Aeroacoustic characteristics of supersonic offset jets

Abstract

The offset jet configuration is one where the jet is discharged at some distance from a solid surface. Although the geometric configuration may look simple, the flow may involve several complexities. In propulsion systems, the high-speed jet generated from the rear engine of an aircraft, flowing nearby the fuselage, can be treated as an offset jet. In this work, an experimental investigation of the interaction noise due to circular high-speed offset jets is performed in an anechoic environment at different nozzle pressure ratios and offset ratios (height of the jet centerline above the plate per nozzle width). A large horizontal plate placed over a height-adjustable stand is used as the offset plate. Acoustic characteristics such as overall sound pressure level and the directivity pattern of free and offset jets are compared for different nozzle pressure ratios. The effect of offset ratio on noise characteristics is also investigated. Flow visualization is also carried out to understand the shock structure and its noise generation mechanism. Acoustic characteristics reveal that noise levels are higher for an offset jet compared to a free jet. Sound pressure levels for offset ratio 0.5 are lower than those for other offset ratios. The noise levels are higher for offset ratio 1.0 due to the presence of feedback tone. Schlieren visualization studies also corroborate the above characteristics.

Keywords

Offset jet installed jet interaction noise Coanda effect

Introduction

Jets interacting with neighboring surfaces are called bounded jets and they have gained some attention from researchers in recent years. Three types of bounded jets are commonly encountered: (a) wall jets, where the fluid is discharged at the boundary, (b) impinging jets, where the fluid is discharged towards the boundary, and (c) offset jets, where the fluid is discharged into a medium above the boundary (wall), and the axis of the jet exit is parallel to the wall. The wall jet can be considered as a limiting case of an offset jet. The offset jet configuration is one where the jet is discharged at some distance from a solid surface. When a plane air jet is discharged into quiescent ambient surroundings, the jet deflects downward and attaches to the boundary. Reduced entrainment from the boundary side of the jet causes low pressure between the jet and the boundary, resulting in the jet deflecting downward, and eventually attaching to the boundary, known as the Coanda effect.

It has gained extensive research interest primarily due to diverse practical and engineering applications such as environmental discharge, fluid injection systems, combustion chambers, etc., In propulsion systems, the high-speed jet generated from the rear engine of an aircraft, impinging on the fuselage (aft/rear), can be treated as an offset jet.

Bourque and Newman,¹ Sawyer² are among the early authors who studied turbulent offset jets. The theoretical model of Hoch and Jiji³ predicts the reattachment distance and also the mean flow characteristics. Pelfrey and Liburdy⁴ gave an experimental investigation of mean flow characteristics, i.e. two components of velocity vectors, pressure distribution, and wall shear stress. Assoudi et al.⁵ have also experimentally studied the mean velocity and turbulence characteristics of an offset jet with different offset ratios and compared them with numerical results.

Specific to the application of aircraft, when the jet exhaust interacts with the wing or any solid surface, that type of offset jet can be called an installed jet. Prediction of aircraft noise due to installed jets is of increasing interest in the design of future civil transport. To achieve noise reduction goals, many new aircraft concepts involve over-the-wing engine design, which provides the shielding effect for the jet exhaust noise propagated towards the ground.

The acoustics of jet surface interaction with flat plates was studied by numerous authors. Powell⁶ was the first author to describe that the jet surface interaction can generate an acoustic tone equivalent to a dipole source due to the trailing edge fluctuating flow that disturbs the jet flow instabilities generation in a feedback loop process. Lawrence et al.⁷ experimentally investigated the interaction noise of a circular subsonic jet with a flat plate. The noise characteristics of rectangular subsonic and supersonic jets interacting with solid surfaces were studied by Brown,⁸ Zaman et al.,^9,10 and Mora et al.¹¹ Far-field noise measurements were done by moving the plate through different axial positions (x/D) and radial positions (h/D), and the effect of the length of the plate and offset height on noise characteristics was studied.

