On Acoustic Multi-Port Characterisation Including Higher Order Modes

Methods to design test-procedures for acoustic multi-ports in ducts with a focus on pressure sampling positions for accurate modal decomposition are demonstrated. Acoustic fields up- and downstream of an in-duct acoustic element are excited by external sources and decomposed into transmitted and reflected aeroacoustic modal pres- sure amplitudes in order to first determine the acoustic scattering of the element. Secondly, the determination of the element source strength requires tests with no external sources, but with known terminations and scattering data. Unfavourable source and sensor positions lead to mode coupling and to ill-conditioned or even singular decomposition matrices, which results in high amplifications of uncertainties within the wave decomposition. An unoptimised but over-determined assembly is compared with a setup containing a minimum of sensors but with optimised positions. Lower uncertainty amplification, despite the usage of fewer sensors, is achieved for most frequencies, especially after the cut-on of t he higher order acoustic modes. A genetic algorithm (GA) is used to achieve this optimised setup by minimising the condition number of the decomposition matrix, which is a multi-dimensional optimisation problem with numerous local minima. To estimate the stability of the optimised configuration, a Monte-Carlo Method (MCM) is deployed to introduce normal distributed complex pressure un- certainties into the decomposition. In order to estimate the wave number, different approaches are compared - namely the classical non-dissipative wav e number estimate, an extended Kirchhoff method for viscous-thermal damping and an eigenvalue solution of the Linearised Navier Stokes Equations by Dokumaci. The presented de- composition method is not only applicable to measurement data but is equally useful to post-process results from numerical computation.QC 20160916IDEAL VEN