### Abstract

There is evidence to suggest that nonlinearity is important in the propagation of high-amplitude jet noise [Gee et al., AIAA J. 43(6), 1398-1401 (2005)]. Typically, the power spectral density (PSD) is used to assess the impact of jet noise on the surrounding environment, but such an assessment requires multiple measurement locations to observe the nonlinear evolution of the PSD. The difference in the PSDs measured at different locations depends on a combination of source level, nozzle diameter, and propagation distance. As a result, full scale measurements have to be extended over large distances, and model scale measurements require high measurement bandwidths. These constraints complicate the measurement and make it difficult to observe nonlinear effects using the PSD. Here a different technique for determining the importance of nonlinearity is investigated. The imaginary part of the cross-spectral density of the pressure and the square of the pressure, also called the quadspectral density (QSD), is related to the rate of nonlinear change of the PSD. Thus, the extent to which the PSD is evolving nonlinearly can be determined at a single measurement location. In the absence of absorption, energy is conserved, and the integration of the product of the QSD with frequency over all frequencies must be zero; when nonlinearity is present, the value of the QSD can be nonzero for many frequencies. Because nonlinearity tends to transfer energy from low frequencies to high frequencies and the QSD is positive at frequency components that are losing energy, using the integral of the QSD over its positive values as a nonlinearity indicator eliminates the need for high bandwidth measurements. Experimental measurements were taken in a plane wave tube with a working length of 9.55 m in which boundary layer losses dominate over atmospheric absorption. Experimental and numerical results show that the ratio of the integral of the QSD over the frequencies for which it is positive (Q_{pos}) to the integral over the frequencies for which it is negative (Q_{neg}) is close to one. Also, because the QSD is third-order in pressure, normalizing its integral by the cube of the rms pressure yields a quantity that is easily compared across experimental conditions. Results for both periodic and broadband signals are presented and the practicality of using the QSD as a single-point indicator of nonlinearity addressed.

Original language | English (US) |
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Title of host publication | Collection of Technical Papers - 12th AIAA/CEAS Aeroacoustics Conference |

Pages | 1675-1680 |

Number of pages | 6 |

Volume | 3 |

State | Published - 2006 |

Event | 12th AIAA/CEAS Aeroacoustics Conference - Cambridge, MA, United States Duration: May 8 2006 → May 10 2006 |

### Other

Other | 12th AIAA/CEAS Aeroacoustics Conference |
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Country | United States |

City | Cambridge, MA |

Period | 5/8/06 → 5/10/06 |

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### All Science Journal Classification (ASJC) codes

- Engineering(all)

### Cite this

*Collection of Technical Papers - 12th AIAA/CEAS Aeroacoustics Conference*(Vol. 3, pp. 1675-1680)

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*Collection of Technical Papers - 12th AIAA/CEAS Aeroacoustics Conference.*vol. 3, pp. 1675-1680, 12th AIAA/CEAS Aeroacoustics Conference, Cambridge, MA, United States, 5/8/06.

**Investigation of a single-point nonlinearity indicator in the propagation of high-amplitude jet noise.** / Falco, Lauren E.; Atchley, Anthony A.; Gee, Kent L.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Investigation of a single-point nonlinearity indicator in the propagation of high-amplitude jet noise

AU - Falco, Lauren E.

AU - Atchley, Anthony A.

AU - Gee, Kent L.

PY - 2006

Y1 - 2006

N2 - There is evidence to suggest that nonlinearity is important in the propagation of high-amplitude jet noise [Gee et al., AIAA J. 43(6), 1398-1401 (2005)]. Typically, the power spectral density (PSD) is used to assess the impact of jet noise on the surrounding environment, but such an assessment requires multiple measurement locations to observe the nonlinear evolution of the PSD. The difference in the PSDs measured at different locations depends on a combination of source level, nozzle diameter, and propagation distance. As a result, full scale measurements have to be extended over large distances, and model scale measurements require high measurement bandwidths. These constraints complicate the measurement and make it difficult to observe nonlinear effects using the PSD. Here a different technique for determining the importance of nonlinearity is investigated. The imaginary part of the cross-spectral density of the pressure and the square of the pressure, also called the quadspectral density (QSD), is related to the rate of nonlinear change of the PSD. Thus, the extent to which the PSD is evolving nonlinearly can be determined at a single measurement location. In the absence of absorption, energy is conserved, and the integration of the product of the QSD with frequency over all frequencies must be zero; when nonlinearity is present, the value of the QSD can be nonzero for many frequencies. Because nonlinearity tends to transfer energy from low frequencies to high frequencies and the QSD is positive at frequency components that are losing energy, using the integral of the QSD over its positive values as a nonlinearity indicator eliminates the need for high bandwidth measurements. Experimental measurements were taken in a plane wave tube with a working length of 9.55 m in which boundary layer losses dominate over atmospheric absorption. Experimental and numerical results show that the ratio of the integral of the QSD over the frequencies for which it is positive (Qpos) to the integral over the frequencies for which it is negative (Qneg) is close to one. Also, because the QSD is third-order in pressure, normalizing its integral by the cube of the rms pressure yields a quantity that is easily compared across experimental conditions. Results for both periodic and broadband signals are presented and the practicality of using the QSD as a single-point indicator of nonlinearity addressed.

AB - There is evidence to suggest that nonlinearity is important in the propagation of high-amplitude jet noise [Gee et al., AIAA J. 43(6), 1398-1401 (2005)]. Typically, the power spectral density (PSD) is used to assess the impact of jet noise on the surrounding environment, but such an assessment requires multiple measurement locations to observe the nonlinear evolution of the PSD. The difference in the PSDs measured at different locations depends on a combination of source level, nozzle diameter, and propagation distance. As a result, full scale measurements have to be extended over large distances, and model scale measurements require high measurement bandwidths. These constraints complicate the measurement and make it difficult to observe nonlinear effects using the PSD. Here a different technique for determining the importance of nonlinearity is investigated. The imaginary part of the cross-spectral density of the pressure and the square of the pressure, also called the quadspectral density (QSD), is related to the rate of nonlinear change of the PSD. Thus, the extent to which the PSD is evolving nonlinearly can be determined at a single measurement location. In the absence of absorption, energy is conserved, and the integration of the product of the QSD with frequency over all frequencies must be zero; when nonlinearity is present, the value of the QSD can be nonzero for many frequencies. Because nonlinearity tends to transfer energy from low frequencies to high frequencies and the QSD is positive at frequency components that are losing energy, using the integral of the QSD over its positive values as a nonlinearity indicator eliminates the need for high bandwidth measurements. Experimental measurements were taken in a plane wave tube with a working length of 9.55 m in which boundary layer losses dominate over atmospheric absorption. Experimental and numerical results show that the ratio of the integral of the QSD over the frequencies for which it is positive (Qpos) to the integral over the frequencies for which it is negative (Qneg) is close to one. Also, because the QSD is third-order in pressure, normalizing its integral by the cube of the rms pressure yields a quantity that is easily compared across experimental conditions. Results for both periodic and broadband signals are presented and the practicality of using the QSD as a single-point indicator of nonlinearity addressed.

UR - http://www.scopus.com/inward/record.url?scp=33845606271&partnerID=8YFLogxK

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M3 - Conference contribution

AN - SCOPUS:33845606271

SN - 1563478099

SN - 9781563478093

VL - 3

SP - 1675

EP - 1680

BT - Collection of Technical Papers - 12th AIAA/CEAS Aeroacoustics Conference

ER -