Analysing the structure of the acoustic analogy based-high frequency Green’s function in non-axi-symmetric sheared flows via a Ray tracing solver

Research output: Contribution to conferenceAbstract

Abstract

The chevron nozzle remains a popular approach aimed at reducing jet noise. It works by breaking up large turbulence structures and by increasing mixing, but it also effects propagation of sound. In this study, we investigate the effect of chevron-type mean flow in an acoustic analogy model where the wave propagation reduces to the solution of the Rayleigh equation and is calculated using a ray theory model for a jet represented by a transversely sheared mean flow. Since the generalised acoustic analogy (GAA) shows that the acoustic pressure is given by the convolution product of a rank-2 tensor propagator and the fluctuating Reynolds Stress, we determine the propagator (that is related to the vector adjoint Green's function of the linearised Euler operator) using the high frequency Ray theory developed by Goldstein (J. S. V., Vol. 80, p. 499, 1982) under an isotropic model of the fluctuating Reynolds stress. We calculate the Rayleigh equation Green’s function at high frequencies for a series of chevron mean flow patterns with multiple lobes. Our results reveal that the chevron jet introduces much more non-periodic spatial modulation of the Green’s function with a local minima in amplitude within the jet. We conclude by discussing how this explains the observed reduction in sound.
Original languageEnglish
Publication statusPublished - 26 Nov 2019
Event72nd Annual Meeting of the APS Division of Fluid Dynamics : Division of Fluid Dynamics - Washington State Convention Center, Seattle, United States
Duration: 23 Nov 201926 Nov 2019
https://www.apsdfd2019.org/

Conference

Conference72nd Annual Meeting of the APS Division of Fluid Dynamics
Abbreviated titleAPS-DFD
CountryUnited States
CitySeattle
Period23/11/1926/11/19
Internet address

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Ray tracing
Green's function
Probability density function
Acoustics
Acoustic waves
Convolution
Flow patterns
Wave propagation
Tensors
Mathematical operators
Nozzles
Turbulence
Modulation

Keywords

  • jet noise
  • acoustic analogies
  • applied mathematics

Cite this

Stirrat, S., Afsar, M., & Sescu, A. (2019). Analysing the structure of the acoustic analogy based-high frequency Green’s function in non-axi-symmetric sheared flows via a Ray tracing solver. Abstract from 72nd Annual Meeting of the APS Division of Fluid Dynamics , Seattle, United States.
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title = "Analysing the structure of the acoustic analogy based-high frequency Green’s function in non-axi-symmetric sheared flows via a Ray tracing solver",
abstract = "The chevron nozzle remains a popular approach aimed at reducing jet noise. It works by breaking up large turbulence structures and by increasing mixing, but it also effects propagation of sound. In this study, we investigate the effect of chevron-type mean flow in an acoustic analogy model where the wave propagation reduces to the solution of the Rayleigh equation and is calculated using a ray theory model for a jet represented by a transversely sheared mean flow. Since the generalised acoustic analogy (GAA) shows that the acoustic pressure is given by the convolution product of a rank-2 tensor propagator and the fluctuating Reynolds Stress, we determine the propagator (that is related to the vector adjoint Green's function of the linearised Euler operator) using the high frequency Ray theory developed by Goldstein (J. S. V., Vol. 80, p. 499, 1982) under an isotropic model of the fluctuating Reynolds stress. We calculate the Rayleigh equation Green’s function at high frequencies for a series of chevron mean flow patterns with multiple lobes. Our results reveal that the chevron jet introduces much more non-periodic spatial modulation of the Green’s function with a local minima in amplitude within the jet. We conclude by discussing how this explains the observed reduction in sound.",
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author = "Sarah Stirrat and Mohammed Afsar and Adrian Sescu",
year = "2019",
month = "11",
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language = "English",
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Stirrat, S, Afsar, M & Sescu, A 2019, 'Analysing the structure of the acoustic analogy based-high frequency Green’s function in non-axi-symmetric sheared flows via a Ray tracing solver' 72nd Annual Meeting of the APS Division of Fluid Dynamics , Seattle, United States, 23/11/19 - 26/11/19, .

Analysing the structure of the acoustic analogy based-high frequency Green’s function in non-axi-symmetric sheared flows via a Ray tracing solver. / Stirrat, Sarah; Afsar, Mohammed; Sescu, Adrian.

2019. Abstract from 72nd Annual Meeting of the APS Division of Fluid Dynamics , Seattle, United States.

Research output: Contribution to conferenceAbstract

TY - CONF

T1 - Analysing the structure of the acoustic analogy based-high frequency Green’s function in non-axi-symmetric sheared flows via a Ray tracing solver

AU - Stirrat, Sarah

AU - Afsar, Mohammed

AU - Sescu, Adrian

PY - 2019/11/26

Y1 - 2019/11/26

N2 - The chevron nozzle remains a popular approach aimed at reducing jet noise. It works by breaking up large turbulence structures and by increasing mixing, but it also effects propagation of sound. In this study, we investigate the effect of chevron-type mean flow in an acoustic analogy model where the wave propagation reduces to the solution of the Rayleigh equation and is calculated using a ray theory model for a jet represented by a transversely sheared mean flow. Since the generalised acoustic analogy (GAA) shows that the acoustic pressure is given by the convolution product of a rank-2 tensor propagator and the fluctuating Reynolds Stress, we determine the propagator (that is related to the vector adjoint Green's function of the linearised Euler operator) using the high frequency Ray theory developed by Goldstein (J. S. V., Vol. 80, p. 499, 1982) under an isotropic model of the fluctuating Reynolds stress. We calculate the Rayleigh equation Green’s function at high frequencies for a series of chevron mean flow patterns with multiple lobes. Our results reveal that the chevron jet introduces much more non-periodic spatial modulation of the Green’s function with a local minima in amplitude within the jet. We conclude by discussing how this explains the observed reduction in sound.

AB - The chevron nozzle remains a popular approach aimed at reducing jet noise. It works by breaking up large turbulence structures and by increasing mixing, but it also effects propagation of sound. In this study, we investigate the effect of chevron-type mean flow in an acoustic analogy model where the wave propagation reduces to the solution of the Rayleigh equation and is calculated using a ray theory model for a jet represented by a transversely sheared mean flow. Since the generalised acoustic analogy (GAA) shows that the acoustic pressure is given by the convolution product of a rank-2 tensor propagator and the fluctuating Reynolds Stress, we determine the propagator (that is related to the vector adjoint Green's function of the linearised Euler operator) using the high frequency Ray theory developed by Goldstein (J. S. V., Vol. 80, p. 499, 1982) under an isotropic model of the fluctuating Reynolds stress. We calculate the Rayleigh equation Green’s function at high frequencies for a series of chevron mean flow patterns with multiple lobes. Our results reveal that the chevron jet introduces much more non-periodic spatial modulation of the Green’s function with a local minima in amplitude within the jet. We conclude by discussing how this explains the observed reduction in sound.

KW - jet noise

KW - acoustic analogies

KW - applied mathematics

UR - https://www.apsdfd2019.org/

UR - http://meetings.aps.org/Meeting/DFD19/Session/Q06.6

M3 - Abstract

ER -

Stirrat S, Afsar M, Sescu A. Analysing the structure of the acoustic analogy based-high frequency Green’s function in non-axi-symmetric sheared flows via a Ray tracing solver. 2019. Abstract from 72nd Annual Meeting of the APS Division of Fluid Dynamics , Seattle, United States.