Brown¹² developed an empirical model to be used in preliminary design system-level studies. They also investigated how airframe surfaces might affect the shock-cell structure in the jet plume and hence the broadband shock-associated noise. Baier et al.¹³ studied the presence of a flat surface on acoustic characteristics of a supersonic jet from a rectangular converging-diverging nozzle for different NPRs. Also, the effect of offset height on noise characteristics was studied. Tam and Chandramouli¹⁴ have provided the theoretical analysis for the experiments conducted by Zaman et al.¹⁰ Some authors have demonstrated screech cessation by introducing different shapes of reflectors. Islam and Seto¹⁵ used a spherical reflector to demonstrate that the screech could be canceled depending on the reflector focal point. Morata and Papamoschou¹⁶ used non-conventional conical reflector surfaces at the nozzle exit, giving rise to new tones that did not fall within the A1, A2, B, or C category at that fully-expanded jet Mach number, indicating potential new oscillation dynamics. The biggest problem of offset jets in propulsion systems is the jet-flap interaction noise, which is generated at the trailing edge of the wing if the engine is mounted under the wing. The pressure near-field of the jet is scattered at the trailing edge. This problem is investigated in numerous papers because of its importance for the aircraft industry. Cavalieri et al.¹⁷ have explored the mechanism involved in sound generation in the case of turbulent subsonic jets with the presence of flat plates in close proximity.

It is evident from the literature that most of the authors have concentrated on mean flow characteristics, such as velocity distribution, pressure distribution, re-attachment length, etc., for different Reynolds numbers and offset ratios. Some authors have concentrated on the acoustic characteristics of rectangular subsonic and supersonic jet interaction with a flat plate. However, the acoustic aspects of circular supersonic offset jets have not been emphasized. Most of the new aircraft designs are pushing the engine closer to the airframe to reduce drag. This arrangement creates additional noise due to jet interaction with the airframe. However, this jet noise is subsonic.

The main objective of this paper is an experimental investigation of jet interaction noise with the offset plate for different offset ratios (ORs) and nozzle pressure ratios (NPRs). Schlieren flow visualization is also carried out for both free and offset jets to understand the shock structure and its noise generation mechanism.

Experimental setup and procedure

Test facility

The experimental test facility, shown schematically in Figure 1, consists of an air supply system, a jet facility, and an anechoic chamber. A 150 HP (110.4 kW) two-stage water-cooled reciprocating air compressor is used to compress the air up to a 9-bar gauge. The compressed air is stored in 2 storage reservoirs with a total capacity of 20 m³. The jet facility, located inside an anechoic room, consists of a settling chamber with an internal diameter of 380 mm and a length of 700 mm. The compressed air is brought to the settling chamber using a pipe system of 4-inch (101.6 mm) diameter. The settling chamber is connected to a pressure regulating valve at one end through a pipe and a convergent opening at the other end to fix the orifice or nozzle. The issuing jet should not carry internal disturbances such as turbulence and its corresponding noise. Flow disturbances such as turbulence are mitigated by flow conditioning meshes of progressive fineness at the entry and by providing a convergent section at the exit of the plenum.

A semi-anechoic chamber with inside dimensions of 2.5 m × 2 m × 2 m from wedge tip to tip is equipped with square pyramid wedges made of polyurethane foam pasted on all the inner surfaces. The chamber floor is lined with carpet. The chamber was calibrated, and the lower cut-off frequency was found to be 700 Hz. The anechoic chamber creates free field conditions and ensures that the acoustic data is least corrupted by external noise. The anechoic chamber has 2 windows, one at the rear for air entrainment and the other at the front for easy flow of air to avoid pressure accumulation.

During the experimentation, pressure is regulated manually with the help of a regulating valve and maintained constant while taking the readings. The blowdown experiment takes about 45 min, and directivity measurements take 2 min for each NPR. The remaining experiments take less than a minute for each NPR.

