Turbofan Aft Noise Predictions Based on Lilley's Wave Model

2013

AIAA Journal

Nomenclature a, b = integers arg min = the argument of the minimum B = blade number C 0 = speed of sound, m∕s C M = a constant E = approximation error f = a test function g = approximation of f g min = arg min kĝk 1 J = Bessel function of the first kind k = wave number K = compressive sample number M = number of nonzero entries M j = Mach number m = circumferential mode N = dimension of a signal n = integer p = pressure, Pa r = radial axis u, v, w = velocity, m∕s V = vane number x = axial axis θ = circumferential angle, rad θ K = circumferential position of Kth microphone, rad ρ = density, kg∕m 3 ω = angular frequency, rad∕s Subscripts 0 = stationary value m = variables related to the mth mode Superscriptŝ = Fourier transform 0 = disturbance

Section: Fan-noise Formulationsmentioning

confidence: 99%

Compressive Sensing and Reconstruction in Measurements with an Aerospace Application

2013

AIAA Journal

“…The unstable components develop exponentially to finally corrupt the desired acoustic solutions. It was a common practice to avoid the numerical instabilities by solving the problem in the frequency domain [3,13,14]. To use the current time-domain code, the LEE model was "degraded" by removing several terms that are singular in a sheared background flow [7].…”

Section: = @Wmentioning

confidence: 99%

Efficient Computation of Spinning Modal Radiation Through an Engine Bypass Duct

Chen

et al. 2008

AIAA Journal

The aim of this work is to accurately and efficiently predict sound radiation out of a duct with flow. The sound propagation inside a generic engine bypass duct, refractions by the shear layer of the exhaust flow, and propagation in the near field are the main focus of the study. The prediction uses either a modified form of linearized Euler equations or an alternative model based on acoustic perturbation equations, which were extended to cylindrical coordinates. The two models were compared on a canonical case of sound propagation out of a semi-infinite duct with flow. Good agreements between the predictions were achieved. The more general case of a generic aircraft engine bypass duct with flow was then investigated with the technique of adaptive mesh refinement to increase the computational efficiency. The results show that both linearized Euler equations and acoustic perturbation equations models can predict the near-field sound propagation and far-field directivity. The acoustic perturbation equations model, however, is more adaptive for its suitability to an arbitrary background mean flow.

“…In addition, formulae describing spinning mode reflecting into a straight, cylindrical duct have been presented [1]. The problem of sound propagation and radiation from a cylindrical duct has also been investigated with a wide range of numerical methods, using finite elements [2,8], mode-matching strategy [9], based on linearised Euler equations (LEE) [10] and the variants of LEE [11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Duct spinning mode’s particle velocity imaging with in-duct circular microphone array

Wei

Bao

20th AIAA/CEAS Aeroacoustics Conference

2014

Nowadays, the measurements within a duct have to be conducted using in-duct microphone array, which is unable to provide information of complete acoustic solutions across the test section. In this work, an imaging method of acoustic spinning modes propagating within a circular duct simply with surface pressure information is introduced. The proposed method is developed in a theoretical way and is demonstrated by a numerical simulation case. The fundamental idea behind the testing method was originally developed in control theory for ordinary differential equations. Spinning mode propagation, however, is formulated in partial differential equations. A finite difference technique is used to reduce the associated partial differential equations to a classical form in control theory. The observer method can thereafter be applied straightforwardly. The algorithm is recursive and thus could be operated in real-time. The observer error of the method is analyzed then. A numerical simulation for a straight circular duct is conducted. The acoustic solutions on the test section can be reconstructed with a good agreement to analytical solutions. The results suggest the potential and applications of the proposed method.