angle 

corresponds to $ = 40°. Data is presented only for the largest jet spacing 

test condition (SiD = 8.1) to isolate the Mach number effect. 

Measurements described here are also limited to unheated jet flows with 

the total temperature (To = 300 0K) approximately equal to the ambient air 

temperature, Ta. By confining the present evaluation to unheated jets, 

changes due to temperature gradients across the heated jet shear layer are 

minimized, thereby isolating the Mach number discontinuity dependence. This 

approach was considered reasonable since the ratio of jet static temperatureto-ambient temperature, Ts/Ta' assumed values of 0.94, 0.85 and 0.7 for 

the three Mach numbers M = 0.6, 0.94, and 1.46. Based on the present analytical model, the shielding mechanism would not be sensitive to these temperature 

discontinuities at the jet shear layer interface. 

The effect of Mach number on jet shielding can now be determined by comparing bSPL(e = 90°) for the sequence of spectra shown in Figure 29. The 

55 
56 

first of the required figures (Fig. 29d) was evaluated in detail in the 

previous subsection. Using this result as a reference the trend in Figure 29 

indicates that shielding in the plane of the jet becomes more effective as 

Mach number increases. For example near the spectrum peak, ~SPL decreases 

from approximately 2.5 dB to 1.25 dB as Mach number changes from M = 0.6 to 

0.94. However, with an additional increase in Mach number to M = 1.46 the 

shielding effect remains constant. Similar trends occur at Strouhal numbers 

below the spectrum peak, with the largest changes again occurring between 

M = 0.6 and 0.94. In general, the onset of shielding shifts to lower Strouhal 

numbers as Mach number increases. 

While shielding effectiveness increases with Mach number near the spectrum peak (and at lower Strouhal numbers), changes at high Strouhal number are 

weaker. A comparison of the sound pressure level difference at St = 2 indicates an improvement in shielding effectiveness of, at most, 0.25 dB between 

M = 0.6 and 1.46. This change in ~SPL is small because the magnitude of the 

noise reduction approaches the maximum expected value (~SPL = 0 dB in the 

absence of phasing) at M = 1.46 since ~SPL is approximately 1.25 dB. 

The degree to which the dual jet system is perceived as two independent 

source jets at a = 180° as Mach number increases can also be determined from 

Figure 29. Here ~SPL(a = 180°) maintains a consistent value of approximately 

4 dB as Mach number is varied. Since ~SPL exceeds the 3 dB value associated 

with two independent jets, this dual jet radiation corresponds to excess 

noise. Similar to previous discussions, the origin of this excess noise is 

postulated to be the reflection and scattering of sound from one jet by the 

adjacent jet. This mechanism is shown to be Mach number independent based on 

Figure 29. 

Temperature Dependence - Evaluation of the heated dual jet data following 

completion of the test program indicated an anomolous acoustic attenuation in 

the experimental measurements. Sound pressure level differences between the 

dual jet and the single jet resulted in negative values for ~SPL in the common 

plane of the dual jet system. This efect is best explained with the azimuthal 

directivity data discussed in a following subsection. Interpretations regarding the influence of temperature on jet shielding can, however, still be 

postulated from the measured data and these observations are presented as part 

of the azimuthal directivity discussion. 

Lateral Spacing Dependence - The influence of jet spacing is shown by the 

series of spectra in Figure 30 as SiD varies from 8.1 to 3.1. Here Mach number and jet temperature are held fixed at M = 0.94 and To = 300 0

K, while the 

polar radiation angle corresponds to W = 40°. Note that the minimum SID value 

in this sequence is slightly larger than the spacing conditions tested during 

the aerodynamic study where values of SiD = 2.7 and 2.3 were employed. The 

difference is due to the addition of a clamping mechanism during the acoustic 
study to retain the source jet at a constant radius as it rotated. Such 

hardware was not required for the stationary aerodynamic measurements permitting a closer jet spacing. 

Relative to the 6 = 90° measurenientplane, shielding is insensitive to 

spacing changes at all Strouhal numbers as SiD decreases from 8.1 to 5.5. For 

example, at Strouhal numbers above the spectrum peak, ~SPL (6 = 90°) is 

consistently 1.25 to 1.5 dB. In contrast, at low Strouhal numbers, shielding 

is weaker with ~SPL = 2 or 3 dB. Near the spectrum peak, shielding remains 

constant with ~SPL = 2.5 dB approximately. 

The spectrum at 6 = 90° for the closest spacing, SiD = 3.1, is similar to 

the SID = 8.1 test condition at high Strouhal number. The only exception is 

the Strouhal range below St = 0.4. In this region, higher absolute sound 

pressure levels occur with ~SPL even exceeding 3 dB. This indicates an 

increase in noise in the common plane of the dual jets for small spacing. It 

is postulated that for the close spacing condition, changes in acoustic source 

distributions are responsible for the noise increase. This is based on directional microphone measurements which show the acoustic source region responsible for the spectrum range below St = 0.4 is located downstream of X/D = 8. 

Based on Figure 23, jet flow merging begins at X/D = 7. Consequently, source 

alterations are considered to be the origin of the increased noise at low 

Strouhal number and small SiD. 

Phasing was also considered to be a possible explanation for the nOLse 

increase in the common plane at St < 0.4. However, in the St range, differences in propagation paths between diffracted and transmitted wavefronts were 

small in comparison to the acoustic wavelength. Consequently, phasing was 

postulated to be weak in this instance. However, other examples of noise 

dependence on phasing between the source jet and shielding jet were observed 

and will be described later. 

For the 6 = 180° orientation, the sequence of spectra in Figure 30 show 

a small decrease in excess noise as spacing changes from SiD = 8.1 to 5.5. 

This trend, however, is reversed by a 2 dB increase in ~SPL near the spectrum 

peak as spacing changes to SiD = 3.1 indicating significant excess noise. 

In general the value of ~SPL exhibits excess noise at 6 = 180° irrespective of 

the spacing. 

Summary and Evaluation of Shielding Effect on Jet Noise Spectrum - For 

non-interfering dual jet flow conditions, shielding is operative in the common 

plane of the dual jet system with the largest effect occurring for increasing 

subsonic Mach numbers. Simultaneously, increasing Mach number shifts the 

onset of shielding to lower Strouhal numbers. 

57 
58 

Specifically, for low Mach numbers (M = 0.6) shielding provides a 1.5 dB 

noise reduction but only at Strouhal numbers above the jet noise spectrum 

peak. As Mach number increases to M = 0.94, the onset of shielding occurs at 

lower frequencies so that approximately a 2 dB noise reduction exists at the 

jet noise spectrum peak. However, a further increase to M = 1.46 has little 

effect on the jet noise reduction with at most a 0.5 dB improvement in shielding effectiveness below the spectrum peak. 

Jet spacing has little effect on jet noise shielding in the common plane 

of the dual jet system as SiD decreases. The only exception occurs at the 

closest spacing of SiD = 3.1 and Strouhal numbers below the jet noise spectrum 

peak (St < 0.4). In this case, acoustic source alteration due to aerodynamic 

merging of the dual jet flow field increases the noise radiation by approximately 1 dB. 

Observers situated at 90° to the common plane of the dual jet system, 

experience excess noise relative to the noise radiated by two independent jets 

at the same orientation. The excess noise level is approximately 1 to 1.5 dB 

above the noise level of the independent jets and is essentially invariant 

with Mach number. The excess noise is also independent of spacing for SiD 

values of 8.1 and 5.5 but for the closest spacing a significant increase 

occurs near the spectrum peak. 

lated to be the reflection and 

adjacent jet for large spacing 

The origin of this additional noise is postuscattering of sound from one jet by the 

and source alteration at the closest spacing. 

Azimuthal and Polar Directivity 

Objective and Approach - The previous discussion of the shielding 

mechanism employed spectra measured at two polar angles, a = 90° and 180°. 

while W was fixed at 40°. Although important conclusions regarding the 

shielding effectiveness were developed, the dual jet sound pressure level 

dependence on azimuthal and polar angle was not defined in detail. The objective of the following subsection is to establish the directivity dependence on 

each of the parameters evaluated experimentally during the present study. In 

addition, theoretical predictions based on different analytical combinations 

of the point source/single jet geometry used to represent the dual jet will be 

compared with measurements. 

General Features of Azimuthal Directivity - Prior to evaluating the 

directivity dependence on each parameter, general features of the radiation 

pattern for the dual jet system will be established. Figure 31 shows the 

sound pressure level measured at W = 20° for the M = 0.6, T = 300 0K, SiD = 8.1 

test condition. The resulting data curve corresponds to the 200° rotation 

range of the dual jet system shown in Figure 7. The measurement, presented 

for the 1/3 octave band centered at 4 kHz (Helmholtz number, kD = 3.22) is 

normalized by the synthesized single jet amplitude at a = 90°. 
Based on Figure 3i, the directivity pattern is sy~metric about 6 = 90°. 

This result is expected since each jet in the dual jet system operates at the 

same test condition. Figure 31 also shows that the local maxima can occur 

within the 0° ( 6 ~ 180° azimuthal range. In particular, the maxima at 30° 

and 145° were not expected from previous studies which were predominantly 

confined to measurements at 6 = 90° and 180° (or 0°). This is because the 

earlier studies assumed the directivity pattern varied monotonically from a 

minimum at 6 = 90° to a maximum at 6 = 0° or 180 0 (the maximum was based on 

the viewpoint that 6 = 0° or 180° corresponded to the orientation for which 

the dual jet system radiated as two independent jets). Consequently, measurements were limited to a few azimuthal angles and the directivity details 

associated with the dual jet radiation field were not evident. 

The local maxima in Figure 31 demonstrates that the dual jet system 

interacts acoustically at angles outside the shielding regime. Thus, in addition to shielding at 6 = 90°, excess noise occurs at other angles. The origin 

of the excess noise will be shown shortly, using the analysis, to be due to 

acoustic reflections from the adjacent jet (scattering by turbulence is also a 

valid mechanism although the analysis does not model this phenomenon). 

The effect of reflections is illustrated using geometric acoustics in the 

sketch of Figure 32. Here, equal angles of incidence and reflection result in 

the observer sensing reflected radiation in addition to direct radiation from 

the source jet when 6 = 135 o. Similarly, reflections of the shielding jet 

radiation by the source jet (not shown) may result in additional noise perceived at the observer station. (However, as will be indicated shortly, this 

latter interaction is a small contribution to the measured noise due to the 

1/3 octave band analysis procedure). The total sound field, therefore, 

contains excess noise when compared with the direct radiation from the two 

acoustically noninteracting jets. These acoustic interaction features will be 

discussed farther in the following subsections. 

It should be noted that the symmetry of the excess noise peaks in Figure 

31 confirms the anechoic characteristics of the facility. A non-anechoic 

environment would create a non-symmetric directivity pattern as the source jet 

is rotated. Thus, the local maxima are not created by reflections within the 

anechoic chamber. 

Verification that the measured peaks at 6 = 30° and 145° are a direct 

consequence of the shielding jet is given by the azimuthal directivity plots 

in Figure 33a. Here the azimuthal range is limited to 80° ~ 6 ~ 190 0 since 

the radiation patterns have been shown to be symmetric about 6 = 90°. 

Measured absolute sound pressure levels are presented for the same test condition shown in Figure 31. Two data sets are indicated corresponding to a) the 

dual jet system, and b) the isolated source jet with the shielding jet capped. 

The constant sound pressure level associated with the isolated source jet 

59 
60 

directivity pattern confirms that the local maxima for the dual jet system are 

created by the presence of the shielding jet. Additional directivity patterns 

are given in Figure 33b for the source jet alone at frequencies spanning the 

acoustic spectrum range. These curves demonstrate that the source jet rotation is not the origin of the local maxima. 

The constant source jet directivity patterns in Figure 33b also confirm 

the simple point source assumption used in the distance correction applied to 

the term in the denominator of Equation 36. Specifically, the correction 

accounted for the source jet-to-microphone distance changes which occurred 

as the source jet rotated during the dual jet study. The correction procedure 

modelled the two jets as point sources centered at the nozzle exit plane. 

To check this point source approach, measured sound pressure levels for the 

single jet at each azimuthal angle in Figure 33 were converted to a common 

source distance corresponding to the 3m radius used for the microphone array. 

This simple conversion employed the same inverse square law decay relationship 

used in calculating the synthesized single jet reference levels (See Appendix 

C). If this approach appropriately modeled the distributed source region of 

the actual jets, then a constant sound pressure level would be expected during 

the single jet azimuthal rotation (an amplitude change of 0.9 dB would occur 

without this correction for the SiD spacing condition shown in Figure 33). 

The constant amplitudes in Figure 33 demonstrate that the point source representation adequately compensates for any distance changes occurring in the 

experimental data. 

Figure 33b also shows that, within the accuracy of the measurements, each 

microphone continues to sense the same polar directivity pattern as the source 

jet rotates. This is critical since jet noise directivity patterns are known 

to change rapidly near the jet axis. In the present experiment, the fixed 

microphone array centered on the shielding jet could sense different source 

jet polar radiation information as e varies. The impact on the combined dual 

jet radiation could lead to erroneous directivity information as illustrated 

schematically by the different acoustic rays, ~l and ~2' in Figure 34. But, 

the constant sound pressure levels for the single jet in Figure 33b establishes that directivity pattern changes have a nominal impact. 

Selection of Analytical Model Simulating Dual Jet Geometry - To permit 

assessment of the theoretical predictions relative to the shielding effects 

described in the previous subsection, the appropriate analytical model which 

best represents the dual jet geometry must first be selected. The issues 

controlling the selection process are illustrated in Figure 3S where the dual 

jet configuration in Part (a) is modeled as a sum of the separate point 

source/single jet geometries shown in Part (b). In the case of the observershielding jet-point source configuration the point source rotates about the 

shielding jet. On the other hand, for the observer-point source-reflecting 

jet geometry, the reflecting jet rotates about the point source. Assuming the 
acoustic point sources representing each jet are incoherent, superposition of 

the analytical predictions for the separate geometries in Part (b) might be 

expected to provide the best simulation of the dual jet problem. It should be 

noted that the shielding jet and reflecting jet are not noise sources in the 

separate analytical models. 

Test Case - Predictions using this superposition model are presented 

in Figure 36 for a selected test case. Here, the input parameters correspond 

to the experimental test condition presented in Figure 33a. Calculated sound 

pressure levels are normalized relative to the direct radiation from each 

acoustic point source. This normalization, which gives ~SPL, is identical to 

the single jet reference level used for the experimental data. The only 

exception is that the theory is a geometric far field model which is insensitive to the different source-to-observer distances in Figure 35b. Consequently PI = PI in Equation 36. In contrast, these differences in distance 

influenced the experimental data and resulted in normalizing the measured dual 

jet data by the synthesized average single jet data which is a function of e. 

Once the normalization is completed distance effects are removed from the 

measured data permitting direct comparison with the separately normalized 

prediction. 

Locating the shielding jet between the point source and the far-field 

observer, as illustrated in Figure 35b, results in predicted ~SPL levels given 

by Curve 1 in Figure 36a. Here negative sound pressure levels occur near 

e = 90° indicating that shielding is operative. However, near e = 130° noise 

levels increase due to reflection of sound in the direction of the observer as 

illustrated earlier in Figure 32. In this case, the phasing between direct 

and reflected point source jet radiation creates reinforcement of the acoustic 

wavefront. This increases the sound pressure level relative to the direct 

radiation from the source alone. 

A further increase of azimuthal angle again results in negative ~SPL 

values near 8 = 140°. Negative values are now considered to be due to cancellation between the direct and reflected wavefronts. Without phasing to create 

a cancellation of acoustic pressure wavefronts such a minimum cannot occur. 

Reversing the above desired jet and acoustic source pos1t1ons gives Curve 

2. Positive ~SPL values now occur at 8 = 90° due to the in-phase superposition of the direct and reflected radiation. In contrast, negative values 

exist at other angles due to cancellation of the wavefronts. 

The total predicted field sensed at the observer station is given by 

Curve 3 in Figure 36a which is obtained by mean-square superposition of Curves 

1 and 2. Assessment of the resulting superposition analytical model is based 

61 
on comparison with the experimental data also shown in the same figure. 

Measured results show reasonable agreement with theory near the common plane 

of the dual jet system. Also, the experimentally observed increase in ~SPL 

which begins near e = 110 0 and the excess noise peak near e = 1300 are calculated. Finally, the oscillatory features at larger azimuthal angles are 

predicted. However, it should be recognized that the random distributed 

source characteristics of the actual dual jet geometry smooth out the oscillatory features in comparison to the analytically predicted details. 

62 

Frequency or Helmholtz Number Sensitivity - While the good comparisons in Figure 36a suggest closure of the theory-experiment assessment, the 

issue of Helmholtz number (or frequency) sensitivity remains to be addressed. 

This is important since phasing between direct and reflected acoustic wavefronts has been incorporated in the analytical model. Figure 37a evaluates 

the predicted sensitivity by presenting ~SPL curves for frequencies within the 

1/3 octave band centered at f = 4 kHz or kD = 3.22. The large variation in 

~SPL values within the 1/3 octave band shows that the analytical model is 

highly sensitive to Helmholtz number. In particular, the good agreement 

between theory and experiment in Figure 36a must, for the moment, be regarded 

as coincidental. 

Gerhold (Ref. 18) did not report the above described Helmholtz senSLtLVLty. Consequently, conclusions regarding the absolute magnitude of his 

predicted directivity patterns must be carefully evaluated. While his calculated results are numerically correct, Figure 37 indicates that small changes 

in Helmholtz number give dramatically different results. 

The origin of the frequency dependent variations near e = 90 0 was traced 

to the observer point-source reflecting-jet geometry shown in Figure 35b. 