Offset jet construction

The orifice of 10 mm diameter (d) is connected to one end of the settling chamber and is used to generate a supersonic jet. A rectangular offset plate of dimensions 800 mm × 200 mm and thickness of 15 mm is placed below the jet, as shown in Figure 1, to generate the offset jet. The offset ratio is defined as the height of the jet centerline above the plate (H) per nozzle width (d). Different offset ratios can be set by moving the plate up and down with the help of an adjustable height stand. The experimental matrix tabulated in Table 1 gives various parameters used in the present study.

Table 1.

Parameters varied during the experimental study.

NPR (R)	2.5 to 4.5 in steps of 0.25
Offset ratio (OR)	0.5, 1.0, 2.0 and 3.3

Blowdown test

The blowdown test is conducted for both free jets and offset jets. Initially, the reservoir tanks are filled with compressed air to a pressure of around 9 bar gauge. After setting up the offset plate at the required offset ratio and instrumentation for recording stagnation pressure and acoustic measurements, the blowdown test is performed. By fully opening the pressure regulating valve, the air is allowed to flow through the orifice until the pressure falls to 0.75 bar gauge (NPR = 1.75). During the blowdown, the stagnation pressure is acquired continuously using a piezo-resistive pressure transducer mounted inside the settling chamber. Acoustic measurements are also carried out continuously by placing the microphone at a distance of 40 jet diameters from the center of the jet exit at an emission angle of 90°. The data acquisition is made using LabVIEW. A similar procedure is repeated for free jets also. The associated range of NPRs during the blowdown is 5.3 to 1.75, and the data acquisition time for the blowdown test is approximately 45 min. The blowdown test result will point out some key NPRs showing interesting features, wherein detailed studies such as directivity are performed to understand the acoustic characteristics clearly. Also, to understand the overall sound pressure level (OASPL) peaks observed in the blowdown study, spectral analysis is conducted on the signals using scripts written in Matlab. Sound Pressure Level spectra were computed from the microphone signal using a Fast Fourier Transform (FFT) size of 4096, giving a frequency resolution of 37 Hz.

Directivity study

The directivity measurements are carried out using an angular traverse system controlled by a stepper drive (National Instruments NI-MID-7604), and the motion is automated using LabVIEW software. These measurements reveal the acoustic intensity distribution in the far field. The microphone is fixed to the rotating arm of the angular traverse system at a distance of 40 d from the jet axis such that it always points towards the center of the jet exit while moving in a circular arc. For obtaining directivity, the microphone is rotated from 35° to 125° in steps of 5°, and data is acquired by pausing the traverse for 5 s at each emission angle. This procedure is repeated for the key NPRs identified from the blowdown tests.

Flow visualization

Schlieren flow visualization studies are conducted to capture the shock structure in the flow field and find the relation between flow and noise. Generally, the imperfectly expanded jets generate shocks and expansion fans at the exit of the orifice. A Sodium LED light source is passed through two bi-convex lenses placed on either side of the jet to visualize the shock structure in the flow field. The lenses of diameter 120 mm and focal length of 110 mm are used. An opaque knife edge is used to obstruct part of the light beam coming out of the second lens. The shock cell images are captured by using a high-speed camera. The images were captured at a frame rate of 1000 FPS with an exposure time of 7.8 µsec.

Uncertainty analysis and data validation

The microphones are calibrated using a B&K pistonphone at a single point frequency of 250 Hz and 124 dB amplitude. A piezoresistive transducer is used for stagnation pressure measurement in the settling chamber that has an uncertainty of ±2% of full scale. The anechoic chamber temperature is almost constant with a maximum temperature variation of ±1^oC in a given run. The sound pressure levels reported in this report are relative to a reference pressure of 20 μPa. The error in the microphone positioning is ±1 mm, and the angle is within ±1°. The error in the offset plate placement is within ±0.5 mm. The frequency resolution based on the FFT size is 37 Hz and ranges from 700 Hz to 70,000 Hz. The OASPL is repeatable within ±1 dB.

