# A Wavelet-Based Time-Frequency Analysis on the Supersonic Jet Noise Features with Chevrons

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Setup

## 3. Results and Discussions

#### 3.1. Near-Field Spectral Levels

#### 3.2. Global Intermittency Analysis

#### 3.3. Single-Point Wavelet Analysis

#### 3.4. Bi-Variate Wavelet Analysis

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Meloni, S.; Proença, A.R.; Lawrence, J.L.; Camussi, R. An experimental investigation into model-scale installed jet–pylon–wing noise. J. Fluid Mech.
**2021**, 929, A4. [Google Scholar] [CrossRef] - Lighthill, M.J. On sound generated aerodynamically I. General theory. Proc. R. Soc. Lond. Ser. A Math. Phys. Sci.
**1952**, 211, 564–587. [Google Scholar] - Lilley, G. On the noise from air jets. AGARD CP
**1974**, 131, 13.1–13.2. [Google Scholar] - Camussi, R.; Bogey, C. Intermittent statistics of the 0-mode pressure fluctuations in the near field of Mach 0.9 circular jets at low and high Reynolds numbers. Theor. Comput. Fluid Dyn.
**2021**, 35, 229–247. [Google Scholar] [CrossRef] - Micci, G.L.; Camussi, R.; Meloni, S.; Bogey, C. Intermittency and Stochastic Modeling of Low- and High-Reynolds-Number Compressible Jets. AIAA J.
**2022**, 60, 1983–1990. [Google Scholar] [CrossRef] - Huber, J.; Fleury, V.; Bulté, J.; Laurendeau, E.; Sylla, A.A. Understanding and Reduction of Cruise Jet Noise at Aircraft Level. Int. J. Aeroacoust.
**2014**, 13, 61–84. [Google Scholar] [CrossRef] - Camussi, R.; Ahmad, M.K.; Meloni, S.; de Paola, E.; Di Marco, A. Experimental analysis of an under-expanded jet interacting with a tangential flat plate: Flow visualizations and wall pressure statistics. Exp. Therm. Fluid Sci.
**2022**, 130, 110474. [Google Scholar] [CrossRef] - Clem, M.; Zaman, K.; Fagan, A. Background Oriented Schlieren Applied to Study Shock Spacing in a Screeching Circular Jet. In Proceedings of the 50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, Nashville, TN, USA, 9–12 January 2012. [Google Scholar]
- Clem, M.; Brown, C.; Fagan, A. Background Oriented Schlieren Implementation in a Jet-Surface Interaction Test. In Proceedings of the 51st AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition, Grapevine, TX, USA, 7–10 January 2013. [Google Scholar]
- Tam, C. Supersonic jet noise. Ann. Rev. Fluid Mech.
**1995**, 27, 17–43. [Google Scholar] [CrossRef] - Edgington-Mitchell, D. Aeroacoustic resonance and self-excitation in screeching and impinging supersonic jets—A review. Int. J. Aeroacoust.
**2019**, 18, 118–188. [Google Scholar] [CrossRef] - Humphrey, N.J.; Edgington-Mitchell, D. The effect of low lobe count chevron nozzles on supersonic jet screech. Int. J. Aeroacoust.
**2016**, 15, 294–311. [Google Scholar] [CrossRef] - Nikam, S.; Sharma, S. Effect of chevron nozzle penetration on aero-acoustic characteristics of jet at M = 0.8. Fluid Dyn. Res.
**2017**, 49, 065506. [Google Scholar] [CrossRef] [Green Version] - Massey, S.; Elmiligui, A.; Hunter, C.; Thomas, R.; Pao, P.; Mengle, V. Computational Analysis of a Chevron Nozzle Uniquely Tailored for Propulsion Airframe Aeroacoustics. In Proceedings of the 12th AIAA/CEAS Aeroacoustics Conference (27th AIAA Aeroacoustics Conference), Cambridge, MA, USA, 8–10 May 2006. [Google Scholar]
- Schlinker, R.; Simonich, J.; Shannon, D.; Reba, R.; Colonius, T.; Gudmundsson, K.; Ladeinde, F. Supersonic jet noise from round and chevron nozzles: Experimental studies. In Proceedings of the 15th AIAA/CEAS Aeroacoustics Conference (30th AIAA Aeroacoustics Conference), Miami, FL, USA, 11–13 May 2009; p. 3257. [Google Scholar]
