The modelling and and the analysis of sound propagation in the flow ducts of aero engines is essential for the development of methods of noise reduction. Aero acoustic source mechanisms can be identified by applying high resolution experimental methods in combination with sound source models. The geometries of the engine stages and other installations in the flow duct can be optimized in order to reduce the transmission of sound without reducing the aerodynamic performance. The same can be done for the design of the duct walls which can also feature a sound absorbing lining.

Analysis of the sound field

The components of an aero engine radiate a highly complex sound field into the flow ducts. Above a characteristic frequency, the air inside a flow duct oscillates in vibration patterns which are called modes. These modes can be classified as azimuthal or radial orders according to the sound pressure nodes in the circumferential and the radial direction of the duct. The shape of the modes varies with the exited frequency, the shape of the duct, and the superimposed flow field. The sound pressure field is a superposition of different modes that fluctuate in time and space. The properties of the sound sources determine the coherence of the sound field. An example of a coherent sound source is the interaction of the wake of a rotor with the stator on its downstream side, which generates a discrete tone. If, on the other hand, the turbulent inflow interacts with the leading edge of a rotor, incoherent broadband noise is generated. The department of Engine Acoustics develops various methods for the modal analysis of sound fields.

Numerical modelling

Analytical models for the sound propagation in flow ducts are only available for simple geometries and elementary flow profiles. By an asymptotic approximation, these models can be extended to ducts with small variations of their cross section. Complex flow profiles and progressive geometries require a numerical analysis. It is based on the linearized Euler equations, which can be solved in the time or frequency domain. The spatial gradients are discretised by standard numerical tools. This leads to linear equation systems of differential equations with a multitude of unknown variables. The solution of such systems is an approximation of the linearized Euler equation at discrete grid points. The number of these points can, depending on the problem, raise up to several million. An appropriate spatial discretization is crucial for the quality of the approximate solution. If the discretization points are chosen adequately, the sound field can be solved for elaborate geometries and complex flow profiles.

Numerical simulation of the sound propagation from a bell mouth intake into the far field. The sound source is given by a duct mode.

Influence of the inhomogenous flow field on the mode shape funtions

A duct mode with an azimuthal order m and a radial order n can be described by the axial wave number and the radial distribution of fluctuation quantities. When the axial flow profile can be approximated by a plug flow, with the axial Mach number constant along the radial coordinate, the fluctuating quantities can be modelled by a superposition of Bessel and Neumann functions. These functions have the advantage of being analytical. The axial wave number is given by the dispersion relation. If the flow profile has a gradient in the radial direction, a generalised Eigenvalue problem has to be applied in order to describe the radial distribution of fluctuation quantities. These Eigenfunctions display significant differences when sound waves of the same mode order (m,n) are compared that propagate in the up or the downstream direction. The difference to the analytical Eigenfunctions is depends largely on the deviation of the superimposed flow from the plug flow profile, but also from the frequency and the mode order (m,n).

Influence of in-duct installations and varying duct cross sections

Sound propagates through the bypass flow duct of an engine before it radiates into the far field. Struts built into the bypass duct and a varying geometry are common in current engine designs. They significantly change the propagation characteristics of the sound waves. Each obstacle in the duct reflects a part of the propagating sound wave. The transmitted part is scattered into characteristic modes. These mechanisms have to be understood properly in order to give a precise prediction of the perceived sound power level in the far field. A combination of different methods is used for this prediction. The first approach is to apply an analytic model. This gives insight into the complex dependencies of the effects involved. The results from the analytic models are verified by experiments in specialised test rigs, for example the MoSy test rig. Additionally, or as an alternative, numerical calculations can be performed (URANS, CAA). They feature a higher spatial resolution of the physical effects.

Sound absorbing wall panels, liners, influence the sound propagation in ducts. Liners are characterised by their impedance. This complex quantity describes the ratio of the sound pressure to the sound particle velocity component perpendicular to the duct wall. Further information on sound attenuation and liners can be found in sound absorption/liner. The desired effect of the attenuation of sound pressure amplitudes can be accompanied by secondary effects such as reflection or scattering of sound field components. This can result in the excitation of higher acoustic mode orders.

Numerical simulation of the transmission, reflection and scattering of a duct mode passing a vane stage