David Munday et al- Supersonic Jet Noise from a Conical C-D Nozzle with Forward Flight Effects

8/3/2019 David Munday et al- Supersonic Jet Noise from a Conical C-D Nozzle with Forward Flight Effects

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SUPERSONIC JET NOISE FROM A CONICAL

C-D NOZZLE WITH FORWARD FLIGHT

EFFECTS

David Munday,*

Nick Heeb

and Ephraim Gutmark

University of Cincinnati

Markus O. Burak

and Lars-Erik Eriksson**

Chalmers University of Technology

Erik Prisell

FMV

Flow and far-field noise measurements are taken on a conical Convergent-

Divergent nozzle similar to the nozzles employed on high-performancetactical jets. Matching flow and far-field computations are presented,

produced by Large Eddy Simulation and the Kirchhoff integral method.The conditions examined are those in which the nozzle is operated at its

design Mach number of 1.56 while forward flight is simulated at Mach

numbers of 0.1, 0.3 and 0.8. Both measurement and LES show thatincreasing forward flight Mach number to the high subsonic range

shortens the initial shock cell size, and weakens the shock cells induced by

the nozzle throat relative to the shock cells induced by the nozzle lip. LESshows that high forward flight speed substantially reduces the noise

radiated into the forward quadrant where shock noise is dominant. It alsoremoves the screech tone entirely.

Nomenclature

a Speed of soundDt Throat diameter

De Exit diameterLES Large Eddy Simulation

Md Design Mach numberMj Fully expanded jet Mach number

M2 Secondary flow Mach numberNPR Nozzle Pressure Ratio

* Graduate Student; member AIAA. , [email protected] Graduate Student; member AIAA., [email protected] Distinguished Professor; Fellow AIAA. ,[email protected]

Ph.D. Student; member AIAA, [email protected]** Professor; member AIAA, [email protected] Strategic specialist; Aero-propulsion


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SPL Sound Pressure LevelSt Strouhal Number; St = fDe/uJOASPL Over-All Sound Pressure Level

uj Fully expanded velocity

Angle from the upstream axis

Introduction

High-speed military aircraft are typically powered by low-bypass turbofan engines with amixed exhaust, re-heat and a variable geometry convergent-divergent exhaust nozzle. As

the altitude and operating condition of the engine varies, the nozzles employed adjusts to

match the mass flow and jet Mach number to some extent, but they have internal flowcontours which are far from ideal and they are rarely shock free. This means that these

engines generally produce shock-associated noise as well as the turbulent mixing noisecharacteristic of subsonic or perfectly expanded jets.

The noise levels produced by these jets are quite strong. They produce near-field

pressures which are hard on personnel, aircraft structure and equipment, and far-fieldnoise which disturbs neighbors around air bases and training areas. Limitation of this

noise will reduce wear and tear on crews and equipment and reduce noise complaints

from those in the neighborhood.

There has been a fair amount of work published on noise reduction for subsonic,

commercial jet engines. The greatest gains in improving subsonic jets have come by

reducing the jet velocity while increasing the jet radius to maintain the desired thrust.Increasing jet radius means increasing engine radius and increasing aircraft drag so this

approach becomes less desirable as the aircraft velocity increases. Other approaches to

decreasing subsonic jet noise usually involve mixing enhancements which reduce thelow-frequency noise while increasing high-frequency noise.

When we shift to supersonic jets we have all the problems associated with mixing noise

to contend with, but we also have additional sources of noise resulting from shocks andPrandtl-Meyer waves forming shock cells or shock diamonds in the jet itself.

Figure 1 shows a typical far-field spectrum of an imperfectly expanded supersonic jet

measured upstream of the nozzle exit. The figure depicts the three main noisecomponents as was also described previously [1, 2].