- Jawahar, H.K.; Meloni, S.; Camussi, R.; Azarpeyvand, M. Experimental Investigation on the Jet Noise Sources for Chevron Nozzles in Under-expanded Condition. In Proceedings of the AIAA AVIATION 2021 FORUM, Virtual Event, 2–6 August 2021. [Google Scholar] [CrossRef]
- Bridges, J.; Brown, C. Parametric testing of chevrons on single flow hot jets. In Proceedings of the 10th AIAA/CEAS Aeroacoustics Conference, Manchester, UK, 10–12 May 2004; p. 2824. [Google Scholar]
- Camussi, R.; Mancinelli, M.; Di Marco, A. Intermittency and stochastic modeling of hydrodynamic pressure fluctuations in the near field of compressible jets. Int. J. Heat Fluid Flow
**2017**, 68, 180–188. [Google Scholar] [CrossRef] - Juvé, D.; Sunyach, M.; Comte-Bellot, G. Intermittency of the noise emission in subsonic cold jets. J. Sound Vib.
**1980**, 71, 319–332. [Google Scholar] [CrossRef] - Tide, P.; Srinivasan, K. Novel chevron nozzle concepts for jet noise reduction. Proc. Inst. Mech. Eng. Part G J. Aerosp. Eng.
**2009**, 223, 51–67. [Google Scholar] [CrossRef] - Tide, P.; Srinivasan, K. Effect of chevron count and penetration on the acoustic characteristics of chevron nozzles. Appl. Acoust.
**2010**, 71, 201–220. [Google Scholar] [CrossRef] - Meloni, S.; Di Marco, A.; Mancinelli, M.; Camussi, R. Wall pressure fluctuations induced by a compressible jet flow over a flat plate at different Mach numbers. Exp. Fluids
**2019**, 60, 48–60. [Google Scholar] [CrossRef] - Meloni, S.; Di Marco, A.; Mancinelli, M.; Camussi, R. Experimental investigation of jet-induced wall pressure fluctuations over a tangential flat plate at two Reynolds numbers. Sci. Rep.
**2020**, 10, 9140. [Google Scholar] [CrossRef] - Meloni, S.; Lawrence, J.L.; Proença, A.R.; Self, R.H.; Camussi, R. Wall pressure fluctuations induced by a single stream jet over a semi-finite plate. Int. J. Aeroacoust.
**2020**, 19, 240–253. [Google Scholar] [CrossRef] - Camussi, R.; Meloni, S. On the Application of Wavelet Transform in Jet Aeroacoustics. Fluids
**2021**, 6, 299. [Google Scholar] [CrossRef] - Kamliya Jawahar, H.; Meloni, S.; Camussi, R.; Azarpeyvand, M. Intermittent and stochastic characteristics of slat tones. Phys. Fluids
**2021**, 33, 025120. [Google Scholar] [CrossRef] - Farge, M. Wavelet transforms and their applications to turbulence. Annu. Rev. Fluid Mech.
**1992**, 24, 395–458. [Google Scholar] [CrossRef] - Meneveau, C. Analysis of turbulence in the orthonormal wavelet representation. J. Fluid Mech.
**1991**, 232, 469–520. [Google Scholar] [CrossRef] - Camussi, R.; Robert, G.; Jacob, M.C. Cross-wavelet analysis of wall pressure fluctuations beneath incompressible turbulent boundary layers. J. Fluid Mech.
**2008**, 617, 11–30. [Google Scholar] [CrossRef] [Green Version] - Torrence, C.; Compo, G.P. A Practical Guide to Wavelet Analysis. Bull. Am. Meteorol. Soc.
**1998**, 79, 61–78. [Google Scholar] [CrossRef] [Green Version]

