On the existence of an overlap region between the Green’s function for a locally parallel axi-symmetric jet and the leading order non-parallel flow solution

Vasilis Sassanis, Mohammed Afsar, Adrian Sescu, Sanjiva Lele

Research output: Contribution to conferenceAbstract

Abstract

We consider determination of the propagator within the generalized acoustic analogy for prediction of supersonic jet noise. The propagator is a tensor functional of the adjoint vector Green’s function that requires solution of the linearized Euler equations for a given mean flow. The exact form of these equations can be obtained for a spreading jet. However since high Reynolds number jets have small spread rates, ϵ < < O(1), this parameter can be exploited to formulate an asymptotic model that encompasses mean flow spatial evolution at leading order. Such a model was used by Afsar et al. (AIAA-2017-3030 for prediction of supersonic jet noise. We show the existence of an overlap between this solution (valid at low frequencies) and one based on a locally parallel (i.e. non-spreading) mean flow, valid at O(1) frequencies. It is clear that there must exist an overlap between these solutions, since the former non-parallel solution was determined at the distinguished limit where the scaled frequency Ω=ω/ϵ=O(1) was held fixed. Hence the inner equation shows that as Ω→∞, non-parallelism will be confined to a thin streamwise region of size O(Ω−1) and will, therefore, be subdominant at leading order when ΩY=Y¯=O(1).

Conference

ConferenceThe 70th Annual Meeting of the American Physical Society Division of Fluid Dynamics
Abbreviated titleAPS DFD17
CountryUnited States
CityDenver
Period19/11/1721/11/17
Internet address

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Green's function
Euler equations
Acoustic noise
Tensors
Reynolds number
Acoustics

Keywords

  • supersonic jet noise
  • Green’s function
  • acoustic analogy

Cite this

Sassanis, V., Afsar, M., Sescu, A., & Lele, S. (2017). On the existence of an overlap region between the Green’s function for a locally parallel axi-symmetric jet and the leading order non-parallel flow solution. Abstract from The 70th Annual Meeting of the American Physical Society Division of Fluid Dynamics, Denver, United States.
Sassanis, Vasilis ; Afsar, Mohammed ; Sescu, Adrian ; Lele, Sanjiva. / On the existence of an overlap region between the Green’s function for a locally parallel axi-symmetric jet and the leading order non-parallel flow solution. Abstract from The 70th Annual Meeting of the American Physical Society Division of Fluid Dynamics, Denver, United States.
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abstract = "We consider determination of the propagator within the generalized acoustic analogy for prediction of supersonic jet noise. The propagator is a tensor functional of the adjoint vector Green’s function that requires solution of the linearized Euler equations for a given mean flow. The exact form of these equations can be obtained for a spreading jet. However since high Reynolds number jets have small spread rates, ϵ < < O(1), this parameter can be exploited to formulate an asymptotic model that encompasses mean flow spatial evolution at leading order. Such a model was used by Afsar et al. (AIAA-2017-3030 for prediction of supersonic jet noise. We show the existence of an overlap between this solution (valid at low frequencies) and one based on a locally parallel (i.e. non-spreading) mean flow, valid at O(1) frequencies. It is clear that there must exist an overlap between these solutions, since the former non-parallel solution was determined at the distinguished limit where the scaled frequency Ω=ω/ϵ=O(1) was held fixed. Hence the inner equation shows that as Ω→∞, non-parallelism will be confined to a thin streamwise region of size O(Ω−1) and will, therefore, be subdominant at leading order when ΩY=Y¯=O(1).",
keywords = "supersonic jet noise, Green’s function, acoustic analogy",
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Sassanis, V, Afsar, M, Sescu, A & Lele, S 2017, 'On the existence of an overlap region between the Green’s function for a locally parallel axi-symmetric jet and the leading order non-parallel flow solution' The 70th Annual Meeting of the American Physical Society Division of Fluid Dynamics, Denver, United States, 19/11/17 - 21/11/17, .

On the existence of an overlap region between the Green’s function for a locally parallel axi-symmetric jet and the leading order non-parallel flow solution. / Sassanis, Vasilis; Afsar, Mohammed; Sescu, Adrian; Lele, Sanjiva.

2017. Abstract from The 70th Annual Meeting of the American Physical Society Division of Fluid Dynamics, Denver, United States.

Research output: Contribution to conferenceAbstract

TY - CONF

T1 - On the existence of an overlap region between the Green’s function for a locally parallel axi-symmetric jet and the leading order non-parallel flow solution

AU - Sassanis, Vasilis

AU - Afsar, Mohammed

AU - Sescu, Adrian

AU - Lele, Sanjiva

PY - 2017/11/19

Y1 - 2017/11/19

N2 - We consider determination of the propagator within the generalized acoustic analogy for prediction of supersonic jet noise. The propagator is a tensor functional of the adjoint vector Green’s function that requires solution of the linearized Euler equations for a given mean flow. The exact form of these equations can be obtained for a spreading jet. However since high Reynolds number jets have small spread rates, ϵ < < O(1), this parameter can be exploited to formulate an asymptotic model that encompasses mean flow spatial evolution at leading order. Such a model was used by Afsar et al. (AIAA-2017-3030 for prediction of supersonic jet noise. We show the existence of an overlap between this solution (valid at low frequencies) and one based on a locally parallel (i.e. non-spreading) mean flow, valid at O(1) frequencies. It is clear that there must exist an overlap between these solutions, since the former non-parallel solution was determined at the distinguished limit where the scaled frequency Ω=ω/ϵ=O(1) was held fixed. Hence the inner equation shows that as Ω→∞, non-parallelism will be confined to a thin streamwise region of size O(Ω−1) and will, therefore, be subdominant at leading order when ΩY=Y¯=O(1).

AB - We consider determination of the propagator within the generalized acoustic analogy for prediction of supersonic jet noise. The propagator is a tensor functional of the adjoint vector Green’s function that requires solution of the linearized Euler equations for a given mean flow. The exact form of these equations can be obtained for a spreading jet. However since high Reynolds number jets have small spread rates, ϵ < < O(1), this parameter can be exploited to formulate an asymptotic model that encompasses mean flow spatial evolution at leading order. Such a model was used by Afsar et al. (AIAA-2017-3030 for prediction of supersonic jet noise. We show the existence of an overlap between this solution (valid at low frequencies) and one based on a locally parallel (i.e. non-spreading) mean flow, valid at O(1) frequencies. It is clear that there must exist an overlap between these solutions, since the former non-parallel solution was determined at the distinguished limit where the scaled frequency Ω=ω/ϵ=O(1) was held fixed. Hence the inner equation shows that as Ω→∞, non-parallelism will be confined to a thin streamwise region of size O(Ω−1) and will, therefore, be subdominant at leading order when ΩY=Y¯=O(1).

KW - supersonic jet noise

KW - Green’s function

KW - acoustic analogy

UR - http://www.apsdfd2017.org/

M3 - Abstract

ER -

Sassanis V, Afsar M, Sescu A, Lele S. On the existence of an overlap region between the Green’s function for a locally parallel axi-symmetric jet and the leading order non-parallel flow solution. 2017. Abstract from The 70th Annual Meeting of the American Physical Society Division of Fluid Dynamics, Denver, United States.