This is demonstrated in Figure 38a where predictions, for the individual point 

source/single jet geometries represented by Curves 1 and 2 in Figure 36a, are 

presented over a frequency range which spans the 1/3 octave band centered at 4 

kHz. The calculations in Figure 38a are confined to e = 90 0

, W = 40 0 

as the 

frequency is varied. The observer-jet-source curve (No.1), which represents 

the shielding effect, varies monotonically. In contrast Curve 2 displays the 

oscillatory features observed in Figure 37. These different far field radiation characteristics 

Figures 38b and 38c. 

tion from Figure 38c 

at low frequencies. 

continue to exist at all frequencies as indicated by 

(Figure 38c shows only Curve 1). An important observais that noise reduction due to shielding is non-existent 

Predictions Based on 1/3 Octave Bands - The above described oscillatory nature of the calculated ~SPL level complicates the comparison of 

theoretical calculations with experimental data. A possible solution to this 

problem is to integrate the predicted spectrum to give 1/3 octave band predictions similar to the measured data. The integrated result is then normalized 
by the bandwidth which is shown in Figure 38a for the 4 ~~z test case. Based 

on this approach, the discrete tone calculation in Figure 36a is replaced by 

the 1/3 octave band prediction in Figure 36b. A comparison of Curve 2 in each 

calculation shows large differences. (On the other hand there are only small 

differences for Curve 3 with the exception of the e = 90 0 prediction and the 

minima at large azimuthal angles). 

The apparent small change in Curve 3 between Figures 36a and 36b is 

coincidental. As indicated by Figure 38a, the frequency integration range 

extends over one cycle of the period for Curve 2. The integrated result for 

e = 90 0 (~SPL = 1.7dB) is within 0.4dB of the discrete tone prediction 

(~SPL = 1.3dB) at f = 4 kHz. If the frequency integration range is shifted so 

as to center it at 4.3 kHz, the same integrated result of ~SPL = 1.7 dB is 

obtained since the oscillatory feature of Curve 2 is periodic. But the 

discrete tone calculation, in this case, gives a different value of ~SPL = 2.5 

dB. Furthermore, increasing or decreasing the filter bandwidth gives a 

different integrated result. 

The above observations provide guidance on the application of the 

discrete tone acoustic source model for experiments involving a random noise 

source. If acoustic measurements are obtained with a large bandwidth filter, 

then application of the discrete tone model will require calculating an 

integrated spectrum which is then normalized by the measurement bandwidth. 

For the example given in Figure 38 this represents calculating the shielding 

effect within the indicated 1/3 octave bands. This appoach is primarily 

required for the observer-source-jet geometry represented by the cyclic 

variations in Curve 2 of Figure 38b. In contrast the observer-jet-source 

geometry can be approximated by the calculated ~SPL at the 1/3 octave band 

center frequency. 

Final Selection of the Analytical Model - Implementing the 1/3 

octave band calculation involves long computing times since the discrete tone 

calculation must first be performed with small frequency increments over the 

complete acoustic spectrum. This problem is evident in Figure 38b where 

numerous cycles of Curve 2 must be calculated before the integrated ~SPL value 

can be determined. Due to computing time constraints during the present 

study, the following simplification was employed to circumvent these difficulties. Based on Figure 38a, the integrated value of ~SPL associated with the 

1/3 octave band calculation is comparable to the average ~SPL value for one 

period of the oscillations in Curve 2. Furthermore, the average value is ~SPL 

(average) = 0 dB as indicated by the ~SPL value for Curve 2 at e = 90 0 in 

Figure 36b. This approximation of ~SPL (average) = 0 dB over the 1/3 octave 

band range continues to hold over a large of azimuthal angles as indicated by 

visually examining the predictions for Curve 2 in Figures 39a-3ge and Curve 2 

in Figure 36b. The only exceptions occur over a small angle range between e = 

160 0 anb 180 0 as indicated in Figure 36b. 

63 
64 

While the above observations are based on predictions for Curve 2 at low 

frequencies similar results are expected at high frequencies. For example, at 

20 kHz (Figure 38b) six cycles of the ~SPL function occur within the associated 20 kHz 1/3 octave band. In this case ~SPL (average) normalized by the 

filter bandwidth will again give, 0 dB. 

Application of the above argued approximation ~SPL = 0 dB for 1/3 octave 

bands is equivalent to removing the reflecting jet in the lower portion of 

Figure 35b. The dual jet configuration is then modeled by the observershielding jet-point source and observer-point source geometries shown in 

Figure 35c. Linear summation of sound pressure levels associated with these 

two geometries results in the predicted frequency dependence given by Curve 4 

in Figure 39. Previous oscillatory features associated with Curve 3 are 

removed by this approach. 

Removal of the reflecting jet (Fig. 35c) does not invalidate the physical 

arguments given earlier in the subsection titled Test Case. The earlier 

discussion explained the local increase in noise near e = 145° is based on 

phasing between direct and reflected sound (Fig. 32). This mechanism still 

exists in the final analytical model selected here. Following the ray paths 

in Figure 32, direct radiation from the source jet and reflected radiation 

(originating at the source jet) from the shielding jet are modeled by the 

source-shielding jet-observer model in the upper portion of Figure 35c. Also, 

the direct radiation from the shielding jet in Figure 32 is modeled by the 

source-observer combination in the lower portion of Figure 35c. Where the 

final analytical model differs is that radiation from the shielding jet 

reflected by the source jet in Figure 32 is not modeled. (Ray paths not shown 

in Figure 32 for this feature.) 

The above arguments contain a recognized limitation for e = 180° (or 0°) 

in Figure 32. In this case, the source jet and shielding jet are identical 

relative to the observer. Now radiation from the shielding jet reflected by 

the source jet located at e = 180° is not modeled. This limitation of the 

current analytical model is exemplified by the lower sound pressure level 

predictions near e = 180°. A more accurate model would include this effect. 

This could be achieved by using the full analytical model in Figure 35b. 

However, this would require long computing times to calculate the complete 

discrete tone spectrum needed for the 1/3 octave band response associated with 

the observer-source-jet geometry. It is recommended that future investigators 

implement this prediction procedure. 

Experimental Assessment of the Final Analytical Model - The 

predicted azimuthal directivity pattern for the final combination of analytical point source/ single jet geometry is shown in Figures 40-42 for a range of 

frequencies including the previous f = 4 kHz' (kD = 3.22) test case. The 
selected frequencies span the acoustic spectrum for the jet operating condition shown in Figure 29a with the 4 kHz result defining the directivity shape 

near the jet noise spectrum peak. Also shown in Figure 40 is the experimentally determined directivity pattern. 

The experimental results for the 800 Hz (kD = .644) test case (Fig. 40a) 

show that shielding is non-existent in the common plane of the dual jet 

system. This agrees with the conclusions obtained earlier from the acoustic 

spectrum in Figure 29a. As e increases from 90° to 180°, excess noise is 

observed. The increase is, however, monotonic without the previously observed 

local maxima. Comparison of the above described experimental results with the 

corresponding predictions (Fig. 40b) shows good agreement near e = 90°. In 

addition, the monotonic increase in bSPL with increasing e is predicted. 

A comparison of the measured and predicted results at 4 kHz (kD = 3.22) 

is shown in Figure 4lb. The shielding effect at e = 90° is closely predicted. 

Also, the experimentally determined increase in bSPL near e = 110° in addition 

to the oscillatory features at larger azimuthal angles is calculated. For 

example, the excess noise peak near e = 130° is closely predicted. However, 

it must be recognized that the random distributed source characteristics of 

the actual dual jet geometry smooth out the oscillatory details predicted 

analytically at large azimuthal angles. 

The experimentally determined azimuthal directivity pattern for f = 20 

kHz (kD = 16.1) is shown in Figure 42a. Relative to the 4 kHz test condition, 

a small improvement in shielding effectiveness occurs at e = 90° for this 

higher frequency. However, this benefit is countered by the earlier onset of 

excess noise which now occurs near e = 110°. As frequency increases, the 

experimentally determined excess noise peak shifts from e = 180° at 0.8 kHz to 

e = 110° at 20 kHz. In the latter case, the onset of excess noise results in 

a constant bSPL level without the oscillatory features observed at 4 kHz. 

The success of the analytical model at 20 kHz is illustrated by the 

theory-experiment comparison available in Figure 42b. Again shielding is 

closely predicted in the common plane of the dual jet system. Also, the 

sudden increase in bSPL resulting in excess noise near e = 110° is predicted. 

Finally, the experimentally observed constant bSPL values for e > 110° are 

also predicted. However, as noted earlier for the 4 kHz test condition, the 

oscillatory details observed in the prediction are absent in the experimental 

result due to the random distributed source characteristics of the jet noise. 

Mach Number Dependence - Having selected the appropriate point source/jet 

combination for modeling the dual jet system, assessment of the predicted 

directivity dependence on the various jet operating conditions can now 

proceed. Mach number sensitivity was assessed by increasing M from 0.6 to 

65 
66 

0.94 (Azimuthal data for M = 1.46 was not obtained due to the difficulty of 

holding a constant shock free operating condition during the long source jet 

rotation time). Figures 43-46 show the Mach number effect at four jet 

frequencies spanning the dual jet acoustic spectrum range. Here the 2 kHz 

condition represents an additional frequency used to monitor changes near the 

spectrum peak. Results are presented for the same operating conditions shown 

in Figure 33. A fixed polar directivity angle, $ = 40°, is employed here to 

facilitate the discussion. Variations with $ will be presented in a following 

subsection. 

Experimentally, the effect of increasing Mach numbers from M = 0.6 to 

0.94 has only a minor effect on the general shape of the directivity pattern 

at all frequencies or Helmholtz numbers. However, specific changes in 

shielding effectiveness do occur at e = 90°. At low frequencies, shielding 

improves as indicated by the 1 dB reduction in ASPL at 800 Hz. At high 

frequencies (20 kHz) shielding effectiveness is invariant with ASPL ~ 1.25 dB. 

These results agree with the trends observed earlier in the discussion of the 

jet noise spectrum dependence (Fig. 29). Near the spectrum peak corresponding 

to 2 kHz, a larger change in ASPL occurs with increasing Mach number at 

e = 90°. 

For e = 180°, Figures 43 through 46 indicate consistent excess noise at 

all frequencies. The specific ASPL levels are observed to be independent of 

Mach number. These general trends are in agreement with the changes observed 

in the previous subsection titled Spectrum Dependence on Isolated Parameters. 

Predicted changes as Mach number increases from M = 0.6 to 0.94 are 

illustrated by the trends in Part (c) of Figures 43-46. The weak dependence 

on Mach number at high frequencies is verified experimentally. Larger changes 

are observed at low frequencies in agreement ~ith experiment. 

The good comparison between theory and experiment suggests that the 

analysis can be used to assess the shielding effect as Mach number increases 

to M = 1.46. Predictions for this Mach number are also shown in Part c of 

Figures 43-46. In general, changes in the azimuthal directivity pattern occur 

only at low frequencies as indicated by comparing the M = 0.6 and 1.46 predictions. High frequencies remain unaltered in agreement with the trend in 

Figure 29. 

The above conclusions regarding Mach number dependence were based on 

comparisons at constant frequency or Helmholtz number. However, relative to 

reducing jet noise levels, the assessment can also be conducted at constant 

Strouhal number. Such a comparison is provided by the prediction in Figure 

45d. The Strouhal number selected here (St = .854) is based on the frequency 

used in the Helmholtz number of Figure 45c and the jet speed corresponding to 

M = 0.6. For the constant Strouhal number condition shown in Figure 45d, Mach 
number changes affect the location of the excess noise peak although changes 

in shielding effectiveness near e = 90 0 are weak. Based on a comparison of 

Figures 45c and 45d Mach number has little impact on azimuthal directivity 

patterns at constant Helmholtz number but for constant Strouhal number the 

radiation patterns are altered. 

It should be noted that assessment of the Mach number dependence at 

constant Helmholtz number and fixed polar angle is equivalent to evaluating 

Mach number effects at constant jet noise source frequency. It would appear 

that this procedure is invalid since Mach number changes are known to alter 

jet noise source characteristics at a fixed frequency. For this reason, Mach 

number dependence is typically evaluated at constant Strouhal number instead 

of constant Helmholtz number or source frequency. However, the present study 

includes relative sound pressure level changes due to propagation effects 

rather than just changes in the jet noise source characteristics. But, 

normalizing the dual jet measurements at each operating condition by the 

averaged single jet reference measurement at the identical operating condition 

accounts for changes in the jet noise spectrum. This applies for either Mach 

number or temperature effects. Consequently, comparisons at constant 

Helmholtz number are possible. A similar concern arises when Mach number 

dependence is evaluated at constant polar angle. But the same normalization 

by the single jet reference measurement eliminates the problem. 

Lateral Spacing Dependence - The effect of jet spacing is shown in a 

series of directivity patterns in Figure 47 as SID varies from 8.1 to 3.1 for 

f = 800 Hz (kD = .644). Similar results are shown in Figures 48-49 for higher 

jet noise source frequencies. In each case, the jet operating condition and 

microphone measurement angle correspond to the same conditions presented in 

the Mach number dependence evaluation. Both measured and predicted directivity patterns are shown. 

Experimentally,the influence of spacing is weak at f = 800 Hz as SID 

decreases from 8.1 to 5.5. A further decrease to SID = 3.1 results in a 

increase in ~SPL due to the changes in jet source distribution described 

earlier. The primary effect occurs near e = 90° with ~SPL increasing from 

approximately 2 dB to 3.5 dB indicating a reversal of shielding and an onset 

of excess noise. At e = 180°, there is little change in the measured ~SPL 

levels as SID decreases. Predicted directivity shapes generally agree with 

experiment at SiD = 8.1 and 5.5. But, differences exist for the SiD = 3.1 

test condition due to the acoustic source changes. 

At the higher frequency of 4 kHz (Fig. 48) spacing changes influence only 

the shape of the directivity pattern as SID decreases from 8.1 to 5.5. For 

example the maximum ~SPL location shifts to higher azimuthal angles as SID 

decreases, but the shielding effect remains constant with ~SPL(e = 90°) = 1 dB 

67 
68 

approximately. These trends are, in general, predicted analytically. However, the theory indicates an improvement in shielding as SID decreases near 

e = 90° while the experiment indicates a constant value of ~PL. 

A further decrease of spacing to SID = 3.1 in Figure 48 results 1n a 

change of the directivity pattern and ASPL levels. But, the changes are 

confined to the excess noise region at large azimuthal angles. This suggests 

that the radiated noise associated with the accelerated jet mixing occurring 

at smaller SID, contributes predominantly to the azimuthal directivity pattern 

beyond e = 130°. It is possible that the resulting merged flow field has the 

characteristics of high aspect ratio rectangular jets which are known to have 

an azimuthally varying directivity pattern. 

At 20 kHz, decreasing SID has a minimal effect on the jet azimuthal 

directivity pattern as indicated by the sequence of curves in Figure 49. 

Sound pressure level changes are limited to approximately a 0.5 dB increase in 

excess noise at large azimuthal angles. Changes in directivity pattern shape 

are limited to a small shift in the maximum ~PL location to higher azimuthal 

angles as SID decreases. The general shape in addition to the shift of the 

maximum ASPL location is predicted analytically. However, predicted oscillations in the directivity pattern are not observed experimentally due to a 

smoothing of the directivity pattern by the random and spatially distributed 

nature of the acoustic source field. Also the predicted small improvement in 

ASPL near e = 90° is not observed experimentally possibly due to the scatter 

in the data. 

Temperature Dependence - The influence of temperature could not be 

clearly determined due to an anomolous acoustic attenuation in the experimental mesurements. The problem is illustrated in Figure SO for M = 0.94, 

SID = 8.1 and ~ = 40°. A comparison of Part (a) and Part (b) indicates ASPL 

assumes negative values as temperature increases from To = 300 K to 811 K. 

This effect was observed consistently at all Mach numbers and all jet 

spacings. 

Phasing between the source jet and source jet radiation reflected from 

the shielding jet was considered as one source of this effect. While such 

phasing was identified as responsible for the maxima observed in the azimuthal 

directively patterns near 130°, phasing was determined to be inoperative for 

the heated flows. If phasing was responsible for the negative ASPL values 

observed in Figure SO, similar results would be expected for the unheated jet 

conditions. The only difference between heated and unheated flows would be 

the acoustic frequency at which this effect occurs. This is because the ray 

paths and propagation speeds change with temperature. Consequently, 1/2 cycle 

phase differences between propagating wavefronts would occur at different 

frequencies for heated and unheated flows. However, the absence of such 

negative ASPL values for unheated jets demonstrates that phasing was not a 

viable physical mechanism. 
While the source of the problem in Figure 50 is presently unknown, the 

influence of tempreature can still be interpreted experimentally. Conclusions 

however, are dependent on the observation that differences between the 

unheated and heated dual jet operating condition in Figure 50 remain approximately constant with jet rotation angle. This suggests that the magnitude of 

the attenuation is only a function of frequency. Therefore, for a fixed 

frequency, the influence of temperature on directivity shape can be isolated. 

Also, since the potential sources of the attenuation in Figure 50 are limited 

to propagation losses or a drift in the microphone sensitivity, presumably the 

impact of these effects on the acoustic measurements would be confined to high 

frequencies. This argument permits extending the evaluation of temperature 

effects on the dual jet noise directivity shape to include a comparison of 

~SPL levels at low frequencies (f = 800 Hz, 4 kHz). 

Based on the above qualifications and limitations, assessment of the 

temperature dependence can now proceed. For the low frequency 800 Hz case 

shown in Figures 5la and SIb, the approximately flat azimuthal directivity 

pattern changes to a radiation pattern with a 3 dB variation between 8 = 90° 

and 180 0 as temperature increases. However, shielding effectiveness remains 

constant at 8 = 90 0 indicating that the major change is due to an increase of 

excess noise near 8 = 180 0

• These general trends are predicted as indicated 

by the calculated directivity patterns shown in Figure SOC. 

For jet source frequencies near the spectrum peak, corresponding to f = 4 

kHz (Figs. S2a and S2b), increasing temperature has little effect on shielding 

at 8 = 90 0

• At larger azimuthal angles, the predominant changes are represented by a shift in the location of the local excess noise maxima to larger e 

as temperature increases. Otherwise, the magnitude of the local peaks remains 

constant. Analytically, these shifts are predicted. 

The above experimentally observed shift in local maxima also occur at the 

highest frequency of 20 kHz described earlier in Figure 50. Analytically, 

this trend is, again, predicted but the calculated magnitude of the shift is 

smaller than the measured result. Comparisons of measured ~SPL values, as in 

the 800 Hz and 4 kHz cases, is not possible in this case due to the previously 

described acoustic attenuation effects. Predictions, however indicate ~SPL 

levels near e = 90 0 are invariant with jet temperature. 

