Numerical study of aeroacoustic oscillations in transonic flow downstream a sudden duct enlargement

A sonic flow passing a sudden enlargement in a plane duct is numerically studied by solving the 2-D compressible Navier-Stokes equations. Different flow patterns are likely to appear in such configuration. For very low pressure ratios the flow is entirely supersonic and stable. For higher ratios, unstable flow patterns emerge. One of these patterns features a normal shock, that oscillates due to a self-exciting mechanism. As the duct is open at the outflow, aeroacoustics coupling occurs when the shock oscillations get in resonance with the longitudinal acoustic modes of the duct. The main flow features are captured by the present numerical simulations but no coupling with longitudinal duct modes is found because of 2-D artefacts. The governing equations are solved using high-order methods based on central finite differences on structured grids. To damp out spurious oscillations supported by central differences a selective background smoothing term and a well established nonlinear shock-capturing term are used. Their suitability is demonstrated by two test cases involving a classical shock-sound interaction problem and an abruptly expanding supersonic inviscid flow.