The narrow peak with a Strouhal number of 0.32 is a screech tone. Screech is excited by

acoustic waves that are generated by interaction between shear layer vortices and shockstructures in the jet, which propagate upstream and excite flow instabilities at the nozzles

lip. These energized structures are convected downstream and further interact with the

shocks to form a feedback loop (cite Powell). Screech has been investigated by Umeda


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and Ishii using the Schlieren technique [3]. In their experimental study the authors tried

to identify the locations and the behavior of the sound sources of the screech tone. Anamplification of the overall sound pressure level of an underexpanded and heated

supersonic jet was observed in the forward quadrant (upstream) and a reduction in the

mixing noise was found in the aft quadrant (downstream). The Strouhal number

corresponding to the screech frequency was found to decrease with forward-flight Machnumber, a result consistent with a formula for prediction of the screech frequency [5].

The broader peak at higher frequency than the screech tone is the broadband shock-associated noise peak. This peak is produced by coherent structures convecting through

the shock cells. This source exhibits a Doppler shift in frequency moving the frequency

higher as the observer moves to aft angles. At aft angles this peak also becomes broaderand reduces in level. The peak direction of radiation of broadband shock-associated

noise is in the forward quadrant, typically around 30. The majority of broadband shock-

associated noise occurs in the vicinity of shocks near the end of the potential core [5].

Both screech and broadband shock-associated noise are added to the turbulent mixingnoise that is present in jets whether they are supersonic or subsonic. This source is

generally dominated by the shock cell noise at forward angles and at frequencies at andabove the screech frequency. Mixing noise remains the dominant source as frequencies

below the screech tone at all angles and is the dominant source observed at aft angles.

Experimental Facility and Procedure

The Gas Dynamics and Propulsion Laboratory at the University of Cincinnati (UC-GDPL) has a scale model of a separate-flow jet engine exhaust system. For the present

experiment a convergent-divergent nozzle is fitted to the primary flow and the secondary

flow is used to simulate forward flight effects. The nozzle under study has an area ratioof 1.23, corresponding to a design Mach number , Md, of 1.56 and a design NPR of 4.00.

The exit diameter, De, is 57.5mm. The radius of curvature at the throat is 0.5 mm and the

exit lip thickness is 0.5mm. A secondary flow nozzle has been constructed to give nearlyuniform flow outside the primary flow nozzle. Several configurations of secondary

nozzles axial location relative to the center nozzle were tested and it was determined that

the shadowgraph images were independent of the particular configuration. Secondary

flow Mach numbers, M2, of 0.1, 0.3 and 0.8 are considered. The nozzle details are shownin Figure 2. The completed test article is show in Figure 3. The model is mounted in the

University of Cincinnati Aeroacoustic Test Facility (UCATF) which is a 24 x 25 x 11

test chamber which has been acoustically treated to be anechoic down to 350 Hz. Figure

4(a) shows the layout of the facility.

Instrumentation

Eight quarter inch microphones are arrayed along the depicted arc at angles from 35 to

150 measured from the upstream axis of the jet. The microphones are placed at 3.43mor 60 exit diameters from the nozzle exit. The facility is more fully described in

Callender, Gutmark & DiMicco [6]. The microphone signals are filtered above 100 kHz


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and recorded at 200 kHz for 10 seconds. The flow variables are monitored at 4 Hz in

order to establish and hold the desired operating condition of the model. Variablesrecorded include the ambient conditions in the chamber as well as the flow stagnation

temperature and pressure.

In order to map the near-field acoustics, eight microphones are mounted on a linear rakewhich is in turn mounted on a large three-axis traverse. The rake is stepped through a

rectangular region just outside the main flow region. The resulting grid of pressure

fluctuations can then be analyzed on an OASPL basis or the particular spectral rangespertinent to different mechanisms can be mapped to look at source location and direction

of propagation. Typical mapped regions are shown in Figure 4(b).