Polar Angle Dependence - Previous subsections demonstrated the azimuthal 

directivity dependence on various jet operating conditions. The following 

discussion documents the polar directivity features. 

Figures S3a-S3d present a sequence of azimuthal directivity patterns at 

polar angles, $, varying fr~m 20 0 to 90 0

• In general the presence of the 

shielding jet provides a maximum noise reduction in the common plane of the 

dual jet system (8 = 90 0

) when the observer is close to the jet axis system 

69 
70 

(small $). Simultaneously, the excess noise reaches a maximum at larger 

azimuthal angles. As $ increases, the noise reduction benefit, in addition to 

the excess noise, decreases. Finally for $ = 90°, ~PL ~ 3.75 dB for all 

values of e. Numerous data sets were examined, and the constant value 

fSPL = 3.75 dB at e = 90° was observed regardless of Mach number, spacing or 

frequency. This ~PL is larger than the sum of two independent jets, and is 

attributed to multiple reflections between the jets. 

Figure 53e also provides predicted ASPL azimuthal curves for the various 

polar radiation angles. A comparison of the measured and predicted trends 

shows good agreement for $ greater than 20°. In particular, the shift of the 

local maximum towards e = 90· as $ increases is well predicted. But for 

$ = 20°, large differences are observed between the measured and predicted 

fSPL levels. These differences, however, occur outside the jet shielding 

azimuthal angle range and are instead associated with the reflection and 

scattering effects responsible for excess noise at large e. 

Limitations of the Theory - Several possible reasons can be cited for the 

differences observed between measured and predicted ASPL levels for small 

polar angles. These will now be discussed in an effort to provide a better 

understanding of the physical phenomena in addition to identifying improvements needed in the analytical model. 

One potential theoretical limitation often cited by researchers deals 

with the jet flow region which the sound waves intersect at small polar angle 

$. In this case, sound reaching the observer interacts with the fully 

developed region of the shielding jet. Under this condition the jet shear 

layer deviates significantly from the plug flow model used in the analysis. 

Also, for small $ the observer is stationed within the zone of silence. It is 

known that for angles within this zone of silence, shear layer thickness 

effects can be significant. This is because an acoustic wave which has 

penetrated the shielding jet flow will reach a Mach number where it is 

reflected from the finite thickness shear layer closest to the source. In 

addition to being reflected part of the acoustic wavelength is transmitted but 

with an exponentially decaying amplitude until it reaches the corresponding 

point on the opposite side of the jet. Here it again begins to interact with 

the shear layer as an acoustic wave but with diminished amplitude due to the 

initial reflection and exponential decay. (The degree of exponential decay 

depends on the details of the jet nozzle.) The final wavefront which emerges 

from the jet can have a reduced amplitude which is not accounted for in the 

present analysis. 

The above described finite shear layer thickness effects suggest a 

significant impact on the predicted noise levels for small $. But, these 

arguments apply only for azimuthal angles near e = 90° and, thus, do not 

explain the differences between theory and experiment for e near 180° in 

Figure 53. 
In fact, near e = 90° differences between theory and experiment are 

small. This is because the shear layer thickness effects are masked by direct 

radiation from the shielding jet which represents the minimum noise level. 

If, for example, the present experiment were conducted with a single point 

sound source and a shielding jet, then the finite shear layer would impact the 

measurements. Under this condition, significant differences between theory 

and experiment would be observed as described by Yu and Fratello (ref. 11) who 

evaluated the shielding effect using this approach. However, the general 

conclusion is that for small wand e near 90° the inability to measure an 

expected deviation between theory and experiment due to the shear layer 

thickness is caused by masking of the effect by direct radiation from the 

shielding jet. 

While the zone of silence and finite thickness shear layer fail to 

account for the theory-experiment differences at large azimuthal angles when 

the observer is close to the jet axis, reflections between the adjacent jets 

in the dual jet system are considered potential sources of the documented 

differences. It is known that multiple reflections occur between the jets for 

acoustic waves initially propagating in the direction of the zone of silence. 

These reflections occur at a curved boundary which tends to scatter the radiation outwards from the common plane of the dual jet system. This results in 

the excess observed at angles on either side of the plane formed by the two 

jet axes. Based on the W = 20° theory-experiment comparison in Figure 53 

further improvement is needed in the analytical model to better predict this 

reflected radiation. 

Summary and ~valuation of Dual Jet Directivity Pattern and the Analytical 

Prediction Method - The experimentally observed dual jet azimuthal directivity 

pattern indicates that shielding is most effective in the common plane of the 

dual jet system at frequencies (or Helmholtz numbers) above the spectrum peak. 

The directivity pattern in this case is defined by a minimum ~SPL value at 

e = 90° followed by an increase near e = 110° (depending on M, SiD, and source 

frequency) which results in a local excess noise maximum of ~SPL = 4 or 5 dB. 

Beyond this region smaller amplitude local excess noise maxima continue to 

occur. For frequencies below the jet spectrum peak, the directivity pattern 

increases monotonically reaching a maximum at e = 180°. 

The existence of the higher frequency excess noise maxima at azimuthal 

angles outside the common plane of the dual jet system follows from the 

conservation of acoustic energy criterion. The noise reduction benefit which 

occurs near e = 90° requires a noise increase at other radiation angles since 

the shielding mechanism essentially redirects acoustic wavefronts. Consequently, application of jet shielding as a noise reduction technique must also 

consider the noise penalties at other azimuthal angles. 

Azimuthal directivity pattern shapes are generally insensitive to Mach 

number changes in the subsonic range between M = 0.6 and 0.94 for all jet 

71 
72 

noise source frequencies or Strouhal numbers. However, changes in shielding 

do occur at 8 = 90° with shielding becoming more effective at low frequencies. 

At high frequencies, shielding is already operative and increasing Mach number 

has little effect. Near the jet noise spectrum peak, a 1 dB change in ~PL is 

observed. 

The primary effect of decreasing jet spacing from SID = 8.1 to 3.1 is to 

shift the location of the maximum excess noise peak to larger azimuthal 

angles. There is little effect on the measured ~SPL levels with the exception 

of two changes. First, at low frequencies (below the jet noise spectrum peak) 

acoustic source changes created by merging of the jet flows increases noise in 

the common plane of the dual jet system. Second, near the spectrum peak, and 

at higher frequencies, a small increase in excess noise occurs at large 

azimuthal angles outside the common plane of the dual jet system. 

Based on the limited temperature data, increasing jet temperature has 

little effect on shielding in the plane of dual jet system. The only exception is an increase in excess noise at large azimuthal angle for low frequencies. Similar to the effect of spacing, temperature changes shift the 

location of the high frequency excess noise maxima to larger 8. 

Relative to polar angle dependence, jet shielding effectiveness in the 

common plane of the dual jets increases as W decreases (observer approaches 

the jet axis system). Simultaneously, for an observer located at large angles 

outside the common plane, excess noise reaches a maximum at small w. As W 

increases, the noise reduction benefit due to shielding in addition to the 

excess noise decreases. At ¢ = 90°, the measured dual jet ~SPL curve is 

invariant with 8. However, measured ~SPL levels exceed 3 dB indicating the 

jets do not radiate as two independent sources. In this case it is postulated 

that jet interaction and consequently acoustic source changes are responsible 

for these effects. Phasing between direct and reflected radiation, as in 

Figure 32, was not considered operative in this case since the measured ~SPL 

curves are invariant with O. (However, such phasing is operative at smaller W 

angles as indicated by the variation with 0 in Figure 33.) 

Prediction of the above described experimental results requires selecting 

the appropriate analytical combination of discrete tone acoustic point 

source/single jet geometry which best represents the dual jet random noise and 

spatially distributed source features. Based on a detailed assessment, the 

realistic dual jet configuration can be approximated by a combination of 

observer-shielding jet-acoustic point source and an observer-acoustic point 

source geometry. Using this analytical model good agreement between measured 

and predicted jet shielding effects is obtained in the common plane of the 

dual jet system. In addition, the previously described experimental trends 
for the jet shielding dependence on Mach number, jet spacing, temperature, and 

polar directivity are calculated. The present analytical model, therefore, 

represents an experimentally confirmed dual jet shielding acoustic prediction 

method. The only exception to the good agreement occurs in the spatial region 

defined by small polar angles and large azimuthal angles where reflections and 

scattering of sound results in experimentally measured excess noise which 

exceeds predictions. 

Sound Pressure Level Contours 

Shielding Dependence on the Jet Noise Spectrum - In an effort to 

understand the shielding dependence on the jet noise source characteristics, 

previous subsections evaluated spectra or directivity information at selected 

Strouhal number or Helmholtz number. A more general, although qualitative, 

assessment can be obtained by considering contours of 8SPL as a function of 

Strouhal number and azimuthal angle. An example of such a plot is given in 

Figure 54a for M = 0.6, To = 300 0K and ~ = 40°. Areas of the figure where 

~SPL is below 3 dB have been shaded. These regions represent conditions for 

which some shielding of the source jet occurs. 

Mach Number Dependence - Figures 54a and 54c show the effect of Mach 

number on jet shielding effectiveness and azimuthal angle. As Mach number 

changes from M = 0.6 to 0.94 the 3 dB contour line is observed to extend to 

lower Strouhal numbers, increasing the jet shielding effectiveness area. 

Relative to the azimuthal angle dependence, shielding is confined to approximately ±20° about 6 = 90° irrespective of Mach number. Also shown in Figure 

54b and 54d are the predicted ~SPL contours. The strong similarity of the 

2 dB and 3 dB contour lines when compared to the measurement indicates good 

agreement between theory and experiment. Included with the predicted contour 

cases is the M = 1.46 condition. 

Lateral Spacing Dependent ~ The influence of lateral spacing changes on 

measured jet shielding contours is shown in Figure 55 for three ratios of SiD. 

Little change in contour shape or effectiveness area is observed as SiD 

decreases from 8.1 to 5.5. However a further change to SiD = 3.1 results in a 

decrease of shielding effectiveness due to contour line changes at low 

Strouhal numbers. Simultaneously, there is an increase in excess noise at 

azimuthal angles beyond 6 = 130° as indicated by the larger effective areas 

contained by the 4 dB and 5 dB contour lines. The origin of this increase was 

identified earlier to be due to acoustic source changes created by merging of 

the dual jet flow. These general trends are in agreement with previous 

conclusions obtained from assessment of jet noise spectra at selected 6 in 

addition to azimuthal directivity patterns. 

Also shown in Figure 55 are the corresponding predicted contours. While 

the SiD = 8.1 and 5.5 calculations are similar to the experiment, the 

SiD = 3.1 result differs due to the source changes. 

73 
74 

Temperature Dependence - Due to the frequency dependent anomalies 

identified earlier in the temperature dependence data, experimentally based 

contour plots cannot be generated. However, predictions are presented in 

Figure 56 for To = 300 0K and 8ll oK. A comparison of the two operating 

conditions shows only a small increase in shielding effectiveness area with 

increasing temperature. 

Polar Angle Dependence - The effect of polar angle on jet shielding is 

shown in Figure 57 where contour plots are presented for 6 different polar 

angles. The shielding effectiveness area is maximized at W = 20° with a 

significant range in both the Strouhal number and azimuthal angle domain. 

Simultaneously the peak excess noise is a maximum for this polar angle. 

Shielding effectiveness and excess noise decrease with increasing polar angle 

until, at W = 90°, shielding is absent and excess noise levels are approximately 4 dB. Similar results were observed at other flow conditions. Also 

shown in Figure 57 are the predicted contours for the corresponding polar 

angles. The general trend agrees with experiment, confirming the capability 

of the analytical model to predict the physical phenomenon. 

Differential Power Spectrum 

Previous sections identified acoustic source changes as a possible 

mechanism for the increase in the dual jet noise level as jet spacing 

decreased. The origin of these acoustic changes includes aerodynamic interaction of the dual jet flow fields and acoustic/flow coupling. The latter 

mechanism is usually observed as a broadband jet noise amplification or attenuation. A quantitative assessment of these mechanisms is obtained from a 

comparison of the dual jet and the synthesized dual jet power spectrum levels. 

This change, represented by the differential power spectrum parameter, aPWL, 

was determined by numerically integrating over the experimentally determined 

measurement surface employed in the present study. A detailed discussion 

describing the integration over 20° ~ W ~ 100 0 and 80 ~ a ~ 195° is given in 

Appendix D. The parameter, ~PWL, is illustrated in Figure 58 for the three 

jet spacings tested in the present study. Also shown is the original dual jet 

and the corresponding synthesized dual jet (not the synthesized average single 

jet) acoustic power spectrum used to calculate ~PWL. 

For the largest SiD value, where aerodynamic interaction was limited to 

Strouhal numbers below 0.1, ~PWL is small (0.3 dB to 0.7 dB) near the dominant 

portion of the jet noise power spectrum. Errors due to experimental inaccuracies and numerical integration in addition to acoustic/flow coupling are 

potential sources of this difference. Experiments by Yu and Fratello 

(ref. 11), however, indicated that acoustic coupling could not be detected 

within a 0.5 dB difference attributed to experimental errors in their study. 
In the absence of such coupling the 0.3 to 0.7 dB difference in Figure 58a 

represents a similar calibration of the experimentai error in the present 

study. 

The above assessment concentrated on the differential power for the 

largest spacing and Strouhal numbers near the jet noise spectrum peak. For 

the same spacing but Strouhal numbers below 0.1, APWL is observed to 

systematically increase as St decreases. Since the acoustic source region for 

this portion of the spectrum is in the dual jet merging region (X/D ~ 23) the 

observed increase in ~PWL is considered to be a calibration of the downstream 

jet merging effect on the radiated power for the largest spacing condition of 

SID = 8.1. 

As SID decreases to 5.5, the differential power spectrum remains 

approximately the same except for a small reduction in APWL at the lower 

Strouhal numbers. This observation is in agreement with earlier discussions 

which indicated a m1n1mum effect on 8SPL level as SID changed from 8.1 to 5.5. 

A further decrease of SID to 3.1 creates an increase in jet noise radiated 

power particularly at low frequencies where a 1 dB change occurs. While this 

1 dB change is perceptable in Figure 58 it is smaller than the 2 dB increase 

in noise observed at large azimuthal angles in previous contour plots as SID 

changes from 8.1 to 3.1. This result indicates that the close spacing condition impacts the directivity shape but has a weaker effect on the total power 

radiation. 

75 

CONCLUSIONS 

1. The sound field radiated by an isolated jet is modified when it 

interacts with the velocity and temperature discontinuity of an adjacent 

shielding jet. The fluid in the shielding jet refracts, diffracts, and 

reflects the isolated jet noise field. These effects alter the jet noise 

directivity pattern with the final radiation field of the dual jet configuration no longer being the superposition of two independent jet noise radiation 

fields. 

2. Sound pressure levels in the plane of the dual jet system are reduced 

relative to the noise level generated by two independent jets. Effectiveness 

of this refraction and diffraction controlled shielding phenomenon improves as 

the polar angle approaches the jet axes. The shielded region extends 20 to 40 

degrees in the azimuthal direction on either side of the dual jet common plane 

depending on the jet operating conditions and the source frequency. Outside 

of this region, an increase of noise occurs due to the redirection of sound 

rays from the shielded region. 

3. Sound pressure levels in a plane orthogonal to the dual jet common plane 

are increased relative to two independent jets. This excess noise, which is 

due to acoustic reflections between the adjacent flow fields, demonstrates 

that acoustic interactions also exist at observer angles where previous 

investigations assumed the jet system operated as two independent sources. 

4. The dual jet azimuthal directivity pattern is strongly frequency 

dependent. At Stouhal numbers below the jet noise spectrum peak location, the 

directivity pattern increases monotonically from a minimum sound pressure 

level in the common jet plane to a maximum noise level at 90 degrees to the 

common plane. For the high frequency end of the jet noise spectrum, the 

azimuthal directivity pattern varies from a minimum noise level, controlled by 

shielding, to a local maximum situated at aproximately 20 to 40 degrees on 

either side of the common jet plane. This maximum, which can exceed the noise 

of two independent jets by 3 dB, is larger than the excess noise condition 

existing in the plane orthogonal to the dual jet common plane. The origin of 

this maximum is attributed to phasing between the direct radiation from the 

source jet and source jet radiation reflected by the shielding jet. As 

frequency decreases this localized maximum shifts away from the common plane 

of the dual jet system. 

5. A balance exists between the noise reduction and noise increase 

occurring over a hypothetical sphere surrounding an aerodynamically non-interfering dual jet system. This balance confirms that acoustic energy is 

conserved by the refraction, diffraction, and reflection processes existing in 

the presence of the adjacent shielding jet. It also demonstrates that a 

beneficial noise reduction at one observer angle is negated by a noise penalty 

at other observer angles. 

77 
78 

6. Jet shielding effectiveness increases with increasing Helmholtz number. 

Relative to the jet noise spectrum shape, shielding is most effective above 

the peak Strouhal number. 

7. Increasing subsonic Mach number enhances the jet noise shielding and 

shifts the onset of shielding to Strouhal numbers below the spectrum peak. At 

high subsonic Mach numbers typical of current jet engines, approximately a 

2 dB noise reduction occurs at the jet noise spectrum peak. Further increases 

to supersonic Mach number provide little improvement for jet shielding. Mach 

number changes have only a minor effect on the shape of the dual jet directivity pattern. 

8. For non-interfacing dual jet flows, jet spacing has little effect on the 

noise radiation in the common plane of the jet system. The primary change is 

a shift of the high frequency localized excess noise maximum to larger 

azimuthal angles. For small jet spacing resulting in the aerodynamic merger 

of the jet flows, sound pressure levels increase relative to two independent 

jets. Resulting changes in the jet noise spectrum shape are controlled by 

acoustic source alterations in the region downstream of the jet merger. Since 

jet merging occurs beyond the end of the potential core where the jet acoustic 

source region generates primarily low frequency noise, the spectrum changes 

associated with close spacing are confined to Strouhal numbers below the jet 

noise peak. Shifting of the localized excess noise maximum to larger 

azimuthal angles continues to occur for close spacing. 

9. Differences between heated and unheated jets are minimal in the common 

plane of the dual jets where shielding is operative. Similar to the effect of 

spacing, the primary change due to temperature is a shift to larger azimuthal 

angles of the localized excess noise maximum. 

