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

Abstract

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 field 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. Nomenclature #00 = reference speed of sound, also reference velocity Cp = constant pressure specific heat, temperature independent et = internal energy per unit volume h = duct half-width i, j,k = coordinate directions in Cartesian tensor notation L = computational length of duct M = mean flow Mach number Pr = Prandtl number p = pressure qj = heat flux vector component in the jth direction Re = acoustic Reynolds number in the calculation Rec = duct Reynolds number T = temperature t = time variable uk -• velocity component in the &th coordinate direction