In order to validate the results, some comparisons have been made with results in the literature. Experimental data is validated by comparing the screech frequency of the free jet issuing from a 10 mm circular orifice with the screech frequency formula given by Gao and Li.¹⁸ Figure 2 shows that the jet screech frequency of the free jet exhibits the same trend observed by Gao and Li.¹⁸

Instrumentation

The far-field acoustic data is acquired using a 1/4-inch condenser microphone (PCB 378C01). The sensitivity of the microphone used is 3.4 mV/Pa and it possesses a flat frequency response in the range of 4 Hz–70 kHz within ±1 dB. The microphone data is acquired at a sampling rate of 150,000 samples/sec, and aliasing errors are eliminated by passing the signal through a low pass filter at 70 kHz. The data are acquired using the National Instruments Data Acquisition board (NI-PCI-6143), which is controlled by LabVIEW software. Time series data is converted into acoustic pressure fluctuations by multiplying with the sensitivity of the microphone. A piezoresistive transducer is used to record the settling chamber pressure continuously during the blowdown study. The data obtained from experiments is time-series data in terms of voltage fluctuations and is processed using scripts written in Matlab 2014.

Results and discussion

Comparison between offset jet and free jet

A blowdown test is performed for an offset jet with an offset ratio, OR 3.3, and for the free jet as per the procedure mentioned above in the section on blowdown test. The sound pressure level contours in the frequency and NPR plane (Figure 3(a) and (c)) and Strouhal number (St) and NPR plane (Figure 3(b) and (d)) for the free and offset jets are shown in Figure 3. The color bar shown on the right-hand side of the figure represents SPL in dB. Maximum noise levels can be seen at approximately NPR 3.1 to 3.2.

From the contour plots, it is clear that mode D tone is observed for both free and offset jets. The modal representations made here are purely inferential based on the literature. However, the broadband shock-associated noise (BBSAN) embedded with tones is more for offset jets shown as thick bands in Figure 3(c) when compared to free jets. It also shows that for NPRs above 3.5, tones disappear for offset jets at higher frequencies ∼32 kHz, unlike free jets. It is observed that the addition of the plate does not change the oscillation dynamics of the jet, and the frequency of the tonal noise appears to be similar for both the free and offset jets.

Figure 4 shows the variation of OASPL with NPR for free and offset jets. It is clearly shown that the offset jet generates more noise compared to a free jet. The additional noise emitted due to the presence of the offset plate has mainly two components: noise due to reflection from the plate, which is less than 3 dB, and trailing edge noise due to the turbulence pressure fluctuations passing over the trailing edge. This sound is produced mainly by a pure tone and its harmonics. It is evident from the literature that impingement tones were generated by jet impingement with a solid surface, and screech tones are mainly emitted from the plume of an imperfectly expanded jet.^19,20

It also shows that during the blowdown, as NPR decreases from 5.4 to 3.3, OASPL decreases gradually. Later on, due to the presence of more tones, OASPL rises suddenly for NPR = 3.2 and then decreases rapidly as NPR decreases. OASPL peaks observed in the blowdown study can be clearly understood by spectral analysis conducted on the signals. The SPL power spectra are also shown at various NPRs. Spectral plots show that tones are more dominant for an offset jet than the free jet as the trailing edge noise propagates forward toward the orifice and triggers a feedback loop for instability waves. Both offset and free jets cease to generate screech tones at higher pressure ratios, and the primary noise source is only turbulent mixing noise.²¹ Spectra plots shown in Figure 4(a) reveal that screech tones are reducing for higher pressure ratios (NPR 4.5). Jothi and Srinivasan²² also observed the same phenomenon for circular free jets with higher pressure ratios. This cessation of screech tones in supersonic jet flows is explained in detail by Raman.²³

Overall sound pressure level peak is observed at NPR 3.12 due to the presence of pure tones and their harmonics (Figure 4(b)). For NPR 2.64, the first tone is observed for the offset jet and no tones were observed for the free jet (Figure 4(c)). Below 2.64 NPR, no tones were observed for both free and offset jets, and the noise level reduces as NPR drops during the blowdown. Figure 4(d) shows the spectral plot for NPR 2.0, where the main noise source is turbulent mixing only. Directivity studies are also carried out to clearly understand the acoustic behavior of an offset and free jet for NPRs ranging from 2.5 to 4.5 in steps of 0.25.

