Assuming an axisymmetric mean flow and acoustic boundary conditions,
a set of 3D axisymmetric equations suitable for each azimuthal sound
mode of fluctuation is derived based on the 3D linearized Euler equations.
The independent 2D model for each azimuthal sound mode is deduced by a Fourier series decomposition.
A computational aeroacoustics approach is then applied to solve each 2D equation system.
The dispersion-relation-preserving finite difference scheme is implemented for spatial
discretization, whereas the 2N storage low dissipation and low dispersion
Runge-Kutta scheme is applied for time integration.
Appropriate boundary conditions are prescribed at the various boundary regions.
The numerical procedure is firstly validated by cases of a straight circular pipe and an annular duct
subjected to a subsonic uniform mean flow, the numerical results of which show very good agreement
with the analytical solutions.
A further numerical example is presented for an axisymmetric inlet duct with an aero-engine
like geometry including an internal spinner. The aeroacoustic computation is based on
an inviscid irrotational mean flow calculated by a second order computational fluid dynamics solver.
The acoustic solutions agree well with the existing finite element and multiple-scales solutions
in the literature. Finally, the cut-on cut-off transition phenomena are investigated based on the
proposed numerical approach. The transition behavior is found to be highly
dependent on the mean flow field in addition to the known geometric effect.
These results demonstrate the feasibility of the proposed model and solution procedure.