10. The maximum experimentally observed noise reduction for two adjacent 

aerodynamically non-interfering jets with the same operating condition is 3 

dB. Although phasing could conceptually improve the noise reduction beyond 

this 3 dB limit, such effects are not experimentally observed with two 

adjacent jets. The present noise reduction limit is based on complete masking 

of one jet when the observer is in the common plane of the dual jet system. 

The resulting radiation perceived by the observer corresponds to direct 

radiation from the shielding jet alone. Since total masking of the source jet 

also applies for dissimilar flows, placement of the quieter jet between the 

observer and the noisy jet may provide significant noise reduction in the 

shielding region. Further shielding studies with dissimilar jets are, 

therefore, recommended. 

11. Improved shielding (exceeding 3 dB) experiments involving a shielding 

jet-discrete tone point source combination indicate only the noise reduction 

of the point source. This measured noise, which depends on phasing between 
wavefronts arriving at the observer station, excludes the direct radiation 

from the shielding jet. In a dual jet geometry, such improvements are masked 

by the direct radiation from the shielding jet which determines the 3 dB noise 

reduction limit. Further improvements in noise reduction for two adjacent 

jets would require coherent acoustic source regions in each jet with 

appropriate phasing between them. 

12. Dual jet noise shielding is modelled by a first principles theory based 

on a discrete tone point source interacting with a constant diameter cylindrical, uniform flow shielding jet. Measured jet noise reduction in the common 

plane of the dual jet is well predicted. In addition, directivity patterns 

outside the common jet plane are predicted. Finally, experimentally observed 

trends based on Mach number, jet spacing, temperature, and source frequency 

are calculated. The analysis, therefore, successfully models the acoustic 

directivity pattern generated by two adjacent, random-noise, distributedacoustic-source jets. 

13. Finite shear layer thickness effects, which are not modelled in the 

analytical prediction, have little impact on the radiated noise in the common 

plane of the dual jets. This conclusion is based on the experimentally 

observed maximum attainable 3 dB noise reduction for the dual jet configuration. In this case, shear layer thickness effects are masked by direct radiation from the shielding jet. 

79 

APPENDIX A 

REVIEW OF PREVIOUS EXPERIMENTAL RESEARCH 

The earliest reference to work on acoustic shielding from circular jets 

appears is the study by Greatrex and Brown in 1958 (ref. 1). Although their 

data show approximately a 3 to 4 dB difference in noise between ~SPL (e = 90°) 

and ~SPL (8 = 180°) the authors indicate an uncertainty in the reliability of 

the measurements. The noise reduction benefit appeared to decrease with 

increasing spacing as SiD increased from 1.2 to 1.4. 

A study of the effects of jet shielding on two jets of unequal size was 

carried out by Morris, Richarz and Ribner in 1973 (ref. 2). A small secondary 

jet was mounted at an angle to the main jet so as to eliminate any aerodynamic 

interference and hence avoid degradation of the main jet performance. The 

object was to alter the directivity pattern of the main jet by refracting, 

reflecting, and diffracting the sound field using the secondary jet. They 

found a maximum reduction of 5 dB. The attenuation increased for both 

increasing secondary jet velocities and temperatures. 

A study of the shielding effect of multi-tube nozzles was done by Gray, 

Gutierrez and Walker in 1973 (ref. 3). They measured the noise produced from 

37 tube nozzles and single tube nozzles using both 1/4 scale and full scale 

configurations. At low velocities, no shielding was detected. However, at 

transonic velocities and above, a nearly complete shielding was observed. 

As part of a larger study on jet noise reduction from shrouded multinozzles, Goethert and Borchers (ref. 4) reported some twin jet results in 

1974. For spacing to diameter ratios between 1.2 to 2.0, they found that the 

total sound power was approximately 1 dB lower than the noise produced by two 

independent jets. At larger spacings, however, only a .1 to .2 dB reduction 

was noted. 

A study of acoustic shielding in annular jets was performed by Ahuja and 

Dosanjh in 1977 (ref. 6). They examined the effect of shielding a noisy, 

round inner jet with an outer jet. When the outer jet was at the same temperature as the inner jet, little shielding benefit was observed. However, when 

the outer jet was heated, up to a 10 dB noise reduction was seen. A genuine 

reduction in acoustic power levels was observed, as opposed to a redistribution of acoustic energy by refraction. The shielding effect was seen at all 

angles, but was stronger at higher frequencies. 

A study of the acoustic shielding from twin, round heated jets was 

presented in 1977 by Bhat (ref. 7). In his test, the effects of spacing, 

dissimilar velocity, dissimilar jet size, and longitudinal stagger on acoustic 

shielding were examined. Sound pressure measurements were made about an arc 

81 
82 

only in the common plane of the dual jet system. For equal size jets with no 

longitudinal stagger, up to a 5 dB difference between the twin jets and a 

single jet incremented by 3 dB was noted at 40° from the jet axis. At 90° 

from the jet axis, no effect was observed. Although the range of lateral jet 

spacing tested was small (from sin = 1.12 to 2.0) an increase in shielding 

effect was observed at the closest spacing. The importance of acoustic source 

changes due to aerodynamic interactions at these close spacings was not evaluated. An increase in shielding effect was also noted for an increase in 

streamwise stagger. 

An acoustic study of heated twin jets was performed by Kantola in 1977 

(refs. 8, 9). Sound pressure measurements were made in an arc around the jet 

nozzle exit at only 3 polar angles, 0°, 45°, and 90° from the dual jet plane. 

Lateral jet spacing, velocity and temperature were varied. Kantola found that 

as the spacing increased from sin = 1.33 to 3.0, the measured overall power 

level (OAPWL) decreased in the plane of the jets. No additional effect was 

noted for larger spacings. In the loud plane, 90° from the plane of the jets, 

OAPWL varied from less than the single jet noise level incremented by 3 dB 

level to greater than the single jet level incremented by 3 dB. Kantola 

interpreted this to indicate mixing suppression and additional noise generation respectively. At frequencies below about 2 kHz, little difference was 

noted between the loud and the quiet measurement planes. At higher frequencies, however, over 8 dB of difference was noted for a microphone at 30° off 

the jet axis. Even for the 90° off axis microphone, up to 2 dB difference was 

seen. The frequency at the onset of shielding was seen to decrease as the 

spacing increased. Kantola attributes this to an internozzle layer of cold 

fluid which exists between the jets and extends further downstream as the 

spacing increases. As the layer extends further downstream, the lower 

frequency jet noise sources are shielded. It was also noted that the 

shielding effect increased with jet velocity up to sonic conditions. 

A study of two round parallel jets with unequal flow was made by 

Shivashankara and Bhat in 1980 (ref. 10). It was found that the sound of the 

high velocity (loud) jet could be shielded by the low velocity (quiet) jet by 

as much as 7.5 dB OASPL. No benefit was perceived at azimuthal angles greater 

than 75° from the plane of the jets. For a lateral spacing to diameter ratio 

of 1.5 to 1.6, total pressure and temperature surveys were taken. By 

comparing velocity profiles obtained with single jet versus the dual jet 

configuration at a streamwise station of x/n = 5, it was concluded that no 

significant mean flow interaction occurred. In the polar directivity plane, 

the frequency at which noise reduction first occurs increases as the observer 

angle increases. 

An experiment on the acoustic shielding provided by a turbulent jet from 

a point source of sound was conducted by Yu and Fratello in 1981 (ref. 11). A 

one inch diameter jet was rotated about a fixed acoustic source. Sound 

pressure measurements were obtained with a fixed microphone array. Four 
different discrete tones and also 1/3 octave band random noise were emitted 

from a small acoustic source. Room temperature air and helium were used as 

the working fluids for the jet. The helium was used to simulate heating at a 

high temperature ratio. Since there was only one jet, no aerodynamic interaction was present, and the effect of acoustic shielding alone could be 

studied. Yu and Fratello found that the peak value of shielding. as measured 

by the differential power level between acoustic source only and both acoustic 

source and jet, increased with frequency, jet velocity, jet heating, and 

longitudinal source position. No trends were identified for the effect of 

lateral spacing on acoustic shielding at values of Kd greater than 2. 

83 

APPENDIX B 

CORRECTIONS TO ACOUSTIC DATA 

Humidity Changes 

Although relative humidity was monitored in the anechoic chamber during 

each test condition, corrections for humidity effects were not applied. This 

decision was based partially on the limited range of applicability of the current prediction procedures. For example, ARP 866A (ref. 45) which is the 

aerospace industry standard, is confined to frequencies below 10 kHz and temperatures between -18°e and 38°C (O°F to 100°F). In contrast, third octave 

band data were acquired for frequencies up to 50 kHz in the present experiment. Also, during testing at high Mach number and jet temperature conditions, the anechoic chamber temperature occasionally approached 60°C (140°F). 

Since ARP 866A predicts approximately a 3 dB change in acoustic sound pressure 

level (at 50 kHz and 10% relative humidity) as temperature increases 10°C, 

comparison of the heated and unheated (25°C average temperature) jet test 

conditons would require large amplitude corrections. These corrections would 

exceed the changes due to jet shielding. A final example of the limited range 

of the current humidity corrections is evident when considering the frequency 

dependence. Attenuation due to humidity is highly nonlinear and increases 

with frequency. Efforts to extrapolate the theory to frequencies above the 

present 20 kHz limit would, therefore, introduce unknown errors. 

Another major reason for not applying humidity correctons was the significant disagreement between correction procedures reported in the literature. 

The approach developed by Bass and Shields (ref. 46) gives differences of 3 dB 

(at 10 kHz, 288.7°K, and 70% relative humidity) relative to the corrections 

obtained from ARP 866A. As indicated earlier, this difference is comparable 

to the magnitude of the jet shielding effect investigated in the present 

study. 

A final constraint on application of humidity corrections was the nonuniformity of the anechoic chamber temperature. Gradients existed in the 

chamber due to the entrainment of cooler outside air through an access door. 

This possibly resulted in recirculation cells inside the chamber complicating 

the application of humidity corrections. In this case, a detailed knowledge 

of the temperature field, between the dual jet system and the microphone 

array, would be needed before applying the correction. 

Based on the above described constraints, it was concluded that correcting hot jet data could potentially introduce errors in the acoustic data. 

Therefore, only uncorrected heated jet data below 20 kHz was evaluated since 

the predicted humidity corrections are small in the region. For the unheated 

jet data, 1/3 octave band spectra were therefore, also limited to frequencies 

85 
86 

below 20 kHz. Most of the previous experiments neglected atmospheric humidity 

corrections. 

Jet Velocity Changes 

Acoustic data obtained during the subsonic dual jet rotation experiments 

was corrected to a common jet Mach number to account for small pressure and 

temperature variations in the air supply system. Total pressure and temperature monitored upstream of the nozzle exit planes was recorded as a function 

of time and jet rotation angle for this purpose. The data was used to convert 

the sound pressure levels to the reference Mach number and temperature associated with each specific test condition. 

The correction was based on a jet scaling law employed by Plumb lee, et 

al. (ref. 43). The noise dependence on jet operating conditions was obtained 

from the proportionality expression for overall sound pressure level (OASPL). 

OASPL ~ 10 log (V. 5 .5 {1 - M cos 9)6/[(1 - M cos 9)2 + a2 M 2]9/2} J c c c (B-l) 

Here, Mc ' the eddy convection Mach number, is assumed to be 0.67 Vj' and 

the weighting factor, a is taken to be 0.3, although it was applied in the 

present study for 1/3 octave band levels. 

Total pressure changes were accounted for by the velocity dependence in 

Equation B-1. Similarly, the effect of total temperature changes was determined from the velocity term which is also an implicit function of the temperature dependent speed of sound inside the jet. As a first approximation, 

the resulting corrections to the acoustic data were applied to the dual jet 

data assuming two independent source jets with shielding inoperative. In most 

cases, the magnitude of the correction was a few tenths of a decibel. 
APPENDIX C 

SYNTHESIZATION OF THE AVERAGE SINGLE JET RADIATION FIELD 

The method selected for quantifying the jet shielding effectiveness 

involved comparing dual jet noise measurements with a simulated single jet 

geometry. The latter configuration was calculated as the average of two, 

independent single jets whose sound pressure levels were added. The radiated 

noise field in this case was free from the propagation effects present in the 

experimental dual jet data, thereby, providing a baseline case without 

shielding. 

Quantitatively, the shielding effectiveness was defined by Equation 36 

where the numerator represents the shielded noise and the denominator represents the average noise from two independent jets. Ideally, for source-tomicrophone distances which are large relative to jet spacing, distance changes 

during rotation of the source jet about the shielding jet would not impact the 

numerator of Equation 40. Similarly, the denominator would be independent of 

the precise~ource jet-to-microphone distance and could be replaced by PI 

since pf = pi· 

However, in the present study, the 3 m radius of the microphone array was 

insufficient to provide a geometric far field measurement location relative to 

the 0.36 m maximum jet spacing. For example, for the ~ = 90 0 microphone 

station the ratio of source jet sound pressure levels associated with 6 = 90 0 

and 6 = 180 0 is given by (3/3.36)2. In terms of decibels, this corresponds to 

a 0.9 dB difference in sound pressure level. To assess the shielding 

effectiveness as the source jet rotated about the shielding jet, it was 

necessary to account for this difference in distance and its corresponding 

impact on the measured sound pressure levels. Due to the small magnitude of 

the shielding effect observed experimentally during the present study such 

changes could not be neglected. 

The above described distance effects were accounted for in the 

denominator of Equation 36. The approach is illustrated schematically in 

Figure C-I. Part (a) of this figure represents the dual jet shielding experiment while Part (b) indicates the procedure involved in converting single jet 

mesurements, also obtained as part of the test program, to the synthesized 

dual jet configuration. Here, distance corrections, based on the inverse 

square law decay model, were applied to the single jet measurements. This 

method analytically shifted the single jet measurement location to the appropriate shielding jet and source jet locations employed during each dual jet 

test geometry. In essence, this procedure ensured the same relative jet locations and azimuthal orientation in the expressions representing the numerator 

and denominator of Equation 36. In this way the impact of distance changes 

87 
88 

was minimized in the present experimental assessment of the shielding mechanism. 

The above described shift in location was based on a simple point source 

model with the noise source situated at the jet exit plane. Precise distances 

were calculated from the nozzle exit plane to the individual microphones. In 

general, the jet-to-microphone distance was determined from the expression 

R2 [(S cos 8 + Rl sin W)2 + (S sin 8)2 + (R 1 cos W)2]1/2 (c-l) 

The resulting synthesized dual jet sound pressure level, which was also a 

function of sin and 6, was then obtained from the equation 

PI = ~ {[Rm/Rl]2 + [Rm/R2]2} 

where 

P1 = simulated dual jet pressure squared 

~ = measured single jet pressure squared (all measurements 

conducted at sin = 3.19) 

Rm = distance from the microphone to the single jet (3.19 m) 

Rl = distance from the microphone to the shielding jet (3.05 m) 

R2 distance from the microphone to the source jet 

(C-2 ) 
APPENDIX D 

DIFFERENTIAL POWER SPECTRUM 

The jet shielding concept is based on the idea that sound radiation from 

an isolated jet is redirected after propagation through an adjacent jet flow 

field. A fundamental assumption during this process is that acoustic energy 

is conserved. However, for sufficiently close spacings, the two adjacent jets 

may interact aerodynamically altering the initial jet noise source characteristics. Under this condition, increased noise levels can be generated by the 

dual jet system relative to two separate and independent jets. 

One method for identifying acoustic source changes involves a compar~son 

of the dual jet and synthesized dual jet power spectra. This comparison, 

represented quantitatively as a ratio of power spectrum levels (PWL), provides 

a differential power parameter, 8PWL, which can be expressed in terms of 

decibels. 

In principle, the individual power spectra needed to calculate ~WL would 

be obtained from acoustic measurements on a hypothetical sphere (or hemisphere 

if symmetry exists) surrounding the dual jet system. However, microphone 

locations in the present experiment were confined to approximately a quarter 

of a hemisphere. The primary limitation was in the polar angle range which 

was defined by 200~ W ~ 100°. Ideally, this measurement range should include 

angles beyond W = 100° since this region contains sufficient acoustic energy 

to influence the power spectrum calculation. Thus the present power spectrum 

calculations must be regarded as estimates. 

It should be noted that the azimuthal angle range, 800~ e ~ 200°, did not 

present a limitation to the power spectrum calculation. Symmetry of the dual 

jet directivity pattern about e = 90° could be used to define the complete 

azimuthal directivity pattern for Oo~ e ~ 360°. In principle, however, 

differences in 8PWL can be determined from measurements limited to the range 

900~ e ~ 180° based on azimuthal symmetry. This approach was used in the 

present study, i.e., pow~+ spectrum levels are based on numerical integrations 

over 90°< e < 180°. 

Although the polar and azimuthal angle range did not account for the 

total acoustic power radiated by the dual jet system, the impact on the 

differential power, 8PWL, was a minimum. This is because for the non-interfering jet spacings tested here, the primary redirection of sound by the 

adjacent jet fiow field was confined to the region 200~ W ~ 90°. Also, due to 

symmetry, relative changes observed in the region 900~ e ~ 180 0 were representative of the changes observed in the remaining three quadrants of the 

azimuthal direction. Under these conditions, it was sufficient to assess 

89 
90 

changes in ~WL as a function of spacing over the range 20° ~ $ ~ 100° and 

90°<6<180°. 

Power spectra were calculated for both the experimentally documented 

jet configuration and a synthesized combination of two independent jets. 

latter geometry was calculated from a single jet measurement using the 

synthesization process defined in Appendix C. 

dual 

The 
REFERENCES 

1. Greatrex, F. B. and D. B. Brown: Progress in Jet Engine Noise Reduction. 

Advances in Aeronautical Sciences, Vol. 1, pp. 364-392, Proceedings of 

the First International Congress in the Aeronautical Sciences, Madrid, 

1958. 

2. Morris, P. J., W. Richarz and H. S. Ribner: Reduction of Peak Jet Noise 

Using Jet Refraction. J. Sound and Vib., Vol. 29, No.4, pp. 443-455, 

1973. 

3. Gray, V. H., O. A. Gutierrez and D. Q. Walker: Assessment of Jets as 

Acoustic Shields by Comparison of Single and Multimode Suppressor Nozzle 

Data. AIAA Paper 73-1001, 1973. 