Detailed flow-field mapping is performed by Particle Image Velocimetry (PIV). The PIV

system is built by LaVision and the entire PIV suite, laser and cameras are mounted on a

traverse which allows the system to be translated, undisturbed, to any streamwise locationallowing many cross-cuts to be measured without the loss of time in changing setups and

without the uncertainties which come from repeated adjustment of components. Theflow is seeded with olive oil droplets with diameters on the order of 1 m. A 500 mJ

New Wave Research nd:YAG double-pulse laser is passed through sheet-forming opticsto illuminate the seed an the images are captured in stereo by a pair of LaVision 1376 x

1040 12-bit PIV cameras.

The high gradient features in the flow are visualized by the shadowgraph technique. An

Oriel 66056 arc lamp is used for illumination. A pair of 12 parabolic first-surface

mirrors with a 72 focal length are employed to collimate the light before the model andthen to focus the beam after. The image is captured with a LaVision Imager Intense

cross-correlation CCD camera with 1376 x 1040 pixel resolution and 12-bit intensity

resolution. This gives a spatial resolution on the order of 0.01 or 0.004 throat diameters.A 28-300 zoom lens is mounted to the camera which allows optimization of the field of

view. The aperture is left completely open and exposure is controlled by mounting a

filter. Averaging 100 images eliminates the turbulence and gives a clear view of theshock and Prandtl-Meyer waves.

Point measurements of static pressure and Mach number are performed using a

supersonic five-hole conical probe. The probe, a United Sensor model SDF-15-6-15-600,has a truncated cone with a half angle of 15, a total pressure port is located at the tip of

the truncated cone and four side ports are evenly spaced around the conic surface. When

the side port pressure values are averaged the Mach number result is insensitive to yaw

angle changes up to 10 [13].

Numerical approach

The evolution of the flow is considered to follow the compressible form of the continuity,momentum and energy equations in which the viscous stress and the heat flux have been

defined using Newton's viscosity law and Fourier's heat law, respectively. This set of

equations is often referred to as the Navier-Stokes equations.


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The code used for the simulations is one of the codes in the G3D family of finite volumemethod codes developed by Eriksson [7]. These codes solve the compressible flow

equations in conservative form on a boundary-fitted, curvilinear non-orthogonal multi-

block mesh. To enable simulations with a large number of degrees of freedom, routines

have been implemented for parallel computations using Message Passing Interface (MPI)libraries. The Favre-filtered Navier-Stokes equations were solved using a finite volume

method with a low-dissipation third-order upwind-biased scheme for the convective

fluxes and a second-order centered difference approach for the diffusive fluxes. Thesubgrid-scale model used in the present work is the Smagorinsky part of the model

proposed by Erlebacher et al. [8] for compressible flows. The temporal derivatives were

calculated using a second-order three-stage Runge-Kutta technique. Detaileddescriptions of the numerical scheme and boundary conditions are given in Eriksson [7],

Andersson [9] and Burak [10].

Computational Domain

The computational domain was discretized using a block-structured boundary-fitted meshwith 249 mesh blocks and approximately 16M nodes. The domain is divided into two

parts: a high-resolution region around the nozzle and a medium dense LES region. See

Figure 5 and Figure 6. The mesh is constructed using a combination of Cartesian andpolar mesh blocks in order to ensure mesh homogeneity in the radial direction throughout

the domain. Along the centerline, a Cartesian mesh block of square cross-section was

used in order to avoid centerline singularity. See Figure 7. At the nozzle inlet total

pressure and total enthalpy are specified. Entrainment velocities at the outer radial boundof the computational domain are obtained by using a 2D extension of the domain

representing the flow outside the LES domain. In order to minimize the reflections at the

domain outlet on the predicted flow, a damping zone was added at the domain outlet. Thecorrect wall friction is obtained through the use of wall functions where needed.

