A hybrid modal decomposition approach for higher-order modes in circular ducts

Before it is possible to determine the effect over a wide frequency range of different aperture devices on the sound field in a duct, the contribution from the individual higher-order modes must be established. Two approaches to decompose the sound field may be taken which are either to use a large number of microphone locations to reconstruct the sound field, or to use a hybrid method involving a reduced set of microphone locations and a model of the sound field in the system. Modeling the higher-order modes in a duct is itself a numerically intensive procedure if fully coupled calculations are required. It is possible to simplify the process for modeling the sound field by using uncoupled calculations for the higher order modes. Results are presented for such a hybrid approach, combining a limited number of microphone locations with an uncoupled model, to establish the sound field in a circular duct. Both point source and plane wave sources are considered and direct measurement of the sound field is compared to the reconstructed field for a normalized wave number range up to 7. Results show acceptable agreement between the hybrid approach and direct measurement with the greatest errors occurring around cut-on of the axially anti-symmetric modes. Thus, it is demonstrated that a hybrid approach may be applied to ducts with simple sources and that the approach can be used to deconstruct the in-duct sound field into the individual higher-order mode contributions