4. Goethert, B. H. and I. U. Borchers: Noise and Thrust Characteristics of 

Shrouded Multi-Nozzles of Circular Cross Section. AIAA Paper 74-45, 

1974. 

5. Borchers, I. U.: An Experimental Study of the Noise Radiation of 

Interfering Free Jets, AlAA Paper 77-1285, 1977. 

6. Ahuja, K. K. and D. S. Dosanjh: Heated Fluid Shroud as an Acoustic 

Shield for Noise Reduction - An Experimental Study. AIAA Paper 77-1286, 

1972. 

7. Bhat, W. V: Acoustic Characteristics of Two Parallel Flow Jets. AIAA 

Paper 77-1290, 1977. 

8. Kantola, R. A.: Shielding Aspects of Heated Twin Jet Noize. AIAA Paper 

77-1288,1977. 

9. Kantola, R. A.: Acoustic Properties of Heated Twin Jets. J. Sound and 

Vib., Vol. 79, No.1, pp. 79-!06, 1981. 

10. Shivashankara, B. N. and W. V. Bhat: Noise Characteristics of TwoParallel Jets of Unequal Flow. AlAA Paper 80-1068, 1980. 

11. Yu, J. C. and D. J. Fratello: Measurement of Acoustic Shielding by a 

Turbulent Jet. AlAA Paper 81-2019, 1981. 

12. Cowan, S. J. and R. W. Crouch: Transmission of Sound Through a Two 

Dimensional Shielding Jet. AlAA Paper No. 73-1002, 1973. 

13. Yeh, C.: A Further Note on the Reflection and Transmission of Sound 

Waves by a Moving Fluid Layer. J. Acoustical Soc. Amer., Vol. 43, No.6, 

pp. 1454-1455, 1968. 

91 
92 

REFERENCES (Cont'd) 

14. Miles, J. W.: On the Reflection of Sound at an Interface of Relative 

Motion. J. Acoust. Soc. Amer., Vol. 29, 1957, pp. 226-228. 

15. Ribner, H. S.: 

Moving Medium. 

Reflection, Transmission and Amplification of Sound by a 

J. Acoust. Soc. Amer., Vol. 29, 1957, pp. 435-441. 

16. Parthasarathy, S. P., R. F. Cuffel and P. F. Massier: Twin Jet 

Shielding. J. Aircraft, Vol. 17, No.9, pp. 618-626, 1980. 

17. Gerhold, C. H.: Two-Dimensional Analytical Model of Twin Jet Shielding. 

J. Acoust. Soc. of America, Vol. 69, 1981, pp. 904-908. 

18. Gerhold, C. H.: Analytical Model of Jet Shielding. AIAA Journal, Vol. 

21, 1983, pp. 694-698. 

19. Gottlieb. P: Sound Source Near a Velocity Discontinuity. J. Acoust, 

Soc. Amer., Vol. 32, 1960, pp. 1117-1122. 

20. Graham, E. W. and B. B. Graham: Effect of a Shear Layer on Plane Waves 

of Sound in a Fluid. J. Acoust. Soc. Amer., Vol. 46, 1969, pp. 169-175. 

21. Howe, M. S.: Transmission of an Acoustic Pulse through a Plane Vortex 

Sheet. J. of Fluid Mech., Vol. 43, 1970, pp. 353-367. 

22. Tester, B. J. and R. H. Burrin: On Sound Radiation from Source in 

Parallel Sheared Jet Flows. AIAA Paper #74-57, 1974. 

23. Mani, R.: A Moving Source Problem Relevant to Jet Noise. J. Sound and 

Vibration, Vol. 25, 1972, pp. 337-347. 

24. Mani, R: The Influence of Jet Flow on Jet Noise, Part 1, The Noise of 

Unheated Jets. J. of Fluid Mechanics, Vol. 73, 1976, pp. 753-778. 

25. Goldstein, M. E.: The Low Frequency Sound from Multiple Sources in 

Axisymmetric Shear Flows, with applications to Jet Noise. J. of Fluid 

Mech., Vol. 70, 1975, pp. 595-604. 

26. Amiet, R. K.: Correction of Open Jet Wind Tunnel Measurements for Shear 

Layer Refraction. Progress in Astronautics and Aeronautics, Ed. Martin 

Summerfield, 1976, pp. 259-280. Also AIAA Paper 75-532, 1975. 

27. Amiet, R. K.: Refraction of Sound by a Shear Layer. J. Sound and 

Vibration, Vol. 58, 1978, pp. 467-482. Also AIAA Paper #77-59, 1977. 
REFERENCES (Cont'd) 

28. Jacques, J. R.: Noise from Moving Aircraft: Some Relevant Models. PhD 

Thesis, Cambridge University, 1975. 

29. Candel, S. M.: Application of Geometrical Techniques to Aeroacoustic 

Problems: AlAA Paper #76-546, 1976. 

30. Tester, B. J. and C. L. Morfey: Developments in Jet Noise ModellingTheoretical Predictions and Comparisons with Measured Data. J. Sound and 

Vibration, Vol. 46, 1976, pp. 791-103. 

31. Schlinker, R. H. and R. K. Amiet: Experimental Assessment of Theory for 

Refraction of Sound by a Shear Layer. NASA CR-145359, 1978. Also AlAA 

Paper #79-0628, 1979. 

32. Schlinker, R. H. and R. K. Amiet: Refraction and Scattering of Sound by 

a Shear Layer. NASA CR-3371, 1980. 

33. Candel, S. M., A. Guedel and A. Julienne: Radiation, Refraction and 

Scattering of Acoustic Waves in a Free Shear Flow. AIAA Paper 76-544, 

1976. 

34. Ahuja, K. K.; Tester, B. J.; Tanna, H. K.; and Searle, N.: Experimental 

Study of Transmission, Reflection and Scattering of Sound in a Free-Jet 

Flight Simulation Facility and Comparison With Theory. AlAA Paper 

77-1266, 1977. 

35. Ahuja, K. K., B. J. Tester and H. K. Tanna: The Free Jet as a Simulator 

of Forward Velocity Effects on Jet Noise. NASA Contractor Report 3056, 

1978. 

36. Morse, P. M. and K. U. Ingard: Theoretical Acoustics, McGraw Hill Book 

Company, New York, 1968. 

37. Gradshteyn, I. S. and I. M. Ryzhik: Table of Integrade Series and 

Products. Academic Press, New York, 1965. 

38. Paterson, R. W., P. G. Vogt, and W. M. Foley: Design and Development of 

the United Aircraft Research Laboratories Acoustic Research Tunnel. J. 

of Aircraft, Vol. 10, No.7, pp. 427-433, 1973. 

39. Laufer, J., R. H. Schlinker, and R. E. Kaplan: Experiments on Supersonic 

Jet Noise. AlAA Journal, Vol. 14, No.4, pp. 489-497, 1976. 

93 
94 

REFERENCES (Cont'd) 

40. Pinckney, S. Z.: A Short Static-Pressure Probe Design for Supersonic 

Flow. NASA TN D-7978, July 1975. 

41. Seiner, J. M. and T. D. Norum: Experiments of Shock Associated Noise on 

Supersonic Jets. AIAA Paper 79-1526, 1979. 

42. Moffat, R. J.: Gas Temperature Measurement. Temperature- Its Measurementand Control in Science and Industry, Volume 3, Part 2, Reinhold Pub. 

Corp., c.1962, pp. 553-571. 

43. Plumbee, H. E., Jr., et al: A Study of the Effects of Forward Velocity 

on Turbulent Jet Mixing Noise. NASA CR-2702, July, 1976. 

44. Laufer, J., R. E. Kaplan and W. T. Chu: Acoustic Modeling of the Jet 

Noise Abatement Problem. Interagency Symposium on University Research 1n 

Transportation Noise, Stanford University, Stanford, California, March 

28-30, 1973, pp. 37-42. 

45. Standard Values of Atmospheric Absorption as a Function of Temperature 

and Humidity. Society of Automotive Engineers ARP 866A, 1975. 

46. Shields, F. D. and H. E. Bass: Atmospheric Absorption of High Frequency 

Noise and Application to Fractional-Octave Bands. NASA CR-2760, June, 

1977. 
SOURCE JET 

RADIATION 

SHIELDING JET 

llL TRANSMITIED 

m--(ATIENUATED) 

SCATIERED 

Figure 1 - Jet Shielding Concept 

95 
96 

SIDELINE 

OBSERVER 

COMBINED ACOUSTIC 

RADIATION FROM 

MULTIPLE JETS 

AIRCRAFT 

4 

3 

x I X" OBSERVER BELOW FLIGHT PATH 

? ;> ;> ;» 7 7 ;> 7 ? ? ;> ;> ;> ;> 7 ;> :/ ;> > > > ;> ? ? 

Figure 2 - Aircraft Sideline Noise Dependence on Sound Propagation Through 

Adjacent Jet Flows 

Figure 4 - View of Dual Jet Nozzles 
A 

\ 

\ 

R \ 

\ 

\ 

x 

Ro 

. P1, C1 

OBSERVER 

PO' Co 

ASSUMED CONDITIONS: 

1) R> >Ro-a=O 

2) PLANE OSA .1 TO Z AXIS 

V 

~ 

Z 

NOTE: THE REFERENCE AXIS FOR THE THEORETICAL AND EXPERIMENTAL (SEE FIG. 7) DEFINITIONS OF e DIFFER BY 90°. 

SEE TEXT - DESCRIPTION OF EXPERIMENT FOR DISCUSSION. 

Figure 5 - Coordinate System with Acoustic Source, Shielding Jet and 

Observer Locations for Theoretical Analysis 

99 
AIR 

FLOW 

S> 

MUFFLERS 

TURBULENCE 

SCREENS 

INLET 

LINED ACOUSTIC CORNERS 

FREE JET 

COLLECTOR 

CONTROL ROOM 

HIGH PRESSURE AIR SUPPLY SYSTEM 

TOP VIEW 

46m 

DIFFUSER MUFFLER 

~,/' 

71~71/J~ ,-"" Jl ~)7f7-777~ 

CENTRIFUGAL FAN 

SIDE VIEW 

Figure 6 - UTRC Acoustic Research Tunnel 

100 

-- EXHAUST 

TOWER 

PARALLEL 

BAFFLES 

J 

DRIVER_I 

17m 
MIC 9 

100 0 

90 0 

MIC 6 

70 0 

() = 270 0 

SHIELDING JET 

MIC 5 

60 0 

MIC 4 

50 0 

MIC 3 

40 0 

Y 

() =0 0 

MIC 2 

30 0 

AZIMUTHAL ANGLE 

SOURCE JET 

x 

MIC 1 

20 0 

"" " 

(} =90 0 

FIXED JET 

CENTERLINE 

NOTE: THE REFERENCE AXIS FOR THE THEORETICAL (SEE FIG. 5) AND EXPERIMENTAL DEFINITIONS OF (j DIFFER BY 90 0 SEE 

TEXT - DESCRIPTION OF EXPERIMENT FOR DISCUSSION. 

Figure 7 - Coordinate System with Microphone and Dual Jet Orientation Used in 

Experimental Program 

101 
FLEXIBLE TUBING 

ROTATING DISK 

SHIELDING JET 

FIXED MICROPHONE 

~ 

MOTOR 

Figure 8 - Schematic Diagram of Source Jet Rotation Mechanism 

102 

Figure 10 - Photograph Showing Schlieren System 

TIME CODE 

GENERATOR! 

TAPE CONTROLLER 

15 TRACK 

TAPE RECORDER 

HARD COpy 

UNIT 

GRAPHICS 

TERMINAL 

f 

1!3 OCTAVE BAND 

SPECTRUM 

ANALYZER 

PRINTING 

TERMINAL 

CENTRAL 

PROCESSING 

UNIT 

POSITION 

ENCODERS 

Figure 12 - Computerized Data Acquisition and Data Reduction System 

HARD DISKS 

(2) 

f 

ANALOG TO 

DIGITAL 

CONVERTER 

ELECTRONIC 

ICE POINT 

THERMOCOUPLES 

PRESSURE 

TRANSDUCERS 
AAA 1 00 '. /j, /j, /j, /j, /j, 

o 30' /j, 000 Ol}l'IHRo SINGLE JET 

/j, 60' /j, ODe 00000 

r 090' 0 00000000 81}

80

2L!. /j,/j, 0 00 0 

80 IAO iaoooo 0 

0

00 

r ~~ :,:11: __ 

i •••• -, BACKG"OUNO 

60 I- t ....... : ••••••••• 

I- a) M =0.6, T = 0 700 K .... '&'&'&'&'&A:I 

--

I ••• . 

40 L __ I 

co 

'0 

..J' 

CL 

C/) 

140 

t SINGLE JET /j,/j,/j,/j,/j,/j,/j,/j,/j,/j,/j,/j,/j,A 

/j,L!./j, 000000000 ~ 120 /j, /j, 0'000 00000000

00

0 

I- AA [l [l 0 000 

A [lDOO 100 I- A ClOO 

A.&$aji •••• 

f- .... i..... til! I BACKGROUND 

o .............. 801- 0 ............................ _ 

AAA.& 

I60 ~ 

I- b) M = 1.46, To = 700 K 

40 I I I J 

102 103 104 105 

FREQUENCY - Hz 

Figure 13 - Single Jet vs Background Noise Levels 

107 
co 

"D 

-.i 

CL 

en 

90 I OPRESENT EXPERIMENT I a) l/; = 30° 

80 

70 

o 

60 ° 

50 

90 

b) l/; = 60° 

I 

80 

70 ... 

6t 5'"' 

° 

50 

90 

c) l/; = 90° 

I 

80 

70 

60 

50' I 

OPLUMBLEE ET AL 

" \ 

0, 

, 

, 

q 

, 

, 

b 

10-2 10-1 10 

STROUHAL NUMBER 

102 

Figure 14 - Comparison Between Current Single Jet Spectrum and Previous Experiment 

of Plumblee, M = 0.6, To = 300K 

108 
t-' 

o 

\0 

130 rl----------------------------------------------------------------------------------, 

120 

110 

co 

"0 100 

-.i 

0.... 

(/) 

90 

80 

70 ' ~ 

o 2 4 6 8 10 

FREQUENCY, kHz 

12 14 16 18 

Figure 15 - Narrowband Spectra Showing Shock Free Operation of Single Supersonic Jet 

M =1.46, To = 300 K, 1/; = 90° 

20 
110 

c: 

l.iJ 

co 

~ 

::> 

z 

I 

() 

« 

~ 

0.8 •• ------------------------------------------------~ 

0.6 

0.4 

0.2 

,~ 

" 1.( " ~/: , J ' ,. I ' • I • 

J I : 

. , . , , , : ' 

• · ' • 

· , ' ' , ,-, ~ 

, I " \ ~ 

I \ ' 

I \ ' 

, 

, 

\i 

. 

. "' , 

, 

, • 

, 

, • 

, ... , ,,' \ , I \. 

I \ • II , ' 

X/D=41.1 

1 rr "".I-./r I' 

o tAl I} I I : J I" 

4 

It! . - . _ I J J -3 t1. i -2 _. I I: , I , I • 

-1 ·0 2 3 

RADIAL DISPLACEMENT, rID 

Figure16- Dual Jet Radial Mach Number Profile, To =300 K, M =0.6, SID =2.7 
cr: 

w 

(Il 

~ 

::J 

Z 

I 

~ ~ 

0.8r'----------------------------------------------------, 

0.6 

0.4 

0.2 

I 

" I' ,: 

I' 

I ' 

i

rr 

, : 

'-I 

, .. · · .. 

, • • • • • • • • 10 • • • 

• ,""", ; 

1\' 

, \ . \ 0 

, 

\ 

" I" ,: 

.. 

• • • 

, • 

• • 

0\ I ' 

,\ I • '~, 1 :.-.-. . .' ...,.-~." , . - · · " - . , • • • 

. • ' o • 

/

r1 i 

, . • , . • 0' . 1-: I) J_! 1 i __ I I .t l 't!.11 . ~ !I_... I 

- -

. : ,. I 

RADIAL DISPLACEMENT, RID DIAMETERS 

Figure 17 - Dual Jet Radial Mach Number Profile, To = 811 K, M = 0.6, SI D = 2.3 

111 
112 

a:: 

w 

1.5 

F,.SOC, 

, ,. • : A .. \ ....-- XlD = 0 :.,~ : .. \~, 

., " .. " , . , : " \ ~ : I , : /"""" X/D = 4.6 , ' • I 

t '. It , " 

I 

" I I .. 

" 

, 

I

I.: I 

1.0 I \ 

~ i ,'- -', ~ , ...... \ 

~ I, \ ., \ 

~ 1 \\ J \ .0 , , , 

« 'I' ,I, ~ I' 1'1 '" 

05 ,,': i'" I: . I • ,\" I, 

: . , ... ,' I: • \ ' I 

~. I : I ~ '.' r- X/D = 41 .1 '. ,...-............... 4 

" I ' ~ \ .: 

. 

• • I ' \_~' : · . • I 

• I · .. o I 1-..1 T.,... '1" --r • 1 •• • 

-4 -3 -2 -1 0 2 3 

RADIAL DISPLACEMENT, rID 

Figure 18 - Dual Jet Radial Mach Number Profile, To =300 K, M =1.46, SID =2.7 
1.5 I 

I I , ... \ _ X/D=O 

, " I , ',' I X/D=4.6 

I / \ \ I 

J : 

I' ,~ ~,.-XID=9.1 I \ I '/ , , I 

, I I , 

, , , 

1.0r ~' \I 

, 

a:: , I , , 

ill . , 

co 

~ 

~ 

Z 

I i I _.--.... It ;:1/ " l~ ./" X/D=18.3 

~ ~ 

0.5 

0 1 .J' r- '--{ ,', I " -, J: r' ,--,-,-- I 

-4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0 3.0 

RADIAL DISPLACEMENT, rID 

Figure 19 - Dual Jet Radial Mach Number Profile, To =811 K, M =1.46, S/D=2.7· 

113 
114 

a: 

ill 

m 

~ 

::> 

z 

I 

0 

« 

~ 

0.6~ ... 