Sound Propagation

For sound evaluation at a far-field observer, Kirchhoff [11] surface integral formulation

was used. For a point outside a surface enclosing all generating structures, this is amethod for predicting the value of a property, , which is governed by the wave

equation. The integral relation is given by

+

=

SxdS

tn

r

rcnrn

r

rty

r

)(11

4

1),(

2

vv

where yv

is the observer location in the far-field and xv

is a location on the surface. ris

related to the observer evaluation of time, t, distance from observer to surface location,

|| xyrvv

= , and the speed of sound in the far-field, c , as


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=c

rtr

The expression within the brackets in the equation above is thus evaluated at retarded

time, i.e. emission time.

Description of Results

The preliminary efforts in this project were to establish valid boundary conditions for theLES, validate the LES code and take preliminary flow and acoustical measurements.

Pitot and hot film traverses were taken inside the inlet piping in the stilling section after

the flow straightening hardware and turbulence educing screens. The area ratio at thisstation A0/A* = 8.07 giving M0 = 0.072 for all NPRs above 1.89. Conditions measured in

the stilling section were used as inlet boundary conditions for the LES. Pitot traverses

were made at the exit of the secondary flow nozzle to confirm that uniform flow existed

in the vicinity of the models outer contour.

Measurements were taken while holding the jet fully expanded Mach number, Mj, to

within 0.01. Temperature ratio was held to within 0.04. Secondary flow Mach number,M2, was held to within 0.03. All these to a 20:1 confidence interval.

Mean Axial velocity contours are shown in Figure 8. In all cases the nozzle is operating

at its design condition, Mj = Md = 1.56, T0/Ta = 1.22. Three secondary flow Mach

numbers are shown. M2 = 0.1, 0.3 and 0.8. In the left column are measurements by PIVwhile in the right column are predictions from LES. The agreement between the two is

very good.

Centerline pressure is compared between a cone probe measurement and LES in Figure 9.In each case the LES data has been shifted 0.3 De upstream to align the first peak. The

shapes of the centerline pressure curves match well, though there is a slowly growing

difference in axial position between the two indicating a small difference in shock cellspacing. For the first two secondary flow conditions we see that the length of the shock

train is over-predicted by the LES. The cone probe run for the M2 = 0.8 run was

terminated early due to a hardware malfunction. The agreement between LES and coneprobe is fairly good as far as we have data to check.

Examining the mean velocity contours in Figure 8 we can see that the lower twosecondary flow Mach numbers clearly show two shock cell structures superimposed on

one another in a double diamond. The first of these structures emerges from inside thenozzle and reflects from the shear layer at around 0.15 to 0.17 De. The reflected wave

crosses the centerline at x/De = 0.8. The second, anchored to the nozzles trailing edgelip, is the shock cell structure seen in smoothly contoured nozzles. This wave crosses the

center at around x/De = 0.5. The two superimposed structures forming the double

diamond have been previously observed for unheated jets from conical C-D nozzleswithout secondary flow by Munday, Gutmark, Liu and Kailasanath [12]. At the higher

secondary flow Mach number (M2 = 0.8) the shock cell structure from the lip becomes


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slightly shorter, crossing the centerline at x/De = 0.4 while the structure from inside the

nozzle becomes much less pronounced.

At high subsonic secondary flow Mach number the structure from inside the nozzle

becomes indistinct in PIV, but it can still be discerned in shadowgraph. Figure 10 shows

shadowgraph images of nine secondary flow Mach numbers ranging from M2 = 0.0 to0.8. The vertical lines aid in tracking features in the images. They are aligned with the

features in the first image (M2 = 0.0) and we can see how the features move relative to

this condition in subsequent images.

Features associated with the lip wave are marked with green lines. The first green line is

at the nozzle lip itself. The second green line, the dashed green line, is aligned with thepoint where lip wave crosses the centerline. This crossing point remains fixed up to M2 =

0.4 after which it begins to move upstream. The third green line tracks the first reflection

of the lip wave from the shear layer which likewise moves upstream past M2 = 0.4.

