SUPERSONIC JET NOISE FROM A CONICAL C-D NOZZLE WITH FORWARD FLIGHT EFFECTS

Transcription

1 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-performance tactical 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 that increasing 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. LES shows that high forward flight speed substantially reduces the noise radiated into the forward quadrant where shock noise is dominant. It also removes the screech tone entirely. Nomenclature a D t D e LES M d M j M 2 NPR Speed of sound Throat diameter Exit diameter Large Eddy Simulation Design Mach number Fully expanded jet Mach number Secondary flow Mach number Nozzle Pressure Ratio * Graduate Student; member AIAA., david.munday@uc.edu Graduate Student; member AIAA., heebns@ .uc.edu Distinguished Professor; Fellow AIAA., Ephraim.Gutmark@uc.edu Ph.D. Student; member AIAA, mabu@chalmers.se ** Professor; member AIAA, lee@chalmers.se Strategic specialist; Aero-propulsion 1

2 SPL St OASPL u j ψ Sound Pressure Level Strouhal Number; St = f D e /u J Over-All Sound Pressure Level Fully expanded velocity Angle from the upstream axis Introduction High-speed military aircraft are typically powered by low-bypass turbofan engines with a mixed 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 flow contours 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 noise characteristic 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-field noise 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 the low-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 and Prandtl-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 noise components 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 shock structures 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 2

3 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. An amplification 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 Mach number, 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 shockassociated 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 broader and 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 shockassociated 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 mixing noise 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 and above 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 ratio of 1.23, corresponding to a design Mach number, M d, of 1.56 and a design NPR of The exit diameter, D e, 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 nearly uniform 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, M 2, of 0.1, 0.3 and 0.8 are considered. The nozzle details are shown in 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 3.43m or 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 3

4 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. Variables recorded 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 rake which 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 ranges pertinent 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 location allowing 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. The flow is seeded with olive oil droplets with diameters on the order of 1 μm. A 500 mj New Wave Research nd:yag double-pulse laser is passed through sheet-forming optics to illuminate the seed an the images are captured in stereo by a pair of LaVision 1376 x bit PIV cameras. The high gradient features in the flow are visualized by the shadowgraph technique. An Oriel 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 and then 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 throat diameters. A 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 the shock 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 , 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. 4

5 The code used for the simulations is one of the codes in the G3D family of finite volume method codes developed by Eriksson [7]. These codes solve the compressible flow equations in conservative form on a boundary-fitted, curvilinear non-orthogonal multiblock 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. The subgrid-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. Detailed descriptions 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 mesh with 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 and polar 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 bound of 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. The correct 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 a method for predicting the value of a property, Φ, which is governed by the wave equation. The integral relation is given by v 1 Φ y, t) = 4π Φ r ( S 2 r 1 Φ 1 r Φ + n r n c r n t τ r v ds( x) where y v is the observer location in the far-field and x v is a location on the surface. τ r is related to the observer evaluation of time, t, distance from observer to surface location, v v r = y x, and the speed of sound in the far-field, c, as 5

6 τ r = t r c 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 the LES, 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 this station A 0 /A * = 8.07 giving M 0 = for all NPRs above 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 model s outer contour. Measurements were taken while holding the jet fully expanded Mach number, M j, to within Temperature ratio was held to within Secondary flow Mach number, M 2, was held to within 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, M j = M d = 1.56, T 0 /T a = Three secondary flow Mach numbers are shown. M 2 = 0.1, 0.3 and 0.8. In the left column are measurements by PIV while 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 D e 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 cell spacing. 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 M 2 = 0.8 run was terminated early due to a hardware malfunction. The agreement between LES and cone probe 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 two secondary 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 the nozzle and reflects from the shear layer at around 0.15 to 0.17 D e. The reflected wave crosses the centerline at x/d e = 0.8. The second, anchored to the nozzle s trailing edge lip, is the shock cell structure seen in smoothly contoured nozzles. This wave crosses the center at around x/d e = 0.5. The two superimposed structures forming the double diamond have been previously observed for unheated jets from conical C-D nozzles without secondary flow by Munday, Gutmark, Liu and Kailasanath [12]. At the higher secondary flow Mach number (M 2 = 0.8) the shock cell structure from the lip becomes 6

7 slightly shorter, crossing the centerline at x/d e = 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 M 2 = 0.0 to 0.8. The vertical lines aid in tracking features in the images. They are aligned with the features in the first image (M 2 = 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 the point where lip wave crosses the centerline. This crossing point remains fixed up to M 2 = 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 M 2 = 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 wave crosses 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 M 2 above 0.7 is becomes difficult to make out the center crossing of this wave, but the reflection can be seen as high as M 2 = 0.8. Instantaneous Mach number contours from LES are shown in Figure 11 for M 2 = 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 a Mach disk at x/d e = The onward traveling shock wave exits the nozzle and reflects from the shear layer at z/d e = 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-nozzle flow 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 flow in Figure 12. The cross-planes range from x/d e = 1 to 9. Moving from x/d e = 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/d e = 7 there is little if any unmixed fluid, but beyond 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. Spectra for the nozzle operating at its design condition and M 2 = 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 Hz in the forward-most angle, shifting to higher frequencies as the observer moves aft. Measurement and simulation are compared in detail for the forward-most angle in Figure 14. The agreement for M 2 = 0.1 is outstanding. The M 2 = 7