Polar plot (Figure 5) shows the OASPL directivity pattern of an offset jet (OR 3.3) for different NPRs. It represents the sound pressure level distribution for emission angles in the range of 35° to 125° As discussed in the blowdown study, the sound pressure levels increase with an increase in NPR. The OASPL rise is predominant at low NPRs, while at higher NPRs, OASPL values almost merge at ϴ = 35° and ϴ = 125°. This indicates the fact that further addition of momentum to the jet flow beyond a particular nozzle pressure ratio does not effectively increase the intensity of acoustic sources.²²

The OASPL directivity comparison for free jet and offset jets is clearly understood from the plots shown in Figure 6(a) and (b). The directivity pattern exhibits a common feature that the OASPL level gradually increases as the microphone moves downstream. This is due to noise radiation from downstream propagating sound waves.²⁴

Figure 6(a) gives the directivity pattern for NPRs 2.5, 3.0, and 3.25 for both free and offset jets. It is observed that OASPL increases monotonically as the microphone moves downstream, specifically for low NPRs. However, for higher NPRs, noise directivity shifts towards higher emission angles (Figure 6(b)). This is due to the presence of shock-associated noise caused by the interaction between large-scale turbulent structures and shock cell systems.^25,26 Also, it is observed that low-frequency noise is more dominant for low emission angles compared to all other angles at all NPRs. This can be attributed to the presence of a dominant shear mechanism and large-scale structures downstream.²⁴ The increase in OASPL is observed for offset jet for emission angles ranging from 75° to 95° due to the reflection of sound waves on the surface of the plate. Minimum OASPL is observed at 60° to 70° emission angles and is due to the interference of two sets of acoustic waves, i.e. upstream and downstream propagation. This interference of acoustic waves is destructive, as their amplitudes subtract and are out of phase. For a 90° emission angle, the sound pressure levels for an offset jet are more than a free jet by 3–5 dB for different NPRs. Noise directivity pattern of free and offset jets is similar except for the magnitude of sound pressure levels. The overall sound pressure levels with offset jets are more than a free jet. This could be due to the contribution of higher tonal noise with offset jet (Figure 7(a) and (b)) and reflection of noise from the plate towards the microphone. Figure 7(a) and (b) show the spectral plots for an offset jet revealing that tonal noise is more for an offset jet than for a free jet.

Effect of offset ratio

A detailed experimental investigation is performed to study the effect of the offset ratio (height of the jet centerline above the plate per nozzle width, H/d) on acoustic characteristics. Experiments were conducted by varying the offset height by using a height-adjustable stand placed below the plate and taking the far-field acoustic measurements by placing the microphone at an emission angle of 90°. Different offset ratios (0.5, 1.0.2.0, 3.3) and NPRs ranging from 2.5 to 4.5 in steps of 0.25 were considered. Figure 8 shows the variation of OASPL with NPR for different offset ratios. For offset ratio 0.5 (i.e. plate at the lip of the orifice), noise levels are attenuated for all NPRs because of shock cell interaction with the plate. This phenomenon can be observed from schlieren photographs and will be discussed in a subsequent section. For low NPR (2.5), no tones were observed, and noise is due to pure turbulent mixing only.²¹ Thus, noise levels are more or less the same for all the offset ratios and are within 3 dB. OASPL increases with an increase in NPR, as expected.

For higher offset ratios, OASPL also increases as a function of NPR. Maximum noise levels are observed for an offset ratio of 1.0. This can be clearly understood from the spectral comparison plot shown for a sample NPR 3.25, shown in Figure 9. It clearly shows that for offset ratio 1.0, more tones were observed compared to all other offset ratios, leading to more noise levels. As the offset ratio increases, the jet reattachment is delayed, and the reflection of sound waves from the plate reduces. This results in a moderate reduction in sound pressure levels for higher offset ratios (2.0 and 3.3) compared to OR 1.0.

