Modal cut-on ratio in ducts with realistic flow profiles and its application to acoustic mode detection

This paper considers the modal cut-on ratio and its use in acoustic mode detection in ducts for a radially varying flow with swirl. These concepts have previously only been considered for the idealised case of uniform axial mean flow and no swirl, and thus in this paper they are generalised and extended to account for radial variations in axial and swirl Mach numbers. The cut-on ratio is shown to no longer satisfy a simple relation with the axial wavenumber, showing that while the cut-on ratio in arbitrary flow is defined its usefulness significantly decreases. Mode distribution functions are also investigated for radially varying flows, both in terms of cut-on ratio and axial wavenumber. In view of the deficiencies of the cut-on ratio highlighted in the paper a recent method for mode detection in ducts that uses just two microphones is generalised to deduce the mode amplitudes in radially varying flows, based on modal axial wavenumber rather than cut-on ratio. This method is shown to perform better than the existing method in radially varying and/or swirling flow in simple test configurations with an idealised source distribution.