### Abstract

Language | English |
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Publication status | Published - 19 Nov 2017 |

Event | The 70th Annual Meeting of the American Physical Society Division of Fluid Dynamics - Colorado Convention Center, Denver, United States Duration: 19 Nov 2017 → 21 Nov 2017 http://www.apsdfd2017.org/ |

### Conference

Conference | The 70th Annual Meeting of the American Physical Society Division of Fluid Dynamics |
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Abbreviated title | APS DFD17 |

Country | United States |

City | Denver |

Period | 19/11/17 → 21/11/17 |

Internet address |

### Fingerprint

### Keywords

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

### Cite this

*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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**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.

Research output: Contribution to conference › Abstract

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 -