\ D 

0.4 

0.2 ~ , ,) 

\ .. -. 

o ' • I I I 

0 5 10 15 20 25 30 35 40 45 

a) AXIAL REGION O::s XlD::s 45 

0.65 

0.60 

0000000000 

o 

o 

o 

o 

0.55 

o 

o 

5 7 0.50 L. --'--~---!:-~-~:--~:--~;--~~!:i o 1 2 3 4 6 8 9 

b) ENLARGEMENT OF AXIAL REGION 0 ::sXlD::s9 

AXIAL DISPLACEMENT, XlD 

Figure 20 - Axial Centerline Mach Number Profile, To = 300 K, M = 0,6 
2.0 

M To(K) 

0.6 0 300 

0.6 cr 811 

0.94 0 300 

0.94 0' 811 

1.5 1.46 ..6. 300 

1.46 J:{ 811 41 l( I 

a:: 

L.U I 

ro 

~ 

::l 

Z 1.0 

I II" 

~ ~ 

0.5 • 

I 

I 

o I I I I I I 

o 2 4 6 8 10 

CORE LENGTH, LID 

Figure 21 - Effect of Mach Number and Temperature on Potential Core Length 

115 
0.20r-1 ---------------------------, 

0.15, 81D=2.70 

a: 8/0=3.11 

w 

CO 

2 81 11-- SID = 3.80 

:J 

z 

2 

I 

() 

« 

0.10 

g; ~ I . ~-o~ ~ 

OC ; di- SID = 5.54 

0.05 r- Oo A ~<I) ~~ 

cP Ql. A ~ 

: ~ • S/0=7.86 

A <> , 

8 

o I [] lAO. I 

0 5 10 15 20 25 30 35 40 45 50 

AXIAL DISPLACEMENT, XID 

Figure 22 - Axial Mach Number Profiles on Mid·Gap Line for Various Dual Jet Spacings 

To =300 K, M =0.6 

116 
0 

-

E 

...J 

I 

f0 

Z 

W 

...J 

0 

z 

0 

a:: 

w 

~ 

25 

20 

15 

10 

5 

o 

o 

X 

I 

2 

MJ 

0.6 0 1, 

0.94 0 

1.46 1:::.. 

0.97 X WANG (REF. 8) 

J1 

0 

A 

0 

A 

ft 

I ~ I I 

4 6 8 10 

JET SPACING, SID 

Figure 23 - Effect of Jet Spacing and Mach Number on Merging Length 

117 
ll8 

~ 

o 

ill 

a: 

~ 

~ a: 

ill 

CL 

~ 

ill 

I900 

800 

700 

600 

-l 

~ 500 

b 

I400 

r-

,-. 

. \ , , . , , . . , , , , . , 

• • . , . · , · , · , 

," 

• ,

, 

, 

'\ . .'11' '\'\ ' . 

'1 

, 

~ 

'\ 

'\ 

I' ,: 

/1

" ..... J.,.--.,. _/. , ",,_'" I ' ,,~,. I· 

."...~ " t--- ,,".' 

300 r- ----." ,..~ 

-4 -~ - ---3 -2 -1 

1 

o 

I 

"1 

RADIAL DISPLACEMENT, rID 

XID =0 

X/D=9.1 

X/D= 18.3 

Figure 24 - Dual Jet Radial Temperature Profile, To = 811 K, M = 0.6, SID = 2.7 
0.08 

0.06 

a

tO I 0.04 

to 

a 

aC/) I 0.02 

..J" 

4: 0 ~ 

z 

w 

a: 

w 

-0.02 

!.L 

l.L 

0 -0.04 

w 

a: 

=> 

(J) 

-0.06 

(J) 

w 

a: -0.08 a 

-0.10 

I I 

0 2 12 14 16 

AXIAL DISPLACEMENT, rID 

Figure 25 - Axial Static Pressure Variation on Jet Centerline, To = 300 K, M = 1.46 

119 
120 

0:: 

w 

en 

~ 

=> 

z 

I 

0 

« 

~ 

1.50 

1.25 

1.00 

0.75 

0.50 

0.25 

a) O::s X/Ds50 

1.50 

1.45 

1.40 \ 

, '1.35 \ 

1.30 \ 

CO 

1.25 

b) ENLARGEMENT OF REGION Os XID::s 12 

1.48 

1.47 

1.46 

1.45 

I I I , 

1.44 b 2 3 4 5 6 

c) DETAIL OF REGION 0::sXID::s6 

AXIAL DISPLACEMENT, XID 

Figure 26 - Axial Centerline Mach Number Profile, To 300 K, M = 1.46 
.--l 

N 

.--l 

I/) 

0 

:0:: 

CO 

II: 

c: 

0 

I/) 

c: 

CO 

c. 

>< UJ -c: 

Q) 

... 

Q) --

C -CO 

I/) 

Q) 

N 

N 

0 

Z 

CJ 

c: 

0 

I/) 

... 

Q) 

C. 

::J 

en -0 

I/) 

J: 

C. 

CO 

... 

C'l 

0 -0 

J: 

Il. 

c: 

Q) 

... 

Q) 

J: 

CJ 

en 

I 

..... 

N 

Q) 

... 

::J 

C'l 

i.L 
122 

-% 

DIFFRACTED/SCATTERED 

TRANSMITTED/RE 

• OBSERVER 

LOCATED AT 

COORDINATES 

R,a,/f -IIfI 

* a) SOURCE JET RADIATION 

/III DIFFAACffDI~~ 

DIRECT AND 

TRANSMITTED/REFRA~CED 

• I 

OBSERVER 

--!I!! 

~ 

INCIDENT 

H-H-~ 

b). SHIELDING JET RADIATION 

Figure 28 - Acoustic Radiation Arriving at Observer Location Due to Source and 

Shielding Jets 
co 

"'0 

-l 

CL 

(f) 

90 

80 

70 

60 

110 

100 

f 

90 

80 

120 

110 

100 

90 

10-2 

. 

. I 

DUAL JET 

ORIENTATION, e 

o 180 0 

o 90 0 

0000 

,...,ggooon PO O 

gD ••• ··.&gD~OO 9 • ..g 0 

~.. gg 

9 SYNTHESIZED SINGLE 

• JET ORIENTATION, e 

A 180 0 

o 90 0 

J 

a) M =0.6 

OO---OOp 

o 0 D Dg 0 

ooD ••• ig~ 00 

o~:·· I II X; I 

.. ;.~~r " .... "" ... 

b) M = 0.94 

0 00 000 

OoDOODnoO 

0 060;> "6i~ Vo 

'i. D o OD 6 66 

0°4! 

D6 

DO 6 

<i 6 

I I I III I I I I I III I I I 1.1 ILL 

10-1 10 

c) M = 1.46 

STROUHAL NUMBER 

Figure 29 - Mach Number Effect on Dual Jet Spectrum, To = 300 K, SID = 8.1, ~ = 40° 

123 
124 

6 

4 

2 

o 

6 

co 4 

"0 

--i 

~ 2 

<I 

to 

6 

4 

2 

o 

10-2 

i 

01:> .0 ........ 0 

- ° - "0°00 

I aPaaDaD 00 I a u 

PODCDo D 

I I I I III , I I 11111 I I 111'1 

d) M = 0.6 

" 000 '''0''- u - DOD g g g-'la DilDO f DD DD 

e) M =0.94 

.oc 000 

'U 0- u Oe 000 

O"D I~ 

0 DUO D DDD DC g D g 

, t I J .1. 0 0 I Li lit 0 1 . .1 __ .11.1.11 

10-1 10 

STROUHAL NUMBER 

f) M = 1.46 

Figure 29 - Concluded 
CD 

"0 

..J 

0... 

CI) 

110 

100 

90 

DUAL JET 

ORIENTATION.e 

o 180 0 

o 90 0 

SYNTHESIZED SINGLE 

JET ORIENTATION, e 

A 180 0 

<) 90 0 

OOV vVOO 

o 000 Po 

Po.· 00 °t •• iii ~ 00 

iiiO 

oa. 

• 

08· 

0 

•• 

so __ l _____ I-----.l L-.J 1.1_1 _ . . 1 I I I IJ . . 1 11. Ll 

1 10 

100 

90 

80 

110 

100 

90 

I-

~ 

tSO 

10-2 

. 

. 

a) S/D=S.1 

000 ",vO o 

o 00 i Po 

00

0 •• i~i ~ 0 0 pD •• ii 0 

Q P. .~ - 9 

9 

g. 

•• I I I 1111 . I I I I III . • I I I III 

b)S/D=5.5 

-

noon 

v "'0 - 0000000 POo gO •••• 0 

0 

~ . •• • ~ii:o • o. 0 

0 

• I I'·' 1111 . I I I 11111 I t I I II 

10-1 10 

C) S/D=3.1 

STROUHAL NUMBER 

Figure 30 - Spacing Effect on Dual Jet Spectrum, To=300 K, M =0.94, ~=40° 

125 
126 

6r--------r--~--~--------r_------_r------~ 

41 1_ lei ~ I~ 

CD I 

-0 

-.i 2 I 

fu • 

<1 .. t9' 

0 1 I '?'j 

-2~'~~~~~~~~~~~~~~~~~~~~~~~~ 

-50 o 50 100 150 200 

AZIMUTHAL ANGLE, e 

Figure 31 - Normalized Dual Jet Sound Pressure Level Dependence on Azimuthal Angte, 

M=O.6, To =300 oK, 5/0=8.1, f=4 kHz, ~=20° 
POTENTIALLY 

PHASED 

SHIELDING 

JET 

DIRECT 

RADIATION 

REFLECTED 

RADIATION 

SOURCE JET 

Figure 32 - Schematic Illustrating Sound Reflection by Adjacent Jet Increasing 

Noise at Observer Station 

127 
86 

co 84 "0 

...J 

ill 

> ill 

-l 82 ill 

a: 

:J 

(f) 

(f) 

ill 

a: 80 

Q... 

0 

Z 

:J 

0 

(f) 78 

76 L' __ ~ __ L-~ __ ~ __ L-~ __ ~ __ ~-J __ ~ __ ~~ 

80 100 120 140 160 180 200 

AZIMUTHAL ANGLE, 0 

a) COMPARISON OF DUAL JET AND SINGLE JET AT f = 4 kHz 

Figure 33 - Dual Jet and Single Jet Sound Pressure Level Dependence on Azimuthal Angle, 

M =0.6, To =300 oK, 5/0=8.1, 1/t=40° 

128 
80f-~~ co 78 "0 

---i 

w 

> 

76 1 w 

.....I 

w 

a: 

~ 

(f) 

(f) 

w 74 a: 

CL 

0 

Z 

~ 

0 

C/) 72 

7011 ~ __ L--L_~~L-~-L~ __ ~~~-: 

80 100 120 140 160 180 200 

AZIMUTHAL ANGLE, () 

b) SINGLE JET DEPENDENCE ON FREQUENCY 

Figure 33 - Concluded 

129 
130 

SOURCE JET 

MODELLED AS POINT 

SOURCE r JETCf 

I '< L Cf 

ELLIPTICAL DIRECTIVITY PATIERN 

USED FOR ILLUSTRATION PURPOSES ONLY 

a) PLAN VIEW OF SOURCE JET SHOWING 

POLAR RADIATION ANGLE CHANGES 

SENSED AT FIXED MICROPHONE 

MICROPHONE 

FIXED 

MICROPHONE 

LOCATION 

,=180· j 

SOURCE JET, 

(} =90 0 

~ SOURCE JET. 

(} = 180 0 

b) END VIEW OF DUAL JET SYSTEM LOOKING UPSTREAM 

Figure 34 - Source Jet Radiation Pattern Sensed by Fixed Microphone During Azimuthal 

Rotation 
;-

SIDELINE 

OBSERVER 

+ 

+ 

+ 

+ 

+ 

c5

SHIELDING 

JET 

a) DUAL JET CONFIGURATION 

SHIELDING JET 

JET 6

S0URCE 

SOURCE (ROTATES 

~ 

_ V_ABOUT SHIELDING 

JETI 

FROM SOURCE REFLECTING 

J

ACK RADIAT~ION - JET (ROTATES 

ABOUT SOURCE) 

DIRECT REFLECTED 

RADIATION RADIATION 

FROM SOURCE 

b) FULL ANALYTICAL MODEL 

RAD~ SHI~ -fooURC

' 

DI~ c) ANALYTICAL MODEL REPRESENTING 

EXPERIMENTAL RESULTS 

REFLECTING 

/--r JET REMOVED 

FROM MODEL 

( \ 

\ I " --/ 

Figure 35 - Selection of Analytical Model Representing Dual Jet Geometry 

131 
132 

6 I F ~ 

4 .. --t _~:( '\'f[ jjI~A 

m 2 Ai£:,,,,", _ .... 

"0 

-.J 

a.. 

Cf) 

<l 01- ' l b'- \ .~ .. 1\', J \ - ,i .-1 

..... _-- I -~URVE 2 Ii-----

-2 \ I ~ l 

CURVE 1cOBSERVER-JET-SOURCE 

CURVE 2-0BSERVER-SOURCE-JET 

-4 f I CURVE 3-LlNEAR SUM I 

80 100 120 140 160 180 

AZIMUTHAL ANGLE, () 

a) DISCRETE TONE CALCULATION, f=4 kHz 

200 

Figure 36 - Comparison of Measured and Predicted Azimuthal Directivity Pattern 

M =0.6, T 0= 300 0 K, SID =8.1, ~ =40 0 
ro 

"0 

....J 

(L 

(f) 

<I 

6 

} ~'-'" . .. ( I _. I I . 

4~ I //' 

! I _,/ 2 I 

" 

• I \.j / "-' I 

o r-.. • .... ----j· .... ut--i- .. .l--.~_, " ~ '. 1'- I \' , 1 , ~ -= ," y, \: , 

'....1 I 2 ' -- j « ! 

-4 

80 

I 

--~~.--~--~--~!~--~~--~--~--~~ 

100 120 140 160 180 200 

AZIMUTHAL ANGLE, e 

b) V3 OCTAVE BAND CALCULATION, f = 4 kHz 

Figure 36 - Concluded 

133 
134 

.6 

4 

2 

co 

"0 

.....i 

CL 

CI) 

<I 

-2 

-4 

I 

-6 L 

80 

2 ~ I ;~;o = 3564 Hz '. OBSERVER-JET-SOURCE 

o = 4000 Hz - - - - - - -, OBSERVER-SOURCE-JET 

3-fO =4490 Hz·- --_.- LINEAR SUM! 

.. ....1-- 1 I I I 

100 120 140 160 180 200 

AZIMUTHAL ANGLE, () 

Figure 37 - Effect of Frequency on Predicted Azimuthal Directivity Pattern, 

M=O.6, To=300 o K, 5/0=8.1, If=40o 
4 r- BAND v, O~TAVE RANGE :j ,. ,--- ... ~ CURVE 3 /"--....... , 

.' " " , " " " " 

. . " 1'. __ ... - . . , 

"" '. . I- , . .,..' ,., ....... ". ",.-" /' ,- ", --. , ~ , . , 

, 

" . , 

2 

CD ·........-CURVE 2 ... ..- . . , . . , ~ 0 ,. , ....J 

0... 

(f) 

<] 

.. . . ... . . . , . . , , , . , " -. '. . ' .......... ..- '. ' 

, ". .... - ' ....... " 

CURVE 1-0BSERVER-JET-SOURCE 

-2 CURVE 2-0BSERVER-SOURCE-JET 

---- CURVE1~ CURVE 3-LlNEAR SUM 

-4 

3000 

I L ~ 

3500 4000 

FREQUENCY, HZ 

4500 

a) FREQUENCY RANGE, 3-5 kHz 

I 

5000 

Figure 38 - Frequency Dependence of Discrete Tone Prediction, M = 0.6, To = 300 ° K, 

SID =8.1, ",=40°, e =90° 

135 
136 

co 

"0 

-.J 

a... 

(f) 

<I 

I 4 ,-- V3 OCTAVE 

2 

CURVE 3 

,. :\ t .. ;~:I''I :, r.'!'. LoU .'---''--' .... r_ <I 1. 

BAND RANGE 

., ·n . --." , ,I .! !' jl .\ ,: {i n .j I I :!; I Ii! •• t .! ; ! i! . i ! I ,,\ '.i 

L\ I. 0\ I. .I. .\ 

• ,1 /', .! ,'1 " \ .' '\ ' .. ,. ,'d "', .~. ,'~I ,.', " ,1 IV'" ,'.I ,., ., .. .. "'1"' •• ,,"',..!",. "1'.1 h ... ,..,. r. 't" . !. i i..! ',i I .• ! · .. i i.~ !;.! ":i i.~· I::! I::! !:? .~! .::! i:':· 1:1i ~:!!::­ ~,:: \;:~, I:!, i:~l !:~',;:' ':!l!: :',;::1 1::\': :,1::, : :,!: :11: :!~ Iii: :, J: ~ \': ~1: :i: :~: ~~: t.: 't :.,: :.: :l': :!i: :'1: :,: :',: :.~: :'f: :,: !,;: :~ ~ : : : : • : : : : :. :::. ';' • • t • • , t I • • I , t I , •• • ~ • ; • ~ :: ;; ~ : • : 

o .......... '. • .. ............. I' '. I I ' •• I •• I •• " , ............. '. '" '.' t II It ,t " '. 

:: ;: :: :: :: l: :::1:::: l: :' i: l: :: :: ::: :::: :: l! :: ii " .' I, ., ',,' II I, lilt I' • " " ,I " II I' " " It " I' " 

~.: :." "1: !i." "': !.;: ''1: :V! ~! !tj: ~V~ :&:: 

L! ................................ '~~ •• 1. I ~ ~ ~ ~. i')! ~:...:.: ': ~ < ~ , \ I I I '. • 

-2 

CURVE 27 

[fRVE1~ I 

~_, ~ , , -', I , , , , I , , ,= 

10 15 20 25 30 

FREQUENCY, kHz 

b) FREQUENCY RANGE, 10-30 kHz 

Figure 38 - Continued 
ll) 

"0 

2 

o 

-2 

~ 

~ ...i 

0.. 

C/) 'v rCURVE 1 

<I -4 

-6 

~ 

-8 

o 

t--.... 

1 

10 

-------~ r-----:----. 

1 i 1 i 1 1 __ II ~ ,- ~ 

20 30 40 

FREQUENCY, kHz 

c) FREQUENCY RANGE, 0-60 kHz 

Figure 38 - Concluded 

----. 

50 60 

l37 
138 

en 

"0 

.....J 

0.. 

