Our aim is to develop a numerical method to study the acoustic propagation in a general rotational flow (not potential). In the time harmonic regime we consider arbitrary 2D geometries and therefore we privilege Finite Element methods on unstructured meshes. We develop a method which combines the resolution of the usual modified Helmholtz equation, well adapted to a Finite Element discretization but strictly valid only for a potential flow, and which takes into account the coupling of acoustics waves with vorticity. It is based on an iterative process in which the vortical part is updated at each iteration and is used as source terms for the velocity potential. The effciency of the method is illustrated on examples in bounded or unbounded propagation domains.