Features associated with the wave from inside the nozzle are tracked by the red lines.The first red line follows the first reflection of this wave from the shear layer. The

second red line, the dashed one, follows the point at which this reflected internal wavecrosses the centerline. The third red line follows the second reflection of this wave from

the shear layer. These features also move upstream, but they also become weaker as

secondary flow Mach number increases. For M2 above 0.7 is becomes difficult to makeout the center crossing of this wave, but the reflection can be seen as high as M2 = 0.8.

Instantaneous Mach number contours from LES are shown in Figure 11 for M2 = 0.1.The lower subfigure shows a close-up view of the inside of the nozzle where PIV can not

reach. We can see that there is a shock wave shed from the nozzle throat producing aMach disk at x/D

e= -0.32. The onward traveling shock wave exits the nozzle and

reflects from the shear layer at z/De = 0.17 or so. The Mach disk sheds a slip line which

is clearly visible in the PIV as well as the LES confirming the details of the in-nozzleflow structure.

Looking at instantaneous total temperature in a series of cross-stream planes shows the

development and mixing of the hot high-speed jet with cool lower speed secondary flowin Figure 12. The cross-planes range from x/De = 1 to 9. Moving from x/De = 1 through

3 we can see the jet boundary become convoluted as large scale structures in the shear

layer mix the hot with cold fluid. By x/De = 7 there is little if any unmixed fluid, butbeyond this point we do see pockets of higher enthalpy as the jet flaps and flickers.

Far-field acoustics were measured in the laboratory and calculated from the LES. Spectrafor the nozzle operating at its design condition and M2 = 0.1 are shown in Figure13 range

of inlet angles. In both the measurement and the simulation we see the typical features

associated with shock associated noise. A screech tone appears at 2200 Hz with a

broadband peak at 2600-5000Hz in the forward-most angle, shifting to higher frequenciesas the observer moves aft. Measurement and simulation are compared in detail for the

forward-most angle in Figure 14. The agreement for M2 = 0.1 is outstanding. The M2 =


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0.3 case is fairly good, with the screech tones in fair agreement, but some difference in

the shape of the broadband hump. We show no measurement for M2 = 0.8 because theouter shear layer, between the Mach 0.8 secondary flow and the ambient atmosphere is a

significant sound source itself, contaminating the measurement. The effect of high

subsonic secondary flow on the spectrum is striking. The screech tone in eliminated and

the overall sound level is substantially reduced.

Distribution of OASPL in azimuth by LES is shown in Figure 15 for M2 = 0.3 and 0.8. It

can be seen that the increased secondary flow substantially reduces the forward radiatingcomponents dominated by shock generated noise. There is s small elevation of sound

radiation to side and aft angles.

Finally we examine the effect of Mj on the sound production for the lower two secondary

flow velocities. For both M2 = 0.1 and 0.3 we can see a strong screech at the off-design

condition, both overexpanded and underexpanded. This screech diminishes and shiftsfrequency at a point slightly above the design Mach number. Increasing secondary flow

velocity causes a larger region of diminished screech. For M2 = 0.1 there is nodiminution in the broad-band shock associated noise near the design condition. For M2 =

0.3 the broad-band shock noise is reduced in the overexpanded condition except for aregion of higher broadband noise from Mj = 1.25 to 1.35. Looking at the same data on an

OASPL bases we see in Figure 17 that there is a minimum in the curve for M 2 = 0.1 near

the design condition (Pe/Patm = 1). Compared to the data of Seiner and Yu the minimumis shallow, due to the fact that while the screech is reduced at the design condition, there

is no reduction in broad-band noise. When the secondary flow Mach number is increased

to 0.3, the minimum becomes shallower still.

Discussion and Conclusions

The goal of this project is to employ a joint experimental/computational approach to

investigate the acoustic properties of conical C-D nozzles and to explore the influence of

forward flight effects on the flow field and sound field. LES provided us a tool to lookwhere it is difficult to measure in terms of location and in terms of operating condition.

Simulating large forward flight effects in the laboratory generates a secondary shear layer

between the flight simulation flow and the ambient air. This introduces additional sound

sources which contaminate the measurement.

