Sudden area expansion in ducts with flow – A comparison between cylindrical and rectangular modelling

The acoustic properties of an area expansion are analyzed for frequencies where flow acoustic interaction may have a significant influence due to flow separation and vortex shedding. It is investigated why this interaction, which is seen in experimental data on a cylindrical duct as a resonance at a particular Strouhal number of order one, is present in rectangular but not in cylindrical modelling that would be expected to be more realistic; both models consider a plug flow. An analytic method that is suitable for identifying possible reasons for the discrepancies between the two geometries is used. The previously published rectangular model is generalized to the cylindrical case and both models are used to simulate results for all elements in the plane wave scattering matrix and for all parameters for which experimental results are available. The comparison between the two models and between models and measured data is thus not restricted to the flow acoustic induced resonance. The results show that the two geometries in general perform equally when compared with the experimental results, but that the rectangular modelling indeed performs better for some cases. This occurs around a critical Strouhal number, and for higher Mach number. Using the analytic form of the solution, it is shown that the observed discrepancy is related to interaction between the damped hydrodynamic mode and a downstream propagating higher order acoustic mode. Such interaction is not present in the corresponding quiescent duct, and is related to the presence of the shear layer. The analysis shows that the structure of the higher order acoustic modes is different for the cylindrical and rectangular case, respectively, causing the difference in resonant behaviour.