Cf) 

<l 

6 CURVE 1-0BSERVER-JET-SOURCE I 

CURVE 2-0BSERVER-SOURCE-JET I 

CURVE 3-LlNEAR SUM 

CURVE 4-FINAL ANALYTICAL MODEL, 4 

t-

-- ....... rCURVE 4 -,-_ ........... " 

r-._ ---~----- ...... '" ----~-L---- ". . ,:.- -~--------~ CURVE 3 ~,--------~- , ./ 

~ .... '-_.' .# ....... ". .'" '. .... ""', " ..... . .-. " 

" .. - "-'" -,- " ... 

2 

. 

, 

CURVE 2 ~" ,,' " , 

. .' " I'"~ -.. __ .,- , 

o 

-2 

-

-4 

3000 

6 

I I I I I 

3500 

......... 

CURVE 1~ 

I I I I I 

4000 

FREQUENCY - Hz 

a) () = 90 0 

I 

' ......... , . 

I I t I I 

4500 5000 

L CURVE 4 CURVE 3 ~ 

'~"-.--"''' .---.----....... ~- ~------- ~-------.--: ....... _ .... ~--------.:::... ---~ ...... ----... 4 .... 

~ 

CURVE 1~ 

- 2 r--- ....... ,,- ...... ......... " ". t:. CURVE 2- ,,- -"" , , , 

. I' , , " 1\ I' ", . " 

. . 

, ,Y , 

. . , 

" 

o 

r-

-2 

..1 -4 

3000 

" 

, , 

....... 

3500 

'" ", . .' ...... ' 

I I ..1 

4000 

FREQUENCY - Hz 

b) () = 125 0 

..1 

4500 

..1 ..l.-

5000 

Figure 39 - Frequency Dependence of Discrete Tone Prediction at Various Azimuthal 

Angles, M =0.6, To = 300 oK, SID =8.1, If; =400 
CD 

"0 

--l 

0.. 

CI) 

<l 

6 

CURVE 3 

4 

.-- , . L."_-

2 ------?"'-

--' ,. 

CURVE2~ • ........... 

",. """''' . o , . 

" , , 

" , ........ " ..... ,-" .. ......... 

-2 

-4 

3000 3500 4000 

FREQUENCY - Hz 

c) () =150 0 

6 

CURVE 4 

------ -...t"*':: ......... , ;>,~ " .... --.-- 4 

".------............. 

... ---. . '. ".- ..... , 

", ", 

, 

, 

.' 

4500 5000 

''-CUR~-~ ....... ""'.... -, .... --.. '~ .. 2 ----------

o 

-2 

-4 

3000 

" '" " ". ", -... ..' 

3500 

, ", 

4000 

FREQUENCY - Hz 

d) () = 160 0 

Figure 39 - Continued 

, 

" '. I'" '''---

, 

, ' .. , ,.,# .. ......... 

.", 

1- 1_- ---'-------

4500 5000 

139 
140 

£Il 

"0 

--l 

0.. 

CI) 

<J 

6 

.----- .-- ......... .---...... CURVE 4 ,. .. ~- ---------........ ~ -" -' ... 

4 

2 

o 

-2 

-4 

3000 

6 

4 

.......... ' .. . ... - .... .... ...... " . J. ..... -":,, , -- .... -_#I> ~~--- - .;.-. CURVE 3 

........... _ ..... 

'~CURVE2 

3500 4000 

FREQUENCY - Hz 

e) e = 170 0 

CURVE 4 

",. .... ---..... 

.",- ... --------- ... :",,¥y'''''-- CURVE 3 

.... - ....... '.~ ,'.t 

4500 

-_.-:" ---- ,,'" .... ~ .... ". 2 .... _,tt 

o 

-2 

-4 

3000 3500 4000 

FREQUENCY - Hz 

f) e = 180 0 

Figure 39 - Concluded 

4500 

5000 

,,' 

5000 
co 

"'0 

-1 

Cl.. 

C/) 

<1 

8 

6 

4 

2 

o 

-2 

80 

8 

6 

4 

~ 

2 

~ 

o 

~ 

'-2 

80 

100 

100 

I 

120 140 160 

a) EXPERIMENT 

I 

120 140 160 

AZIMUTHAL ANGLE, () 

b) THEORY 

180 200 

! 

I 

I 

: 

i 

I 

180 200 

Figure 40 - Comparison of Measured and Predicted (Based on Final Theoretical Model) 

Azimuthal Directivity Pattern, M = 0.6, To = 300 oK, t/; = 40 0, f = 800 Hz 

141 
142 

co 

"0 

....J 

c... 

(J) 

<I 

8 

6 

4 

2 

o 

-2 

8 

6 

4 

2 

o 

-2 

80 100 

lII-

- lI 

80 100 

120 140 160 180 200 

a) EXPERIMENT 

i 

.-

/ \ /' V \f , 

I ~ , 

120 140 160 180 200 

AZIMUTHAL ANGLE, () 

b) THEORY 

Figure 41 - Comparison of Measured and Predicted (Based on Final Theoretical Model) 

Azimuthal Directivity Pattern, M =0.6, To =300 0 K, 1f =40 0 f =4 kHz 
co 

"0 

...i 

CL 

(/) 

<I 

8 

6 

4 

2 t to 

-2 

80 

8 

6 

4 

2 

o 

-2 

80 

100 

100 

120 140 160 

a) EXPERIMENT 

120 140 160 

AZIMUTHAL ANGLE, (J 

b) THEORY 

180 200 

180 200 

Figure 42 - Comparison of Measured and Predicted (Based on Final Theoretical Model) 

Azimuthal Directivity Pattern, M =0.6, To =300 oK, ,p=40°, f =20 kHz 

143 
144 

8 

6 

4 

2 

o 

-2 

80 100 120 140 160 180 200 

CD 

U 

....J a) MEASUR~MENT, M = 0.6 0.. 

C/) 

<] 

8 

6 

4 

2 

o 

-2 

80 100 120 140 160 180 200 

AZIMUTHAL ANGLE, () 

b) MEASUREMENT, M = 0.94 

Figure 43 - Mach number Dependence of Measured and Predicted Azimuthal Directivity 

Pattern, To = 300° K, SID =8.1, 1f =40°, f = 800 Hz 
co 

"0 

~ 

CL 

if) 

<I 

8 

6 

J4 

J- ~ = 0.6f,., ... M = 0.94 t>,. _ '1 ! '- (: __ ... u........ . .... .... ,. -' ......... q,. .. ...... 

.. , 

2 F·u.-.'f---.u-.. -[---~::-,..· ----- - ---- . - .".'" 

M = 1.46 

... 

o 

... 

-2 I I I I I 

80 100 120 140 160 180 200 

}AZIMUTHAL ANGLE, e 

c) PREDICTION, M = 0.6,0.94, 1.46 

Figure 43 - Concluded 

145 
8 

6 

4 

2 

o 

-2 

80 100 120 140 160 180 200 

CD 

"0 a) MEASUREMENT, M = 0.6 --i 

CL 

C/) 

<l 

8 

6 

4 

2 

o 

-2 

80 100 1 20 140 160 180 200 

AZIMUTHAL ANGLE, (J 

b) MEASUREMENT, M = 0.94 

Figure 44 - Mach Number Dependence of Measured and Predicted Azimuthal Directivity 

Pattern, To=300 o K, 5/0=8.1, ~=40°, f=2 kHz 

146 
fl) 

-0 

-la... 

rJ) 

<1 

'8 

6 

4 

2 

o 

-2 

rM ,0.94 -:--.. 

¥.~ 

~ L.-' "','", . ""7 ',,\ -'-I /M=O~ ., ~ ,:",' '.'\ .. ~ "~ "' 

#,-,#1' "" " ~ .'~' I 

r:::::;:::.:::- ::':.---M=1.46 I 

! 

tI 

~ 

-.L -.L ...l. 

80 100 120 140 160 180 200 

AZIMUTHAL ANGLE, e 

c) PREDICTION, M = 0.6,0.94, 1.46 

Figure 44 - Concluded 

147 
8 

6 

4 

2 

o 

-2 

80 100 120 140 160 180 200 

CD 

"0 

a) MEASUREMENT M = 0.6 -l 

Q.. 

(f) 

<l 

8 

6 

4 

2 

o 

-2 

80 100 120 140 160 180 200 

AZIMUTHAL ANGLE, e 

b) MEASUREMENT, M = 0.94 

Figure 45 - Mach Number Dependence of Measured and Predicted Azimuthal Directivity 

Pattern, To =3000 K, 5/0=8.1,11=40°, f=4 kHz 

148 
8 

6 

4 

M=0.6 

2 

-_ ..... _-.. -<.- M = 0.94.1 .46 

G 

-2 

co 80 100 120 140 160 180 200 "0 

-l c) PREDICTION, M = 0.6, 0.94, 1.46 CL 

CJ) 

<l 8 I i 

I 

~ I 

6 

4 

2 F. __ --:=--~--ti~ I -'.. '.' 1 J -. I 

.,-

o I ~ I 

-2 h' __ ~ ____ ~ __ -L __ ~ ____ ~ __ -L __ ~~ __ ~ __ ~ ____ ~ __ ~ __ ~ 

80 100 120 140 160 180 200 

AZIMUTHAL ANGLE, (j 

d) PREDICTION, CONSTANT STROUHAL NUMBER, ST = 0.854 

:Figure 45 - Concluded 

149 
8 

6 

4 

2 

o 

-2 

en 80 100 120 140 160 180 . 200 

"0 

--l a) MEASUREMENT, M = 0.6 CL 

(f) 

<I 

:s 

6 

4 

til 

2 

o 

-2 

80 100 120 140 160 180 200 

AZIMUTHAL ANGLE, 8 

b) MEASUREMENT, M = 0.94 

Figure 46 - Mach Number Dependence of Measured and Predicted Azimuthal Directivity 

:Pattern, To =300o K, 5/0=8.1, 1f=40°, f=20 kHz 

150 
co 

-0 

-i 

CL 

en 

8 

6 

4 

<I 2 

o 

·2 

80 100 120 140 160 180 200 

AZIMUTHAL ANGLE, () 

IG) PREDICTION, M = 0.6,0.94, 1.46 

:Figure 46 - Concluded 

151 
~8 

6 

4 

2~ 

o 

--2 L _---1. __ _'____-I-_~ _ __'_ _ __'_ _ __'L.._._.L_ _ _'___ _ _'__....L.. _ __' 

OJ 80 100 "'0 120 140 160 180 200 

-1 

Q... a) MEASUREMENT, Sf 0 = 8.1 

C/) 

<l 

8 

6 

4 

2 

o 

-2 l. __ --' _____ l __ L-. 

80 100 120 140 1 60 180 200 

AZIMUTHAL ANGLE, e 

b) MEASUREMENT, SID = 5.5 

Figure 47 - Spacing Dependence of Measured and Predicted Azimuthal Directivity Pattern, 

M =0.94, To =3000 K, 1/;=40°, f =800 Hz 

152 
en 

"0 

-1 

0... 

U) 

<I 

8 

6 

4 

2 

o 

-2 

8 

6 

4 

2 

o 

-2 

80 100 120 140 160 180 200 

c) MEASUREMENT, SID = 3.1 

r S/D=8.1 

I _ ..... _------~ ~ ~=:=.-.- ~ -- ... ---_ .. -- -:-----:r:- :-.:--:::;:: --_ ... _---

\ ~ I- S/D=3.1 

f- SID = 5.5 

80 100 120 140 160 180 200 

AZIMUTHAL ANGLE, e 

d) PREDICTION, SI D = 8.1, 5.5, 3.1 

Figure 47 - Concluded 

153 
8 

6 

4 

2 

o 

-2 

CD 80 100 120 140 160 180 200 

-0 

-1 a) MEASUREMENT SI D = 8.1 

0... 

Cf) 

<1 

8 

6 

4 

2 

o 

-2 

80 100 1 20 140 160 180 200 

AZIMUTHAL ANGLE, e 

b) MEASUREMENT, 81 D = 5.5 

Figure 48 - Spacing Dependence of Measured and Predicted Azimuthal Directivity Pattern, 

M =0.94,10 =300 0 K, ~=400, f=4 kHz 

154 
8 

6 

4 

2 

o 

-2 

80 

en 

"'0 

..J 

0... 

(J) 

<I 8 

6 

4 

2 

o 

-2 

80 

100 120 140 160 

c) MEASUREMENT, SID = 3.1 

~.-.,,\: .... , '" .--.-. "'SID = 3.1 

100 120 140 160 

AZIMUTHAL ANGLE, e 

d) PREDICTION, SID = 8.1,5.5,3.1 

Figure 48 - Concluded 

180 200 

180 200 

155 
OJ 

-0 

-l 

0... 

(f) 

<] 

S 

6 ~I----~r-----;------+------+------r----~ 

4 

.. 

2 L:.: k~ 

o ~I ----~------r_----4_----_+------~--~ 

-2 

SO 

S 

6 

4 

2 

o 

-2 

so 

100 120 140 160 

a) MEASUREMENT S/D=S.1 

100 120 140 160 

AZIMUTHAL ANGLE, e 

b) MEASUREMENT, SID = 5.5 

1S0 200 

1S0 200 

Figure 49 - Spacing Dependence of Measured and Predicted Azimuthal Directivity Pattern, 

M =0.94, To =300° K, ~ =40°, f =20 kHz 

156 
co 

"0 

.....I 

CL 

(/) 

<l 

8 Ir-------r-------~------,_------_r------~------_, 

6 ~I------~------+-----~~----~--------+------~ 

4 1 1 .. "'- -~..., ~ n -O"f J OW 

2 I till 

o 1--

-2 LI __ L-_-L~L_~~ __ ~~ __ ~~ __ ~_L~ 

80 100 120 140 160 180 200 

c) MEASUREMENT, SID = 3.1 

8 

6 I~----+------r----~~----+------r----~ 

4 I I I if . _ 71' ,,_ j I " • t ~.. _ I :'t,. 24 

2 I ,:! I· "::J ,. .. t<'f \l 

o 

-2 

80 100 120 140 160 180 200 

AZIMUTHAL ANGLE, e 

d) PREDICTION, SID = 8.1, 5.5, 3.1 

Figure 49 - Concluded 

157 
158 

8r.------~----_.------,_------r_----~------~ 

6rl------~----_r----~r_----~------~----~ 

41 I ~, cP 

2~ ~ 

O~,--_t-----t-----+-----+-----+----~ 

-2 

80 100 120 140 160 180 200 

m 

-0 

-l a) MEASUREMENT, To = 300 0 K 

£l.. 

(f) 

<I 

8 

6 ~I ------~------~------+-------+_------+_----__1 

41 I A'"OAGr:::£l: I ..... "'" -;.9" I 

21 ~ 0 1 

O~V ... ~1f)J 

-2 ~._.l-----L_-'--_..L---l_--L_..L_-lL---1._.J...----1 

80 100 120 140 160 180 200 

AZIMUTHAL ANGLE, e 

b) MEASUREMENT, To =811 0 K 

Figure 50 . Temperature Dependence of Measured and Predicted Azimuthal Directivity 

Pattern, M =0.6, SID =8.1, 1f=40°, f =20 kHz 
8rl------~r_------,_------_,r_--------------_,------~ 

---To=300° K 

------To=589° K 

--- To =7.000 K 

6 1-1 ---+-----'I-----+-- --- To =811 0 K 

CD 41 1 IN~'. 1 "0 

....r 

c... 

(f) 

<:i 21 H· "f' 

Or I ----~----1-----1-----1------~--~ 

-2 L--~;c;o---L-~~---:;-:~-L--~---L-~--1.~ 80 100 120 140 160 180 200 

AZIMUTHAL ANGLE, e 

c) PREDICTION, To = 300 0 K, 589 0 K, 700 oK, 811 oK 

Figure 50 . Concluded 

159 
160 

III 

"0 

.....J 

0... 

(f) 

<1 

8 

61~----+-----~-----+------~----~----~ 

41 ~Ob~l 

2 I ~ lYtZ"" I IT "'7'A I ,au 

O~I ----~----_+----_+----_4----~----~ 

-2 L' __ ~ __ ~ __ L--J __ -L __ ~ __ ~~~~~~~~~~ 

80 100 120 140 160 180 200 

~ MEASUREMENT, To=300° K 

8 

61 I em ,v I 

4~ 1_ ~-~I- °1 

2rl:)~-

O~I----~~----~-----+------+-----~----~ 

-21~--~--~--~--~--~--~--~--~--~--~--~-J 

80 1 00 120 140 160 1 80 

AZIMUTHAL ANGLE, e 

b) MEASUREMENT, To = 811 ° K 

200 

Figure 51 . Temperature Dependence of Measured and Predicted Azimuthal Directivity 

Pattern, M =0.6, SID =8.1, if; =40°, f =800 Hz 
CD 

"0 

......I 

0... 

Cf) 

<1 

8 r--------,---------r-------~------------------~------~ -- To=300° K 

----- To=589° K 

--- To=700° K 

61 - --- To=811 ° K -t------i 

I4 rt-t--+-=b~-~~-:;;:--I. ,1 .,; .. ;...."":. ----

IO~I------J__----~------J__----~------+_----~ 

I-

-2 I I I ! 

80 1 00 1 20 140 160 180 200 

AZIMUTHAL ANGLE, e 

c) PREDICTION, To=300° K, 589 0 K, 700 0 K, 811 0 K 

Figure 51 . Concluded 

161 
162 

co 

"0 

-1 

Cl.. 

(f) 

<I 

8f 

6~1 ----~----~--~-----+----~--~ 

41 ,dJ ~,d 

2.k e ~ 

O[ 

-2 

80 100 120 140 160 180 200 

~ MEASUREMENTTo =300 o K 

8 rj--------r--------r------_,~------,_------_,--------, 

6 ~ _q;, 

4 I AD ~ IQl V I 

21 «~~~ 

0~1 ----~----r_--~-----+----~--~ 

-2Lj __ J-__ L-~~~ __ _L __ ~ __ ~ __ ~~ __ ~ __ ~~ 

80 100 120 140 160 180 200 

AZIMUTHAL ANGLE, e 

b) MEASUREMENT, To =811 ° K 

Figure 52 . Temperature Dependence of Measured and Predicted Azimuthal Directivity 

Pattern, M =0.6, SID =8.1, f =40°, f =4 kHz 
IJ:J 

-0 

.....J 

0.... 