**Figure 1.**Schematic of the various nozzle configurations used in the present study: (

**a**) SMC000 or baseline nozzle; (

**b**) SMC002; and (

**c**) SMC006.

**Figure 3.**Near-field SPL spectra at M = 1.3 h/D = 3.5 and various axial locations. (

**a**) SMC000 nozzle; (

**b**) SMC002 nozzle; (

**c**) SMC006 nozzle.

**Figure 6.**Wavelet scalograms at M = 1.3, h/D = 3.5: (

**a**,

**b**) Baseline nozzle at x/D = 2 and x/D = 18, respectively; (

**c**,

**d**) SMC002 nozzle at x/D = 2 and x/D = 18 respectively; (

**e**,

**f**) SMC006 nozzle at x/D = 2 and x/D = 18 respectively.

**Figure 7.**Fourier spectra of the wavelet coefficients absolute values related to the Screech tone in the baseline configuration. Results are at the same Mach number of the previous plots.

**Figure 8.**Stochastic analysis for the various frequencies of interest. (

**a**) $\mu \left(\right|{w}_{x}\left|\right)$ at x/D = 2; (

**b**) $\mu \left(\right|{w}_{x}\left|\right)$ at x/D = 2; (

**c**) $\sigma \left(\right|{w}_{x}\left|\right)$ at x/D = 2; (

**d**) $\sigma \left(\right|{w}_{x}\left|\right)$ at x/D = 18.

**Figure 9.**LIM contour maps at M = 1.3 and h/D = 3.5: (

**a**,

**b**) Baseline nozzle at x/D = 2 and x/D = 18, respectively; (

**c**,

**d**) SMC002 nozzle at x/D = 2 and x/D = 18, respectively; (

**e**,

**f**) SMC006 nozzle at x/D = 2 and x/D = 18, respectively.

**Figure 10.**LIM2 contour maps at M = 1.3 and h/D = 3.5: (

**a**,

**b**) Baseline nozzle at x/D = 2 and x/D = 18, respectively; (

**c**,

**d**) SMC002 nozzle at x/D = 2 and x/D = 18, respectively; (

**e**,

**f**) SMC006 nozzle at x/D = 2 and x/D = 18, respectively.

**Figure 11.**Wavelet Coherence contour maps between two consecutive microphones at M = 1.3 and h/D = 3.5: (

**a**,

**b**) Baseline nozzle having the reference microphone at x/D = 2–4 and x/D = 16–18 respectively; (

**c**,

**d**) SMC002 nozzle having the reference microphone at x/D = 2–4 and x/D = 16–18, respectively; (

**e**,

**f**) SMC006 nozzle having the reference microphone at x/D = 2 and x/D = 18, respectively.

**Figure 12.**Wavelet phase angle contour maps between two consecutive microphones at M = 1.3 and h/D = 3.5: (

**a**,

**b**) Baseline nozzle having the reference microphone at x/D = 2–4 and x/D = 16–18, respectively; (

**c**,

**d**) SMC002 nozzle having the reference microphone at x/D = 2–4 and x/D = 16–18, respectively; (

**e**,

**f**) SMC006 nozzle having the reference microphone at x/D = 2 and x/D = 18, respectively; the reported contours are normalized by $\pi $.

Nozzle ID | N | Length (mm) | Angle (${}^{\circ}$) | Penetration (mm) | D${}_{\mathit{e}}$ (mm) | $\mathbf{\Gamma}$ |
---|---|---|---|---|---|---|

SMC 000 | 0 | 16.9333 | 0.089 | |||

SMC 002 | 4 | 10.6667 | 5 | 0.4650 | 17.8667 | 0.089 |

SMC 006 | 6 | 7.5333 | 18.2 | 1.1750 | 15.9000 | 0.292 |

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**MDPI and ACS Style**

Meloni, S.; Jawahar, H.K.
A Wavelet-Based Time-Frequency Analysis on the Supersonic Jet Noise Features with Chevrons. *Fluids* **2022**, *7*, 108.
https://doi.org/10.3390/fluids7030108

**AMA Style**

Meloni S, Jawahar HK.
A Wavelet-Based Time-Frequency Analysis on the Supersonic Jet Noise Features with Chevrons. *Fluids*. 2022; 7(3):108.
https://doi.org/10.3390/fluids7030108

**Chicago/Turabian Style**

Meloni, Stefano, and Hasan Kamliya Jawahar.
2022. "A Wavelet-Based Time-Frequency Analysis on the Supersonic Jet Noise Features with Chevrons" *Fluids* 7, no. 3: 108.
https://doi.org/10.3390/fluids7030108