A finite element formulation of the eigenvalue problem in lined ducts with flow

Astley, R.J.; Eversman, Walter

doi:10.1016/0022-460x(79)90528-5

Cited by 44 publications

(50 citation statements)

References 6 publications

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“…Thus, the governing equations are reduced to "1^ + V"(pu) = 0 (2)(3) and P ("^ + u-Vu) = -vp. (2)(3)(4) To obtain a single equation for pressure from the two existing equations, which also involve the velocity, the divergence of to. (2)(3)(4) is found .…”

Section: Internal Propagationmentioning

confidence: 99%

“…(2)(3)(4) To obtain a single equation for pressure from the two existing equations, which also involve the velocity, the divergence of to. (2)(3)(4) is found . (2)(3)(4)(5)(6) This equation governs situations in which flow is present but the effects of viscosity, body forces, and volume sources may be neglected.…”

Section: Internal Propagationmentioning

confidence: 99%

“…(2)(3)(4) is found . (2)(3)(4)(5)(6) This equation governs situations in which flow is present but the effects of viscosity, body forces, and volume sources may be neglected.…”

Section: Internal Propagationmentioning

confidence: 99%

“…Furthermore, viscous terms are typically small enough to be neglected when considering propagation in the absence of mean flow. Thus, the governing equations are reduced to "1^ + V"(pu) = 0 (2)(3) and P ("^ + u-Vu) = -vp. (2)(3)(4) To obtain a single equation for pressure from the two existing equations, which also involve the velocity, the divergence of to.…”

Section: Internal Propagationmentioning

confidence: 99%

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Acoustic Finite Element Analysis of Duct Boundaries

Bernhard

1982

The Journal of the Acoustical Society of America

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Section: Internal Propagationmentioning

confidence: 99%

Section: Internal Propagationmentioning

confidence: 99%

“…(2)(3)(4) is found . (2)(3)(4)(5)(6) This equation governs situations in which flow is present but the effects of viscosity, body forces, and volume sources may be neglected.…”

Section: Internal Propagationmentioning

confidence: 99%

Section: Internal Propagationmentioning

confidence: 99%

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Acoustic Finite Element Analysis of Duct Boundaries

Bernhard

1982

The Journal of the Acoustical Society of America

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“…This approach has been used elsewhere in the past for cylindrical ducts, for example by Ko 4 , which has led to the commercially available software package from ESDU 5 . The evaluation of the fully scattered acoustic field is not a trivial problem and is commonly the domain of finite element style calculations [6][7][8] . Needless to say multimode broadband calculations of this type require a large amount of computer processing time and as a result do not lend themselves to rapid, convenient optimization routines.…”

Section: Introductionmentioning

confidence: 99%

Optimization of Annular and Cylindrical Liners for Mixed Exhaust Aeroengines

Law

2007

13th AIAA/CEAS Aeroacoustics Conference (28th AIAA Aeroacoustics Conference)

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The increase in bypass ratios for modern day turbofan engines has led to fan rearward broadband noise emerging as one of the principal aircraft noise sources. The most widespread method for mitigating this noise source is the installation of acoustic liners in the ducting downstream of the fan. Mixed exhaust designs have the potential to be quieter than a three quarter cowl aeroengine due to the additional surface available for liner application. As a result, the Silent Aircraft concept design contains an embedded distributed propulsion system to exploit this opportunity. This paper outlines a suitable method for optimizing the annular and cylindrical liners that make up the exhaust system. To gain maximum benefit, liners should be designed to absorb the modal disturbances that are the most significant for an observer on the ground. The optimization uses an advanced noise footprint cost function to achieve this. Consequently, the liners and the length of the installation have been chosen to meet the aggressive noise target set for the aircraft. In addition, we explore the effect that modal scattering between axial liner junctions can have on the acoustic performance of the system. We find that energy interchange between radial modes will often have a detrimental effect on the overall attenuation, although this can be addressed by selecting the order of the liners in a more considered way. The assumption that scattering between liners can be neglected during optimization to allow design of the individual components therefore appears to be valid in this case. However, subsequent attention has to be directed to the order in which they are placed. Current and next generation mixed exhaust aeroengines will be restricted to smaller liner segment lengths than the Silent Aircraft. This analysis suggests that scattering and hence liner order is likely to more important for these designs.

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Finite element modelling of sheared flow effects on the radiation characteristics of acoustic sources in a circular duct

Steck¹,

Eversman²

1993

Numerical Methods in Fluids

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The recent interest in propeller noise generation, stimulated by development of new propeller types for commerical propjets, has generated a need for the ability of measure the noise characteristics of propellers. However, wind tunnel noise measurements are affected by reflections from the wind tunnel walls. Computer codes predicting the free‐field noise of a propeller and its noise field in a circular wind tunnel allow validating the use of wind tunnel measurements to predict free‐field noise characteristics. A wind tunnel contains flow which is uniform in the duct axial direction, but can vary in the radial direction. It can be shown that a third‐order differential equation governs the acoustic pressure field for such a duct containing radially sheared subsonic flow. This third‐order problem is then posed as a coupled pair of equations which are second‐order in terms of acoustic density and first‐order in terms of an artificial variable which represents the effects of the flow being sheared. It is shown that this form of the problem allows a natural extension of the existing numerical solution techniques for non‐sheared flow. The sheared flow problem is presented, and a finite element method is developed to yield a solution for propeller‐type acoustic forces. The finite element code and method are refined with numerical experiments, and results are presented for a specific propeller and duct geometry. Good agreement is shown between this method and an alternate approach to the sheared flow problem using a piecewise constant representation of the velocity in the boundary layer. This validates both the numerical methods.

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A finite element formulation of the eigenvalue problem in lined ducts with flow

Cited by 44 publications

References 6 publications

Acoustic Finite Element Analysis of Duct Boundaries

Acoustic Finite Element Analysis of Duct Boundaries

Optimization of Annular and Cylindrical Liners for Mixed Exhaust Aeroengines

Finite element modelling of sheared flow effects on the radiation characteristics of acoustic sources in a circular duct

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