CJ) 

<] 

8 , To-3000 K I 

----- To=589° K 

---To=700° K 

61~-----r------r_---- ----To=811 ° K.------1 

4 I 1/ ,K' .... h'< , <I _.. _d 

2 I ,(.,.- p..,;' :ow."X_ t''''''' C l 

Olr----~~-----r------r_----_r------~----~ 

~' £ 

80 100 120 140 160 180 200 

AZIMUTHAL ANGLE, e 

c) PREDICTION, To=300° K, 589 0 K, 700 0 K, 811 0 K 

Figure 52 . Concluded 

163 
164 

CD 

"0 

....J 

CL 

rJ) 

<I 

8 rl--------r-------~------_,--------,_------~------__, 

6 1 , 'A I l ..... bO;: , 

41 ,,.,,, ,_ .. ,sA 1 

21 ~Rr 

01r-----1------+------r-----~----~----~ 

-2 

80 100 120 140 160 180 200 

a) MEASUREMENT, if; = 20° 

8 

6~1 ----_4------r-----+-----~----_4----~ 

41 tdJ ~ ~~i 

2.1.: b • 

Orl----~~----;-----_+------r_----~----~ 

_21~--~--~--~--~~--~--~--~--~---~~--~--~ __ ~ 

80 100 120 140 160 

AZIMUTHAL ANGLE, e 

~ MEASUREMENT,if;=40° 

180 200 

Figure 53 . Polar Angle Dependence of Measured and Predicted Azimuthal Directivity 

Pattern, M =0.94, To =300° K, SID =8.1, f =4 kHz 
8rl--------r-------or-------,r-------,--------,--------~ 

6~----~----~~----~------~----~----~ 

41 IWlfT_1 

21 -~I 

Ol~----~----~~----~------~----~----~ 

-2 

80 100 120 140 160 180 200 

co 

"0 

c) MEASUREMENT, I/; = 60 0 -lQ... 

(/) 

<I 8 

6~1 ------~----~------~----~------~----~ 

4 

2~1------~----~------~----~------~----~ 

Orl------r------r------r------r------r-----~ 

_2l~ __ ~ __ ~ __ ~ __ L_~ __ ~--~--~--~--l~~ 

80 100 120 140 160 180 200 

AZIMUTHAL ANGLE, 8 

d) MEASUREMENT, 1/;=90 0 

Figure 53 . Continued 

165 
166 

8 

~ 

6 

>f=60° ~ '"

40 1['"200 

I,t~. L " ~ 

OJ 4 

"0 p( ,o~~ K. ::..~ 

~ 

" : . , >f = 90 0 , . " '. \ ' , , , 

r·[-----· ~; ..... -.. ~ . / , 

---J--t- '-_":"1 ---f..~ , '...-\--~ - \ \ "' .. -' . / 'L ....J 

0. 

C/) 

<I 

2 1'-

r 

o 

l-

·2 

80 

,. n " J . . ". , , / .' \ /. " . _.- ~ -

I I 

100 120 140 160 

AZIMUTHAL ANGLE, e 

e) PREDICTION, 1/;=20°, 40°, 60°, 90° 

Figure 53 . Concluded 

, : 

"'-' 

I 

! 

i -.l 

180 200 
kD St 41 r77777i;11 

10e :[ , 

~~ 1 

3 

2r- .5 

.5 

.4 

.3 

.2 

.4~ .1 

80 1 00 120 140 160 1 80 200 

AZIMUTHAL ANGLE, e 

a) MEASUREMENT M = 0.6 

I 1 

';r 2 

3 

2 

.5 

.4 

.5 

.4 

.3 

.2 

.~ 

80 1 00 1 20 140 160 180 200 

AZIMUTHAL ANGLE, f) 

c) MEASUREMENT M = 0.94 

kD St 

L I 31 41-- j)j}),,,,,,\ \(OJ})liil«\ 

1 ° t . ,," " "" ." 

~ 2 

5 

4 

3 

2r .5 

.4 

.3 

.2 

.5 

.4 t .1 

80 100 120 140 160 180 200 

AZIMUTHAL ANGLE, f) 

b) PREDICTION, M = 0.6 . 

5 

4 

3 

2 

1 

.5 

.4 

2 

.5 

.4 

.3 

.2 

.1 

80 1 00 1 20 140 1 60 180 200 

AZIMUTHAL ANGLE, e 

d) PREDICTION M = 0.94 

kD St 

10 

5 

4 

3 

2 

.5 

.4 

.3 

.2 

.1 

VP///7/7~7~a~I,\~.~x~\r(OU~_TIIMI~IniiTi~{{~v~II~IIMI~iiTI\~(~C~Ji 

.5~ .05 

.4 .04.,.- . . , 

80 1 00 120 1 40 160 180 200 

AZIMUTHAL ANGL\;, e 

e) PREDICTION M = 1.46 

Figure 54 - Mach Number Dependence of Measured and Predicted Contour Plots, 

To = 300 oK, SID = 8.1, ~ = 40 ° 

167 
168 

kD St 

10f 1 

5[ 2 4 

3 5 

2 .4 

.3 

.5 

.4 

.2 

.1 

..,uu 

80 1 00 1 20 140 160 180 200 

AZIMUTHAL ANGLE, (j 

a) MEASUREMENT, SID = 8.1 

kD St 

10 

5 

4 

3 

2 

.5 

.4 

2 

.5 

.4 

.3 

.2 

.1 

.,) I I •• Lo 

1 00 1 20 140 1 60 180 200 

AZIMUTHAL ANGLE, (j 

c) MEASUREMENT, SI D = 5.5 

kD St 

10 

5 r 2 

4 

3 .5 

2 

.4 

.3 

.2 

.5l .1 

.4\ 

80 100 120 140 160 180 200 

AZIMUTHAL ANGLE, (j 

b) PREDICTION, SID = 8.1 

kD St 

10 

5 

4 

3 

2 

.5 

.4 

2 

.5 

.4 

.3 

.2 

.1 

i,,>V)POi (j tC(J 

3dB 

80 1 00 120 140 160 1 80 200 

AZIMUTHAL ANGLE, (j 

d) PREDICTION, SID = 5.5 

Figure 55 - Spacing Dependence of Measured and Predicted Contour Plots, M = 0.94, 

To = 300 0 K, if; = 40° 
kD St 

10.0. 2.0 I rsuu~~~>6~~~n-------­ II 

5. O. 1.0 

4.0 

3.0t 0.5 

0.4 

2.01 0.

3 (2 1.0 

0.1 

0.5 

0.4 I , I 

80 100 120 140 160 180 200 

AZIMUTHAL ANGLE, 0 

e) MEASUREMENT, SID = 3.1 

10.0 r 2.0 ~t 

1.0 

5.0 

4.0 

3.0f 0.5 

0.4 

2.01 0.

3 

0.2 

10r 

0.1 

0.5 

0.4 

80 100 120 140 160 180 200 

AZIMUTHAL ANGLE, 0 

f) PREDICTION, S/D=3.1 

Figure 55 - Concluded 

169 
170 

kD 8t 

10 f 11 

5 2 

4 

3 [ .5 

2 .4 

.3 

.5 

.4 

.2 

.1 

80 1 00 1 20 1 40 1 60 1 80 200 

AZIMUTHAL ANGLE, e 

a) To=300 oK 

kD 

5 

4 

3 

2 

.5 

.4 

.3 

.2 

.5 I .1 

.4 

.3 [.05 

.2 .04 

80 1 00 1 20 140 160 180 200 

AZIMUTHAL ANGLE, e 

b)To =811°K 

Figure 56 - Temperature Dependence of Predicted Contour Plots, M = 0.94, 51 D = 8.1, 

1,l-=40o 
kD ~t V///7///M II \ \ I 

10 

5 

4 

3 

2 

.5 

.4 

2 

.5 

.4 

.3 

.2 

.1 

3dB 

80 1 00 120' 140 1 60 180 200 

AZIMUTHAL ANGLE, 0 

a) MEASURED, yY=20° 

kD St 

1 0 ~ 'j ~~\f\ \ 

Sf 2 ~ .5 

.4 

2 .3 

.2 

.1 

.5r .4 

80 100 120 140 160 180 200 

AZIMUTHAL ANGLE, 0 

c) MEASURED, yY=40° 

kD St /XX' \'0{/& \\vr3777/1 (\ \\1 I ~ . 

, 2 

10 

5 

4 

3 

2 

.5 

.4 

.5 

.4 

.3 

.2 

.1 

80 1 00 120 140 160 180 200 

AZIMUTHAL ANGLE, 0 

b) PREDICTED, yY = 20 ° 

kD St 

I 

10 

5 t 2 

4 

3 .5 

2 .4 

.3 

.2 

.1 

.5 

.4 

80 100 120 140 160 180 200 

AZIMUTHAL ANGLE, 0 

d) PREDICTED, yY = 40 ° 

Figure 57 - Polar Angle Dependence of Measured and Predicted Contour Plots, 

M =0.94, To =300 oK, SID =8.1 

171 
172 

kD & 

! 1'~~~7~7~A7U11rl-,r-/I'\----------~7~G 2 -~ 

10 

5 

~ t .5 

.4 

2 .3 

1 f·2 

.5 .1 

.4 4dB 

4dB 4dB 

<:::> 0 

4dB 

80 100 120 140 160 180 200 

AZIMUTHAL ANGLE, (j 

e) MEASURED,1/;= 60° 

kD St 

lOr \ I V4~B 5 

4 

3 t .5 .4 

2 .3 

.2 

.5 ~ .1 r I 3dB 

~ 

.4 

80 100 1 20 140 160 1 80 200 

AZIMUTHAL ANGLE, (j 

g) MEASURED,1/;= 80° 

kD St 

10' 2 

5 

4 

3 t .5 

2 .4 

.3 

.2 

.5' .1 

.4 

80 100 120 140 160 180 200 

AZIMUTHAL ANGLE, (j 

f) PREDICTED 1/;=60° 

kD St 

10' 2 

5 

~ t .5 

.4 

2 .3 

.2 

.5 I .1 

.4 

80 1 00 1 20 140 160 180 200 

AZIMUTHAL ANGLE, (j 

h) PREDICTED 1/;=80° 

Figure 57 - Continued 
kD St 

211 (\ 

(\ 

10~ ~4dB 4dB 

C> 

t 1 ~ I L~nl 

5 

4 

3r 0.5 0.4 

2 0.3 

0.2 

g1t 0111 4dB 

C> i S:::::=:=4dB i i i 

80 100 120 140 160 180 200 

AZIMUTHAL ANGLE, e 

i) MEASURED, 1/t = 90 0 

. Q kD 81 "- ._0' , S 4dB 

10 

5 

4 

2 

3~ 0.5 

0.4 

2f 0.3 

0.5 

0.4 

0.2 

0.1 

7,\l 

\)~ 

3dB 

~ 

4dB 

6 

4dB 

80 1 00 1 20 140 160 180 200 

AZIMUTHAL ANGLE, e 

~ MEASURED,1/t=100° 

kD St.-______________________ -, 

I I 

10' 2 

5 

4 

3t 0.5 

0.4 

2 0.3 

0.5 

0.4 

0.2 

0.1 

3dB EVERYWHERE 

80 1 00 120 140 160 180 200 

AZIMUTHAL ANGLE, e 

j) PRED1CTED 1/t = 90 0 

kD St "M' ow;kl, n. " '" Ii Ii j("" i " Ii .. Ii 

10 

5 

4 

2 

3 ~ 0.5 

0.4 

2f 0.3 

0.5 

0.4 

0.2 

0.1 

80 1 00 120 140 1 60 180 200 

AZIMUTHAL ANGLE, e 

I) PREDICTED, 1/t = 100 0 

Figure 57 - Concluded 

173 
174 

-l 

S 

CL 

<1 

2 

o 

-1 

-2 

102 

4 46. 66 444 

4 44 

44 4 4 

103 104 

FREQUENCY - Hz 

St "", ,,, .. 

105 

.02 .05 .1 .2 .4 234510 

kD" ". , , .,.' "" "", , " 

.1 .2.3.5 2 34 5 10 20 50 

a) DIFFERENTIAL POWER. SID = 8.1 

95 

90 

-l 

~ 85 

80 

,- 75 

102 

0 

00 

0 

9 

103 104 

FREQUENCY - Hz 

St ' . ! , "., ,!!'!" • ! ,. ! 

105 

.. 02.' .05 .1 .2.4 2 34 5 10 

kD eI !. I I "11 I ",! ' .. ' " ' .. 

. 1 .2 .3.5 2 345 10 20 50 

b) POWER. SID = 8.1 

Figure 58 - Spacing Dependence of Measured Dual Jet Power Spectrum, 

M = 0.94, T = 300 0 K 

o 
2 

.....l 

S 0 CL 

<1 

-1 

-2 

102 103 104 105 

f~Hz 

St ",1",,1 1'1 " 

0.02 0.05 0.1 0.5 5 10 

kD ,I , I, ,,,, «. ",1 «, II 

0.1 0.5 5 10 50 

c) DIFFERENTIAL POWER, Sf D = 5.5 

95 

90 

00000 

RocoDe 0 0 

!:f DO 

D 

e .....l 

S 85 

9 

CL 

80 

75 

102 

, , 

0 gD 

9 

0 

D 

I IIIII 

103 

, I I IIIII , , I IIIII 

104 105 

f-Hz 

St ' ", "'" I ' "", '" 

0.02 0.05 0.1 0.5 5 10 

kD." ,' .... , I, ... ' I" 

0.1 0.5 5 10 50 

d) POWER, Sf D = 5.5 

Figure 58 - Continued 

175 
176 

-..J 

~ CL 

<1 

2 

o 

-1 

-2 

102 

A 

A A 

.... 

103 

A AA AA 

104 105 

f-Hz 

8t I ,,', "" , ",,,, I I 

0.02 0.05 0.1 0.5 5 10 

kD .. I I ,.,," • "", I I' 

0.1 0.5 1 5 10 50 

e) DIFFERENTIAL POWER, 8/D= 3.1 

95 

90 

-..J 

~ 85 

CL 

80 

75 

1(12 

I , 

0000 0 

O~DDDDD 00 

OD D D 

OD 

D 

0 

°D D 

0 

D 0 D 

I IIIII I I I IIIII . , , IIIII 

103 104 105 

f-Hz 

8t ,,' I" ", , ' , 

0.02 0.05 0.1 0.5 5 10 

kD" .1."" 1.",1 I,S! 

0.1 0.5 5 10 50 

f) DIFFERENTIAL POWER, 81D = 3.1 

Figure 58 - Concluded 
SHIELDING JET 

a) DUAL JET GEOMETRY VIEWED FROM DOWNSTREAM 

SYNTHESIZED ;-', SYNTHESIZED 

SHELDING JET LOCATION ~t rl- I SOURCE JET 

CORRESPONDING TO ABOVE \ 7-; LOCATION 

FIGURE 

~R2 S 

OBSERVER~R1 =305~~cr. ~ .... - SINGLE JET(SOURCE JET) 

MEASUREMENT LOCATION 

Rm = 3.19m II I 

b) TWO INDEPENDENT JETS AT SAME ORIENTATION AS DUAL JET GEOMETRY 

Figure C·1 - Schematic Illustrating Synthesization of Sound Field Radiated by Two 

Independent Jets 

177 


1. Report No. I 2. Government Accession No. 3. Recipient's Catalog No. 

NASA CR-3966 

4. Title and Subtitle 5. Report. Date 

April 1986 

Jet Shielding of Jet Noise 6. Performing Organization Code 

7. Author(s) John C. Simonich, Roy K. Ami et, and 8. Performing Organization Report No. 

Robert H. Schlinker 

10. Work Unit No. 

9. Performing Organization Name and Address 

United Technologies Research Center 11. Contract or Grant No. 

East Hartford, CT 06108 NASI-16689 

13. Type of Report and Period Covered 

12. Sponsoring Agency Name and Address Contractor Report 

National Aeronautics and Space Administration 14. Sponsoring Agency Code Washington, DC 20546 

505-31-33-12 

15. Supplementary Notes 

langley Technical r~onitor: J. C. Yu 

Fi nal Report 

16. Abstract A theoreti ca I and experimental study was conducted to develop a val idated 

first principles analysis for predicting the Jet noise reduction achieved by 

shielding one Jet exhaust flow with a second, closely spaced, identi cal Jet. A 

general ized dual Jet noise analytical model was formulated In which the acoustic 

radiation from a source Jet propagates through the velocity and temperature 

discontinuity of the adjacent shielding Jet. Assessment of the theory Involved 

conducting dual Jet noIse and single Jet noise experiments to estabJ ish the 

difference In directivity pattern. Analytical variables evaluated experimentally 

included Jet Mach number (subsonic and supersonic), Jet diameter, Jet spacing, flow 

temperature, and acoustic source frequency. 

Jet shielding was found to reduce noise levels In the common plane of the dual 

Jet system with shielding extending to observer angles on either side of this plane. 

OutSide of this region an increase of noise occurs due to the redirection of sound 

rays from the shielded regIon In addition to acoustic reflections between the 

adjacent flow fields. A balance exists between the noise reduction and noise 

increase confirming that acoustic energy Is conserved. Jet shielding effectiveness 

increases with Helmholtz number and Is most effective for frequencies above the Jet 

noise spectrum peak. Increasing subsonic Mach number enhances shielding and shifts I the onset of shielding to lower frequencies. For nonlnterferlng dual Jet flows, I 

shielding remains constant with Jet spacing. Smal I spacing, resulting In the 

aerodynamic merger of the Jet flows, cause changes in the acoustic source region 

which increase the dual Jet noise relatlv9 to two single Jets. Changes of Jet 

temperature were found to have a minimal effect. These measured dual Jet shielding 

effects are successfully predicted by the first principles theoretical model. 

17. Key Words (Suggested by Author(s)) 18. Distribution Statement 

Jet Noise Jet Shielding 

Subsonic Jet Noise Unclassified - Unlimited 

Supersonic Jet Noise 

Jet Noise Reduction Subject Category 71 

19. Security Oassif. (of this report) 20. Security Classif. (of this page) 21. No. of Pages 22. Price 

Unclassified Unclassified 177 A09 - --

NASA-Langley, 1986