Inflow/outflow conditions for time-harmonic internal flows

Inflow/Outflow conditions are formulated for time-harmonic waves in a duct governed by the Euler equations. These conditions are used to compute the propagation of acoustic and vertical disturbances and the scattering of vertical waves into acoustic waves by an annular cascade. The outflow condition is expressed in terms of the pressure, thus avoiding the velocity discontinuity across any vortex sheets. The numerical solutions are compared with the analytical solutions for acoustic and vertical wave propagation with and without the presence of vortex sheets. Grid resolution studies are also carried out to discern the truncation error of the numerical scheme from the error associated with numerical reflections at the boundary. It is observed that even with the use of exponentially accurate boundary conditions, the dispersive characteristics of the numerical scheme may result in small reflections from the boundary that slow convergence. Finally, the three-dimensional interaction of a wake with a flat plate cascade is computed and the aerodynamic and aeroacoustic results are compared with those of lifting surface methods.