A well-established approach to determine the amplitudes of acoustic modes inside a duct is the measurement (or the calculation) of the sound pressure amplitudes on a regular grid inside the duct. For a decomposition of the pressure field into the azimuthal modes, a circumferential grid has to be used. The amplitudes of the azimuthal modes depend on both the axial and the radial position inside the duct. Therefore, it is not possible to estimate quantitative parameters such as the sound power level from data for one position only. However, a full decomposition of the sound field into radial and azimuthal mode orders can be performed by fitting the data measured at multiple axial and radial positions to a model for the sound propagation. In an experimental setup, the microphones can either be mounted flush with the wall or in microphone rakes (see picture on the right hand side). Full radial mode analyses at high frequencies require measurements with a dense grid of measurement positions. This can be accomplished by a sensor arrangement that can be traversed in the circumferential direction.

(X)TPP methods

The unsteady flow inside a turbo-engine can be considered as a superposition of a mean flow, whose properties remain constant in time, and fluctuating quantities. The fluctuations consist of acoustic waves and fluctiations of the entropy and vorticity. Whilst acoustic fluctuations propagate in all directions as waves, entropy and vorticity fluctuations are purely convective. With a mode analysis based on the Triple Plane Pressure mode matching (TTP) method, the fluctuations in a CFD unsteady flow solution are assumed to consist only of acoustic waves. Any strong entropy and vorticity fluctuations present in the flow solution are known to cause errors in this mode analysis technique. Therefore, the mode analysis has been extended to account for entropy and vorticity fluctuations. This result is the eXtended Triple Plane Pressure mode matching (XTPP) method. It significantly improves the quality of results and the robustness of the mode analysis. With the XTPP method, it is now possible to carry out the acoustic mode analysis closely downstream of installed components, e.g. stators. The reduction of the analysis to the vicinity of components also reduces the size of the computational domain downstream of a stator and thus saves computational costs.

Unsteady pressure distribution at the blade passing frequency (BPF) downstream of a Turbo-Fan aquired with microphone rakes.

Analysis of broad band noise by filtering turbulent pressure fluctuations

In the analysis of turbomachinery noise, the broad band contributions are as interesting as the modal amplitudes of the rotor-stator interaction tones. Wall mounted microphones measure the vorticity fluctuations from the fan stages combined with turbulent fluctuations in the boundary layer. The turbulent fluctuations and the acoutic waves propagate with different velocities and the signals are compromised by the effects of other noise sources and reflections. When several wall mounted microphones are combined into a linear array, the data can be used to separate the different signal components. Using the cross-spectral matrix measured with the array, a spatial Fourier analysis can be performed in order to obtain a wavenumber-frequency spectrum. Because the frequency and the wavenumber are directly linked by the propagation velocity, the hydrodynamic and acoustic components of the signals can be identified and separated. Also, the acoustic pressure fluctuations can be separated according to their propagation directions and unwanted noise sources in the opposite direction of the noise source under analysis can be isolated. The frequency spectra of the individual components of the signal can be calculated from inverse Fourier transforms over the respective wave numbers. This approach is superior to a simple power spectrum analysis and allows a much more detailed analysis of sound sources or sound reduction devices. It is applied for example to estimate the damping characteristics of acoustic liners or to determine reference data for models of sound source mechanisms.