The OASPL difference between free jet and offset jet (ΔOASPL = OASPL_offset- OASPL_free) is calculated for different offset ratios and shown in the contour map (Figure 10). It shows that the sound pressure levels are more for an offset jet with OR 1.0 and for NPRs ranging from 3.0 to 3.5. To see the envelope where the tonal noise is dominant, the discrete tones in the spectra are removed by clipping the tones, and OASPL is calculated with and without tones. The difference between OASPL with and without tones gives the tonal noise in decibels. Tonal noise levels of an offset jet with different offset ratios and NPRs are shown in the contour plot shown in Figure 11. It clearly shows that the tonal dB levels are more for offset jets with OR 1.0 and NPRs ranging from 3.0 to 3.75. Both the contour plots, Figures 10 and 11, reveal the region where more noise levels and tones were present in the envelope for an offset jet.

Flow visualization

Figure 12(a) and (b) show the shock cell structure for free and an offset jet with OR 3.3 at different NPRs. For OR = 3.3, the jet attaches to the plate downstream and the effect of an offset plate cannot be seen in the schlieren image shown. Hence, the shock cell structure and the number of shock cells for both free and offset jets look the same. Figure 12 shows that the expansion fan and oblique shocks are formed alternatively at the orifice exit as the jet is under-expanded. Also, it can be observed that the shock strength and shock cell spacing decrease as it progresses downstream and finally attains subsonic conditions. The Schlieren photograph for NPR 2.5 shows that the shock structure is weak. It also shows that as NPR increases, shock cell length and shock cell spacing increase. This represents that the shock-associated noise contribution will be more for higher NPRs. Hence, the overall sound pressure level increases as NPR increases, irrespective of the offset ratios (Ref. Figure 8).

Figure 13(a) shows the Schlieren photograph of an offset jet with OR 0.5, i.e. offset plate at the lip of the jet exit for different NPRs. It clearly shows that for an offset ratio of 0.5, expansion fan and shock waves interact with the plate and shock strength decreases as the jet progresses. Thus, noise levels are attenuated for this offset ratio (Figure 8). The shock cell structure deterioration has also been observed by Baier et al.¹³ for a low offset ratio. For offset ratio 1.0, the shock is almost as strong as a free jet, and the jet plume oscillates after the second shock wave. The jet then moves toward the plate due to the Coanda effect and eventually reattaches with the plate at a downstream location (Figure 13(b)). This reattachment causes the reflection of sound which contributes to more noise levels compared to other configurations.

Conclusions

The acoustic characteristics of supersonic offset jets were experimentally investigated and compared with the free jet. Experiments were conducted on a free jet and offset jet with different offset ratios at different NPRs. The blowdown study results indicate that the overall sound pressure levels are higher for offset jets than free jets due to trailing edge noise and the reflection of sound from the plate. Directivity studies revealed that overall sound pressure level increases in the downstream direction for low NPRs. However, due to the dominance of shock-associated noise for higher NPRs, noise directivity shifts towards higher emission angles. Noise levels are more for higher NPRs for emission angles between 75° and 90° due to the reflection of sound waves on the surface of the plate. Effect of offset ratio (OR) on OASPL result shows that for offset ratio 0.5, noise levels are attenuated for all NPRs because of shock cell interaction with the plate. Schlieren images also reveal the shock interaction with the plate for OR 0.5. The noise level for an offset jet with OR 1.0 is more compared to other offset ratios due to the presence of feedback tone.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

K Srinivasan

Appendix

References

Bourque

Newman

. Reattachment of a two-dimensional incompressible jet to an adjacent flat plate. Aeronaut Q Aug 1960; 11: 201–232.

