Direct numerical simulation of acoustic shear flow interactions in two-dimensional ducts

The interaction between an imposed monochromatic, time-dependent acoustic disturbance and a steady mean shear flow in a two-dimensional duct is studied using direct numerical simulation. Unlike previously reported numerical results, the long-time acoustic response is captured through implementation of accurate nonreflecting boundary conditions. Below a certain cutoff frequency, the acoustic held is a nearly planar traveling wave propagating axially along the duct. Above this cutoff frequency, oblique waves are generated due to both acoustic refraction and cross-stream dependent source oscillation, leading to an alternating pattern of higher acoustic pressures at the wall and the centerline, downstream of the disturbance source. At resonant conditions, the growth of the oblique wave, which is nearly transverse, dominates the axial wave, leading to a phase change of 180 deg after their interaction, The thickness of the acoustic boundary layer and its response to imposed disturbances are also in good agreement with theory. These results are consistent with previously published theoretical predictions and represent their first numerical verification.