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Duct Acoustics Research at ISVR using Analytical Methods

The use of analytical and semi-analytical methods in duct acoustics research can provide fast and efficient simulation techniques, which also often give insight into the physics of the sound propagation and radiation.

Describing the sound field in terms of "spinning" modes is an approach which forms the basis for a large quantity of duct acoustics research using analytical methods. This is the common link between the examples of duct acoustics research listed below.

Describing the sound field in terms of "spinning" modes is a well-known approach commonly utilized in duct acoustics.

In the context of turbofan duct systems, typical assumptions related to the use of a modal description of the sound field include the following key issues:

1. What is the geometry of the duct?

Turbofan intake and bypass ducts may be approximated as circular, axisymmetric ducts.  The bypass may be modelled by a circular-annular duct.

2. Do the duct walls have acoustic lining?

Passive noise control using acoustic lining is one of the principal noise control methods used in turbofan duct systems. These type of linings are locally-reacting, which do not allow any lateral sound propagation through the lining.

Duct wall boundary conditions are formulated in terms of the specific acoustic impedance of the acoustic lining. In the presence of flow, the Ingard-Myers boundary condition is used for a straight duct, which prescribes continuity of particle displacement at the wall.

3. What is the mean flow?

The particle velocity, pressure, density and temperature can be expressed as the sum of a steady, mean component plus a small, unsteady perturbation. The acoustic part is the small perturbation.

The effects of viscosity and heat-conduction can typically be neglected, so the mean flow is assumed isentropic and inviscid.

Since the duct geometry is axisymmetric, also the mean flow is assumed to be axisymmetric. The simplest approximation commonly used is to assume a "plug" or uniform mean flow. Alternatively, a shear mean flow may be assumed where the velocity varies with the radial distance from the centre of the duct.

 

Utilizing assumptions 1-3 in the modelling, "spinning" mode solutions can be formulated. Expressing the sound field in terms of modes is also convenient to describe the sources of noise. There are two main reasons for this:   

Tones can, in general, be modelled by taking a prescribed azimuthal mode order m.  For example, rotor-stator interaction tones have m=iB+jV, where B is the number of fan blades, V is the number of stator vanes, and i,j are integers.

Broadband noise can, in general, be modelled by taking a multi-mode source, with an equal power per mode distribution over all the propagating modes. 

Examples of research into sound propagation and radiation in turbofan intake and bypass ducts conducted recently at ISVR include:

Axially-segmented intake liner

Liner splices

Sound transmission in ducted shear flows

Radiation from intake ducts

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