Direct computation of aerodynamic sound

Aeroacoustic theory, which attempts to predict the acoustic far field produced by an unsteady flow, is well established for simple flows with compact vorticity fields. For turbulent shear flows which have extensive vorticity fields, a detailed agreement with experiment has been elusive, owing to a lack of knowledge of the structure of the acoustic sources. We examine the feasibility and accuracy of using the Navier-Stokes equations to directly compute (without models) a flow and its acoustic field. Given such information, aeroacoustic theory may be directly evaluated. A high-order-accurate numerical method for the Navier-Stokes equations is presented. Nonreflecting boundary conditions which allow the passage of sound waves and vortical structures through computational boundaries are developed.; The efficacy of the method is firmly established by considering model problems including the scattering of sound waves by a vortex, and the sound generated by a two dimensional mixing layer. For vortex scattering, the sound waves are strongly refracted by the slowly decaying vortex flow, an effect incorrectly treated in previous theories. We develop a corrected theory which gives excellent agreement with the numerical results. For the mixing layer, the computations show that the acoustic field at the fundamental and first two subharmonic frequencies emanates from the region of the flow where the layer rolls up into vortices, and pairs twice, respectively. The acoustic waves produced by the pairings are beamed downstream, as previously observed by Laufer and Yen (1983) for the round jet. The acoustic field is also predicted by solving Lilley's equation; source terms necessary to solve the equation are determined from the Navier-Stokes computations. Predictions for the acoustic field based on our solution of Lilley's equation do not agree with the Navier-Stokes computations. Reasons for the discrepancy are examined in detail.