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

M. Z. Afsar, A. Sescu, S. J. Leib

Research output: Contribution to journalSpecial issue

Abstract

This paper uses asymptotic analysis within the generalized acoustic analogy formulation (Goldstein. JFM 488, pp. 315-333, 2003) to develop a noise prediction model for the peak sound of axisymmetric round jets at subsonic acoustic Mach numbers (M a).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 (PDE). We then address the predictive capability of the solution to this PDE 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.
LanguageEnglish
Number of pages19
JournalPhilosophical Transactions A: Mathematical, Physical and Engineering Sciences
Publication statusAccepted/In press - 11 Jul 2019

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air jets
Asymptotic analysis
Asymptotic Analysis
Analogy
Acoustics
Green's function
Acoustic waves
noise prediction
Strouhal number
Green's functions
acoustics
Prediction
Air
predictions
Modeling
partial differential equations
Partial differential equations
Propagator
Turbulence
turbulence

Keywords

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

Cite this

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title = "Modeling and prediction of the peak radiated sound in sub-sonic axisymmetric air jets using acoustic analogy based asymptotic analysis",
abstract = "This paper uses asymptotic analysis within the generalized acoustic analogy formulation (Goldstein. JFM 488, pp. 315-333, 2003) to develop a noise prediction model for the peak sound of axisymmetric round jets at subsonic acoustic Mach numbers (M a).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 (PDE). We then address the predictive capability of the solution to this PDE 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.",
keywords = "acoustic analogies, asymptotic methods, computational fluid dynamics, jet noise modeling",
author = "Afsar, {M. Z.} and A. Sescu and Leib, {S. J.}",
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T1 - Modeling and prediction of the peak radiated sound in sub-sonic axisymmetric air jets using acoustic analogy based asymptotic analysis

AU - Afsar, M. Z.

AU - Sescu, A.

AU - Leib, S. J.

PY - 2019/7/11

Y1 - 2019/7/11

N2 - This paper uses asymptotic analysis within the generalized acoustic analogy formulation (Goldstein. JFM 488, pp. 315-333, 2003) to develop a noise prediction model for the peak sound of axisymmetric round jets at subsonic acoustic Mach numbers (M a).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 (PDE). We then address the predictive capability of the solution to this PDE 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.

AB - This paper uses asymptotic analysis within the generalized acoustic analogy formulation (Goldstein. JFM 488, pp. 315-333, 2003) to develop a noise prediction model for the peak sound of axisymmetric round jets at subsonic acoustic Mach numbers (M a).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 (PDE). We then address the predictive capability of the solution to this PDE 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.

KW - acoustic analogies

KW - asymptotic methods

KW - computational fluid dynamics

KW - jet noise modeling

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JO - Proceedings A: Mathematical, Physical and Engineering Sciences

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JF - Proceedings A: Mathematical, Physical and Engineering Sciences

SN - 1364-5021

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