Propagation of sound in ducts with shear flow

Savkar, S. D.

doi:10.1016/0022-460x(71)90695-x

Cited by 41 publications

(7 citation statements)

References 5 publications

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“…Equations (13)(14)(15) can not be combined to obtain a secondorder differential wave equation in the dependent variable. However, differentiating Eq.…”

Section: Rotational Mean Flow and Irrotational Acoustic Propagationmentioning

confidence: 98%

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Applications of Velocity Potential Function to Acoustic Duct Propagation Using Finite Elements

Baumeister

Majjigi

1980

AIAA Journal

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A finite element velocity potential program has been developed for NASA Lewis at the Georgia Institute of Technology to study acoustic wave propagation in complex geometries. For irrotational flows, relatively low sound frequencies, and plane wave input, the finite element solutions show significant effects of inlet curvature and flow gradients on the attenuation of a given acoustic liner in a realistic variable area turbofan inlet. In addition, as shown in the paper, the velocity potential approach can not be used to estimate the effects of rotational flow on acoustic propagation since the potential acoustic disturbances propagate at the speed of the media in sheared flow. Approaches are discussed that are being considered for extending the finite element solution to include the far field as well as the internal portion of the duct. A new matrix partitioning approach is presented that can be incorporated in previously developed programs to allow the finite element calculation to be marched into the far field. The partitioning approach provides a large reduction in computer storage and running times. C 2 ,C 3 = f H i K L M m P Po P°r t U u u°V V v°X y z Zeff Z f Nomenclature constant of integration, N/m 2 , Eq. (22) constants of integration, m/s, Eqs. (23) and (24) velocity of sound, m/s diameter at rotor position, m frequency, Hz height of duct, m = number of grid points in axial direction = length of duct, m = Mach number of axial mean flow, U/c 0 = spinning mode number = acoustic pressure,p(x,y,t)\ N/m 2 = entrance acoustic pressure,p 0 (0,y,t); N/m 2 = spatial acoustic pressure,/7°(x,^); N/m 2 = radial coordinate, m = time, s = axial mean flow velocity, U(x,y); m/s = acoustic axial velocity, u(x,y,t),m/s = spatial acoustic axial velocity, u° (x,y); m/s = transverse mean flow velcoity, V(x,y); m/s = acoustic transverse velocity, v(x,y t t); m/s = spatial acoustic transverse velocity, v° (x,y); m/s = axial coordinate, m = transverse coordinate, m = impedance, g/cm 2 s = effective impedance, g/cm 2 s = axial position -specific acoustic impedance rj = dimensionless frequency DQ//CQ or Hf/c 0 6= angular position, rad P 0 = density, g/m 3 $ = steady potential function, $(x,y);m 2 /s $ * = potential function, $ * (x,y, t); m 2 /s y = acoustic potential function,

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“…Equations (13)(14)(15) can not be combined to obtain a secondorder differential wave equation in the dependent variable. However, differentiating Eq.…”

Section: Rotational Mean Flow and Irrotational Acoustic Propagationmentioning

confidence: 98%

“…Presented as Paper 79-0680 at the AIAA 5th Aeroacoustics Conference, Seattle, Wash., March 12-14, 1979; submitted April 11, 1979; revision received Sept. 13,1979. This paper is declared a work of the U.S. Government and therefore is in the public domain.…”

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confidence: 99%

Applications of Velocity Potential Function to Acoustic Duct Propagation Using Finite Elements

Baumeister

Majjigi

1980

AIAA Journal

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“…19,20 The origin x ¼ 0 of the x-coordinate along the pipe is chosen at the pipe outlet. The positive x-direction is pipe outwards.…”

Section: Theorymentioning

confidence: 99%

Comments on the low frequency radiation impedance of a duct exhausting a hot gas

Hirschberg

Hoeijmakers

2014

The Journal of the Acoustical Society of America

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The influence of convection and temperature on the radiation impedance of an open duct termination exhausting a hot gas is commonly described by a complex theory. A simplified analytical expression is proposed for low frequencies. Both models assume a free jet with uniform velocity bounded by infinitely thin shear layers. The convective velocity that should be assumed when applying these models to a non-uniform outflow is uncertain. A simplified version of the so-called Vortex Sound Theory demonstrates that the convective velocity one should assume is lower than the jet centerline velocity.

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“…The mean flow is assumed to be uniform in the x direction and the choice of the simple profile was made in order to compare with the previous results and also because this profile compares with the l/7th power law profile. 5 The variables used for nondimensionalizing the physical quantities are the ambient speed of sound c, the half-duct width L, ambient temperature T^, and the ambient fluid density p^. The pressure is made dimensionless using p^c 2 .…”

Section: The Mathematical Formulationmentioning

confidence: 99%

Nonisentropic propagation of sound in uniform ducts using Euler equations

1986

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The problem of sound propagation in uniform ducts is examined using the Euler equations. First, a numerical spatial marching technique is examined for the case of no mean flow. The technique uses an initial value formulation. It is found that the scheme is stability limited, in agreement with previous results obtained using the Helmholtz equation. Also duct mode analysis is performed and the following is observed. When the mean flow in the duct is treated as isentropic, the solutions agree with existing solutions. However, this implies no pressure gradient for the mean flow in the streamwise direction. If a mean pressure gradient is imposed, it is found that the lowest mode attenuates as it propagates against the flow direction. It is also found that the same mode grows due to an instability, if it propagates downstream. This instability is related to combustion instability.

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Propagation of sound in ducts with shear flow

Cited by 41 publications

References 5 publications

Applications of Velocity Potential Function to Acoustic Duct Propagation Using Finite Elements

Applications of Velocity Potential Function to Acoustic Duct Propagation Using Finite Elements

Comments on the low frequency radiation impedance of a duct exhausting a hot gas

Nonisentropic propagation of sound in uniform ducts using Euler equations

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