8 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 M 2 = 0.8 because the outer 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 M 2 = 0.3 and 0.8. It can be seen that the increased secondary flow substantially reduces the forward radiating components dominated by shock generated noise. There is s small elevation of sound radiation to side and aft angles. Finally we examine the effect of M j on the sound production for the lower two secondary flow velocities. For both M 2 = 0.1 and 0.3 we can see a strong screech at the off-design condition, both overexpanded and underexpanded. This screech diminishes and shifts frequency at a point slightly above the design Mach number. Increasing secondary flow velocity causes a larger region of diminished screech. For M 2 = 0.1 there is no diminution in the broad-band shock associated noise near the design condition. For M 2 = 0.3 the broad-band shock noise is reduced in the overexpanded condition except for a region of higher broadband noise from M j = 1.25 to 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 (P e /P atm = 1). Compared to the data of Seiner and Yu the minimum is 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 look where 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 of shock 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 jet is 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. 8

9 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. We find 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 Materiel Administration (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 9 th Aeroacoustics Conference. AIAA Shih, F. S., Alvi, D.M. (1999). Effects of Counterflow on the Aeroacoustic Properties of a Supersont Jet. Journal of Aircraft, 36: Umeda, Y., and Ishii, R. (2001). On the sound sources of screech tones radiated from choked circular jets J. Acoust. Soc. Am, 110: Tam, C.K.W. (1991). Jet noise generated by large-scale coherent motion Aeroacoustics of Flight Vehicles: Theory and Practice, NASA RP 1258, Vol Seiner, J.M., Yu, J.C. (1984). Acoustic near-field properties associated with broadband shock noise AIAA Journal, 22: Callender, B., Gutmark, E. and Dimicco, R. (2002). The design and validation of a coaxial nozzle acoustic test facility, AIAA Eriksson, L.-E Development and validation of highly modular flow solver versions in g2dflow and g3dflow. Internal report 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, Andersson, N 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. 9

10 10. Burak, M Large Eddy Simulation for the Analysis of Jet Noise Suppression Devices. Licentiate thesis, Division of Fluid Dynamics, Chalmers University of Technology, Gothenburg. 11. Kirchhoff, G. R Zur theorie der lichtstrahlen. Annalen der Physik und Chemie 18, Munday, D., Gutmark, E., Liu J. and Kailasanath, K. (2008). Flow and Acoustic Radiation from Realistic Tactical Jet C-D Nozzles. 14th AIAA/CEAS Aeroacoustics Conference (29th AIAA Aeroacoustics Conference), May 5-7, 2008, Vancouver, British Columbia, AIAA 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

11 Screech Turbulent mixing noise Figure 1 Far-field acoustic spectrum (forward quadrant; ψ = 30, M D = 1.575, M J = 1.575, M 2 = 0.1). 0 1 * e (a) (b) 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 wetted surface between this nozzle and the existing hardware, Station * is the throat, station e is the exit plane of the nozzle (b) nozzle details. D e = 57.5mm, Area Ratio = 1.23, curvature radius at throat = 0.5 mm. Exit lip thickness = 0.5mm. 11

12 (a) Figure 3 Convergent-divergent nozzle installed. (a) complete test article. (b) close-up of nozzle. (b) (a) Figure 4 Plan view of UC-GDPL s Aeroacoustic Test Facility. (a) far-field acoustic arrangement. (b) nearfield acoustic arrangement. (b) 12

13 Highresolution LES domain Medium-resolution LES domain Buffer zone 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. 13

14 PIV, M 2 = 0.1 PIV, M 2 = 0.3 LES, M 2 = 0.3 PIV, M 2 = 0.8 LES, M 2 = 0.8 u [m/s] Figure 8 Mean Axial velocity M j = M d = 1.56, T 0 /T a =

15 M 2 = 0.1 M 2 = 0.3 M 2 = 0.8 Figure 9 Centerline pressure M j = M d = 1.56, T 0 /T a =

16 M 2 = 0.0 M 2 = 0.1 M 2 = 0.2 M 2 = 0.3 M 2 = 0.4 M 2 = 0.5 M 2 = 0.6 M 2 = 0.7 M 2 = 0.8 Figure 10 Shadowgraph. One hundred images averaged to suppress turbulence and emphasize shock cells. M j = M d = 1.56, T 0 /T a = Solid lines descend from reflections at the shear layer in M 2 = 0.0. Dashed lines descend from waves crossing the centerline in M 2 = 0.0. Green lines pertain to the wave from the lip. Red lines pertain to the wave from inside. 16

17 Figure 11 Instantaneous Mach number M j = M d = 1.56, T 0 /T a = 1.22, M 2 =

18 x = 1De x = 2De x = 3De x = 4De x = 5De x = 6De x = 7De x = 8De x = 9De Figure 12 Instantaneous total temperature by LES, M j = M d = 1.56, T 0 /T a = 1.22, M 2 = 0.1. Mics LES Figure13 Far-field acoustic spectra, M j = M d = 1.56, T 0 /T a = 1.22, M 2 =

19 M 2 = 0.1 M 2 = 0.3 M 2 = 0.8 Figure 14 Upstream far-field acoustic spectra compared, M j = M d = 1.56 T 0 /T a = 1.22, ψ = 35 Figure 15 Far-field SPL directivity from LES. o M 2 = 0.1, o M 2 =

20 (a) (b) Figure 16 Measured 35 Far-field spectra for a range of jet Mach numbers for, T 0 /T a = (a) M 2 = 0.1. (b) M 2 =

21 OASPL [db] at ψ = M2 = 0.1 M2 = 0.3 Seiner & Yu P e /P atm = NPR J /NPR D Figure 17 Measured 35 Far-field OASPL for a range of jet Mach numbers for, T 0 /T a =