# 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

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**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