Sawyer

. Two-dimensional reattachment jet flows including the effects of curvature on entrainment. J Fluid Mech 1963; 17: 481–498.

Hoch

Jiji

. Two-dimensional turbulent offset jet-boundary interaction. ASME J Fluids Eng, Mar 1981; 103: 154–161.

Pelfrey

JRR

Liburdy

. Mean flow characteristics of a turbulent offset jet. Trans ASME J Fluids Engg 1986a; 108: 82–88.

Ali

Habli

LePalec

, et al. Experimental and numerical study of an offset jet with different velocity and offset ratios. Eng Appl Comput Fluid Mech 2015; 9(No. 1): 490–512.

Powell

. On the edge tone. J Acoust Soc Am 1961; 33: 395–409.

Lawrence

JLT

Azarpeyv

Self

, Interaction between a flat plate and a circular subsonic jet. In: 17th AIAA/CEAS aeroacoustics conference, AIAA Paper 2011-2745, Portland, Oregon, 5–8 June 2011.

Brown

. Jet–surface interaction test: far-field noise results. New York: American Society of Mechanical Engineers Paper GT2012-69639, 2012.

Zaman

KBMQ

Brown

Bridges

. Interaction of a rectangular jet with a flat-plate placed parallel to the flow. In: NASA Glenn Research Center.

10.

Zaman

KBMQ

Fagan

Bridges

, et al. An experimental investigation of resonant interaction of a rectangular jet and a flat plate. J Fluid Mech 2015; 779: 751–775.

11.

Mora

Baier

Kailasanath

, et al. Acoustics from a rectangular supersonic nozzle exhausting over a flat surface. J Acoust Soc Am 2016; 140: 4130–4141.

12.

Brown

. Developing an empirical model for jet-surface interaction noise. In: AIAA SciTech 2015, National Harbor, Maryland, 13–17 January 2014.

13.

Baier

Karnam

Gutmark

. Near-field measurements of a low aspect ratio supersonic nozzle interacting with a surface. In: AIAA SciTech Forum, San Diego, California, 7–11 January 2019.

14.

Tam

CKW

Chandramouli

. Jet-plate interaction tones relevant to over-the-wing engine mount concept. J Sound Vib 2020; 486: 115378.

15.

Islam

MTK

Seto

. Control of supersonic jet noise with a spherical reflector. JASA 2004; 116: 2539.

16.

Morata

Papamoschou

. Effect of nozzle geometry on the space-time emission of screech tones. AIAA Paper, 2021.

17.

Cavalieri

Jordan

Gervais

. Scattering of wavepacket by a flat plate in the vicinity of a turbulent jet. Nantes, France, Acoustics 2012 Apr 2012. HAL-00811053.

18.

Gao

. A multi-mode screech frequency prediction formula for circular supersonic jets. J Acoust Soc Am 2010; 127(3): 1251–1257.

19.

Tam

CKW

Seiner

. Proposed relationship between broadband shock associated noise and screech tones. J Sound Vib 1986; 110: 309–321.

20.

Raman

. Supersonic jet screech: half-century from powell to the present. J Sound Vib 1999; 225: 543–571.

21.

Tanna

. An experimental study of jet noise Part-I: turbulent mixing noise. J Sound Vib 1977; 50(3): 405–428.

22.

Jothi

TJS

Srinivasan

. Turbulent mixing noise from underexpanded non-circular slot jets. Acta Acustica United With Acustica 2013; 99: 514–523.

23.

Raman

. Cessation of screech in under expanded jets. J Fluid Mech 1997; 336: 69–90.

24.

Tam

CKW

Golebiowski

Seiner

. On the two components of turbulent mixing noise from supersonic jets. American Institute of Aeronautics and Astronautics, 1996, p. 1716.

25.

Tam

CKW

. Supersonic jet noise. Annu Rev Fluid Mech 1995; 27: 17–43.

26.

Tam

CKW

Tanna

. Shock associated noise of supersonic jets from convergent divergent nozzles. J Sound Vib 1982; 81(3): 337–358.