Calculation of modes in azimuthally non-uniform lined ducts with uniform flow

In a recent article, a method was proposed to calculate the mode scattering by an azimuthally non-uniform impedance liner section inserted in an infinite duct. The method allowed the problem to be formulated as a two-dimensional Helmholtz eigenvalue problem, which could be solved with general purpose software rather than custom written codes, but appeared to be limited to ducts without flow. In this short communication, the relevant system of equations is reformulated so that problems with flow can also be treated. The resulting eigenvalue calculation shows good agreement with a well-tested one-dimensional solver when applied to a circular duct section with constant impedance.