We have demonstrated that the LES approach employed captures the physics necessary to

produce the double-diamond shock cell structure that is characteristic of conical C-D

nozzles even at their design condition. There are some small differences in terms ofshock cell spacing, shock train length and shear layer spreading rate, but overall the LES

captures the flow features and accurately reproduced the far field acoustic radiation.

The influence of increasing the secondary flow Mach number on the double-diamond jetis to reduce the initial shock cell size and to weaken the waves emanating from inside the

nozzle relative to the waves shed from the nozzle lip.


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LES and CAA enabled us to predict the acoustic radiation at higher secondary flow Mach

number (higher simulated forward flight speed) than we would be able to measure. Wefind that the influence of high subsonic forward flight is to eliminate the screech and to

strongly reduce the forward radiated sound characteristic of shock containing jet noise.

Acknowledgements

The authors would like to acknowledge the support of the Swedish Defense MaterielAdministration (FMV) which provided financial support for this research and Volvo

Aero Corporation which provided technical guidance in the design of the nozzle and

selection of test conditions. The computations were performed on computing resources

at the National Supercomputer Centre in Sweden (NSC).

References

1. Seiner, John M. (1984). Advances in High Speed Jet Aeroacoustics. AIAA/NASA 9th

Aeroacoustics Conference. AIAA-84-2275.

2. Shih, F. S., Alvi, D.M. (1999). Effects of Counterflow on the Aeroacoustic

Properties of a Supersont Jet. Journal of Aircraft, 36:451-457.

3. Umeda, Y., and Ishii, R. (2001). On the sound sources of screech tones radiated

from choked circular jets J. Acoust. Soc. Am, 110:1845-1858.

4. Tam, C.K.W. (1991). Jet noise generated by large-scale coherent motion

Aeroacoustics of Flight Vehicles: Theory and Practice, NASA RP 1258, Vol. 1.

5. Seiner, J.M., Yu, J.C. (1984). Acoustic near-field properties associated withbroadband shock noiseAIAA Journal, 22:1207-1215.

6. Callender, B., Gutmark, E. and Dimicco, R. (2002). The design and validation of acoaxial nozzle acoustic test facility, AIAA-2002-369.

7. Eriksson, L.-E. 1995 Development and validation of highly modular flow solverversions in g2dflow and g3dflow. Internal report 9970-1162. Volvo Aero Corporation,

Sweden.

8. Erlebacher, G., Hussaini, M. Y., Speziale, C. G. & Zang, T. A.1992 Toward the

large-eddy simulation of compressible turbulent flows. Journal of Fluid Mechanics 238,155-185.

9. Andersson, N. 2005 A study of subsonic turbulent jets and their radiated sound using

Large-Eddy Simulation. PhD thesis, Division of Fluid Dynamics, Chalmers University of

Technology, Gothenburg.


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10. Burak, M. 2007 Large Eddy Simulation for the Analysis of Jet Noise Suppression

Devices. Licentiate thesis, Division of Fluid Dynamics, Chalmers University ofTechnology, Gothenburg.

11. Kirchhoff, G. R. 1883 Zur theorie der lichtstrahlen. Annalen der Physik und Chemie

18, 663-695.

12. Munday, D., Gutmark, E., Liu J. and Kailasanath, K. (2008). Flow and Acoustic

Radiation from Realistic Tactical Jet C-D Nozzles. 14th AIAA/CEAS AeroacousticsConference (29th AIAA Aeroacoustics Conference), May 5-7, 2008, Vancouver, British

Columbia, AIAA-2008-2838.

13. Cooper, M., and Webster, R. (1951). The use of an uncalibrated cone for

determination of flow angles and Mach numbers at supersonic speeds, NACA-TN-

2190.


