### Abstract

This paper uses asymptotic analysis within the generalized acoustic analogy formulation (Goldstein 2003 JFM488, 315-333. (doi:10.1017/S0022112003004890)) to develop a noise prediction model for the peak sound of axisymmetric round jets at subsonic acoustic Mach numbers (Ma). The analogy shows that the exact formula for the acoustic pressure is given by a convolution product of a propagator tensor (determined by the vector Green's function of the adjoint linearized Euler equations for a given jet mean flow) and a generalized source term representing the jet turbulence field. Using a low-frequency/small spread rate asymptotic expansion of the propagator, mean flow non-parallelism enters the lowest order Green's function solution via the streamwise component of the mean flow advection vector in a hyperbolic partial differential equation. We then address the predictive capability of the solution to this partial differential equation when used in the analogy through first-of-its-kind numerical calculations when an experimentally verified model of the turbulence source structure is used together with Reynolds-averaged Navier-Stokes solutions for the jet mean flow. Our noise predictions show a reasonable level of accuracy in the peak noise direction at Ma = 0.9, for Strouhal numbers up to about 0.6, and at Ma = 0.5 using modified source coefficients. Possible reasons for this are discussed. Moreover, the prediction range can be extended beyond unity Strouhal number by using an approximate composite asymptotic formula for the vector Green's function that reduces to the locally parallel flow limit at high frequencies. This article is part of the theme issue 'Frontiers of aeroacoustics research: theory, computation and experiment'.

Original language | English |
---|---|

Article number | 20190073 |

Number of pages | 19 |

Journal | Philosophical Transactions A: Mathematical, Physical and Engineering Sciences |

Volume | 377 |

Issue number | 2159 |

Early online date | 14 Oct 2019 |

DOIs | |

Publication status | Published - 1 Dec 2019 |

### Fingerprint

### Keywords

- acoustic analogies
- asymptotic methods
- computational fluid dynamics
- jet noise modeling

### Cite this

*Philosophical Transactions A: Mathematical, Physical and Engineering Sciences*,

*377*(2159), [20190073]. https://doi.org/10.1098/rsta.2019.0073

}

*Philosophical Transactions A: Mathematical, Physical and Engineering Sciences*, vol. 377, no. 2159, 20190073. https://doi.org/10.1098/rsta.2019.0073

**Modelling and prediction of the peak radiated sound in sub-sonic axisymmetric air jets using acoustic analogy based asymptotic analysis.** / Afsar, Mohammed Z.; Sescu, Adrian; Leib, Stewart J.

Research output: Contribution to journal › Special issue

TY - JOUR

T1 - Modelling and prediction of the peak radiated sound in sub-sonic axisymmetric air jets using acoustic analogy based asymptotic analysis

AU - Afsar, Mohammed Z.

AU - Sescu, Adrian

AU - Leib, Stewart J.

PY - 2019/12/1

Y1 - 2019/12/1

N2 - This paper uses asymptotic analysis within the generalized acoustic analogy formulation (Goldstein 2003 JFM488, 315-333. (doi:10.1017/S0022112003004890)) to develop a noise prediction model for the peak sound of axisymmetric round jets at subsonic acoustic Mach numbers (Ma). The analogy shows that the exact formula for the acoustic pressure is given by a convolution product of a propagator tensor (determined by the vector Green's function of the adjoint linearized Euler equations for a given jet mean flow) and a generalized source term representing the jet turbulence field. Using a low-frequency/small spread rate asymptotic expansion of the propagator, mean flow non-parallelism enters the lowest order Green's function solution via the streamwise component of the mean flow advection vector in a hyperbolic partial differential equation. We then address the predictive capability of the solution to this partial differential equation when used in the analogy through first-of-its-kind numerical calculations when an experimentally verified model of the turbulence source structure is used together with Reynolds-averaged Navier-Stokes solutions for the jet mean flow. Our noise predictions show a reasonable level of accuracy in the peak noise direction at Ma = 0.9, for Strouhal numbers up to about 0.6, and at Ma = 0.5 using modified source coefficients. Possible reasons for this are discussed. Moreover, the prediction range can be extended beyond unity Strouhal number by using an approximate composite asymptotic formula for the vector Green's function that reduces to the locally parallel flow limit at high frequencies. This article is part of the theme issue 'Frontiers of aeroacoustics research: theory, computation and experiment'.

AB - This paper uses asymptotic analysis within the generalized acoustic analogy formulation (Goldstein 2003 JFM488, 315-333. (doi:10.1017/S0022112003004890)) to develop a noise prediction model for the peak sound of axisymmetric round jets at subsonic acoustic Mach numbers (Ma). The analogy shows that the exact formula for the acoustic pressure is given by a convolution product of a propagator tensor (determined by the vector Green's function of the adjoint linearized Euler equations for a given jet mean flow) and a generalized source term representing the jet turbulence field. Using a low-frequency/small spread rate asymptotic expansion of the propagator, mean flow non-parallelism enters the lowest order Green's function solution via the streamwise component of the mean flow advection vector in a hyperbolic partial differential equation. We then address the predictive capability of the solution to this partial differential equation when used in the analogy through first-of-its-kind numerical calculations when an experimentally verified model of the turbulence source structure is used together with Reynolds-averaged Navier-Stokes solutions for the jet mean flow. Our noise predictions show a reasonable level of accuracy in the peak noise direction at Ma = 0.9, for Strouhal numbers up to about 0.6, and at Ma = 0.5 using modified source coefficients. Possible reasons for this are discussed. Moreover, the prediction range can be extended beyond unity Strouhal number by using an approximate composite asymptotic formula for the vector Green's function that reduces to the locally parallel flow limit at high frequencies. This article is part of the theme issue 'Frontiers of aeroacoustics research: theory, computation and experiment'.

KW - acoustic analogies

KW - asymptotic methods

KW - computational fluid dynamics

KW - jet noise modeling

U2 - 10.1098/rsta.2019.0073

DO - 10.1098/rsta.2019.0073

M3 - Special issue

VL - 377

JO - Proceedings A: Mathematical, Physical and Engineering Sciences

JF - Proceedings A: Mathematical, Physical and Engineering Sciences

SN - 1364-5021

IS - 2159

M1 - 20190073

ER -