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A FREQUENCY-DOMAIN SOLVER FOR THE NON-LINEAR PROPAGATION AND RADIATION OF FAN NOISE
Cyrille Breard
Analytical Methods, Inc. 2133 152nd Avenue NE Redmond WA 98052, USA cyrille@amiwest. com
Abstract A numerical procedure for the numerical simulation of a fbw – impedance tube is presented and validated by the author [16]. This method is extended in the present paper to numerical simulation of noise radiation from lined ducts and to non-linear propgation of plane-wave in 2D and axisymetric lined duct.
275
K. C. Hall et al. (eds.),
Unsteady Aerodynamics, Aeroacoustics and Aeroelasticity of Turbomachines, 275-289. © 2006 Springer. Printed in the Netherlands.
Nomenclature
|
Po , Uq , V0 , Wo, p0 |
Mean fbw quantites: pressure, velocities, density |
|
p, u, V, w |
Complex pressure, velocities perturbation quantities |
|
x, y/r |
Axial, transversal/radial coordinates |
|
X, V |
Computational coordinates |
|
m |
Circumferential coordinates |
|
n |
Radial mode number |
|
SPL |
Sound pressure level (dB) = 20logl0(j£—), pref = 1СГ5 |
|
S |
Switch = 0 for 2D and =1 for axisymetric |
|
i |
12 = -1 |
|
Co |
Local speed of sound = ^ |
|
u |
Pulsation = 2nf |
|
k |
Wave number = j- |
|
kr |
Radial wave number |
|
kx |
Axial wave number |
|
P(m, n ) |
Amplitude of the (m, n) mode |
|
J Y |
mth order Bessel functions of the first and second kind |
|
R |
Radius of the nacelle |
|
Rc |
Radius of the wall curvature |
|
MX |
Axial mean Mach number = — |
|
Vto |
Tangent component of the mean velocity at the wall |
|
vt |
Tangent component of the perturbation velocity at the wall |
|
PPW |
Points per wavelength |
|
Z |
Impedance of the liner |
|
Vn |
Normal component of the perturbation velocity at the wal |
1. Introduction
The requirement of accurate and fast prediction of propagation and radiation of fan noise is now part of the design of aeroengine and nacelle. Acoustic lining material is the most effective way of suppressing indesirable noise radiated from the nacelle. Computational aero-acoustics (CAA) have already demonstrated the great potential in modelling accurately complex aero-acoustics problems. However, CAA will serve as a tool for design purpose in the industrial environment only if the computational cost is reduced dramatically. Very interesting research work from Stanescu & al [6] has been presented recently, showing scattering of fan noise radiation due to fuselage, wing and pylon presences in the time domain. However, Ozyoruk & al. [5], Astley & al. [8] recently presented a frequency-domain solver for propagation, scattering and radiation, and showed that such methods become attractive for industrial application due to their shorter computational time compared to the time domain method. Aircraft, nacelle and aero-engine manufacturers have been using liners to attenuate forward-arc fan noise for many years. And keeping in mind that the impedance (property of liner) is defined in the frequency domain, it is very suitable and accurate to consider radiation problem with acoustic liner in the
frequency domain. Moreover, a frequency domain solver is in general faster to compute than time-domain solver as acceleration technique can be used. Furthermore, solution of the prediction can be immediately used for more analysis without post-processing of the prediction, a feature in industry environment makes frequency-domain solver more appropriate. A numerical procedure for the numerical simulation of a ft>w – impedance tube is presented and validated by the author [16]. This method is extended in the present paper to numerical simulation of noise radiation from lined ducts and to non-linear propgation of plane-wave in 1D and axisymetric lined duct.