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Figure 2 Nozzle simulating the exhaust of a tactical jet. (a) entire model showing station definitions; Station

0 is the location where inlet measurements are made in the stilling chamber, Station 1 is joint in the wettedsurface between this nozzle and the existing hardware, Station * is the throat, station e is the exit plane of the

nozzle (b) nozzle details. De = 57.5mm, Area Ratio = 1.23, curvature radius at throat = 0.5 mm. Exit lip

thickness = 0.5mm.

(a) (b)

0 1 * e

Turbulent mixing noise

Screech

Figure 1 Far-field acoustic spectrum (forward quadrant; = 30, MD = 1.575, MJ = 1.575, M2 = 0.1).


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Figure 4 Plan view of UC-GDPLs Aeroacoustic Test Facility. (a) far-field acoustic arrangement. (b) near-

field acoustic arrangement.(a) (b)

Figure 3 Convergent-divergent nozzle installed. (a) complete test article. (b) close-up of nozzle.(a) (b)


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Medium-resolution

LES domain

Buffer

zone

High-

resolution

LES domain

Figure 5 The computational domain is divided into two sections: a high-resolution region for high resolution

of boundary layers and initial shear layers and a medium-resolution LES region optimized for propagation of

acoustic waves.

Figure 6 A slice through the domain at y=0, i.e. a xz-plane in the high-resolution LES region.

Figure 7 Slice through the computational domain at constant x, i.e. a yz-plane. Combining Cartesian and

polar grid blocks enhances the radial direction grid homogeneity throughout the domain.


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Figure 8 Mean Axial velocity Mj = Md = 1.56, T0/Ta = 1.22.

PIV, M2 = 0.1

PIV, M2 = 0.3

PIV, M2 = 0.8

LES, M2 = 0.3

LES, M2 = 0.8

u [m/s]


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Figure 9 Centerline pressure Mj = Md = 1.56, T0/Ta = 1.22.

M2 = 0.1

M2 = 0.3

M2 = 0.8


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M2 = 0.0

M2 = 0.1

M2 = 0.2

M2 = 0.3

M2 = 0.4

M2 = 0.5

M2 = 0.6

Figure 10 Shadowgraph. One hundred images averaged to suppress turbulence and emphasize shock cells.

Mj = Md = 1.56, T0/Ta = 1.22. Solid lines descend from reflections at the shear layer in M2 = 0.0. Dashed lines

descend from waves crossing the centerline in M2 = 0.0. Green lines pertain to the wave from the lip. Red

lines pertain to the wave from inside.

M2 = 0.7

M2 = 0.8


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Figure 11 Instantaneous Mach number Mj = Md = 1.56, T0/Ta = 1.22, M2 = 0.1.


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Figure13 Far-field acoustic spectra, Mj = Md = 1.56, T0/Ta = 1.22, M2 = 0.1.

Mics LES

Figure 12 Instantaneous total temperature by LES, Mj = Md = 1.56, T0/Ta = 1.22, M2 = 0.1.

x = 1De x = 2De x = 3De

x = 4De x = 5De x = 6De

x = 7De x = 8De x = 9De


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M2 = 0.1

Figure 14 Upstream far-field acoustic spectra compared, Mj = Md = 1.56 T0/Ta = 1.22, = 35M2 = 0.3 M2 = 0.8

Figure 15 Far-field SPL directivity from LES . o M2 = 0.1, o M2 = 0.8


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Figure 16 Measured 35 Far-field spectra for a range of jet Mach numbers for, T0/Ta = 1.22. (a) M2 = 0.1.(b) M2 = 0.3.

(a)

(b)


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Figure 17 Measured 35 Far-field OASPL for a range of jet Mach numbers for, T0/Ta = 1.22.

100

105

110

115

120

125

130

0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4

Pe/Patm = NPRJ/NPRD

OASPL[dB]at=

3

5

M2 = 0.1

M2 = 0.3

Seiner & Yu

Documents

David Munday et al- Supersonic Jet Noise from a Conical C-D Nozzle with Forward Flight Effects