Acoustic wave propagation in transversely sheared flows.

Department of Mechanical Engineering
Caltech

Abstract-
Aerodynamic noise has become a very crucial issue in many situations, and a number of theoretical formulas are in use to predict the radiated sound field. In this study, acoustic wave propagation phenomena in transversely-sheared flows are investigated theoretically and computationally. As model problems, three types of aero-acoustic problems are presented: (i) sound radiation from a time-harmonic point source in a steady boundary layer (application to noise due to wall turbulence); (ii) that in a steady mixing layer (broad-band jet noise); and (iii) shock wave leakage across an unsteady supersonic mixing layer (jet screech noise). In each problem, theoretical predictions are compared with direct numerical simulation (DNS) in two-dimensions. In the first problem Green's functions in a transversely-sheared boundary layer are derived including three types of waves: direct waves, channeled waves, and diffracted waves. Likewise, in the second problem Green's functions in a transversely-sheared mixing layer are re-derived or newly formulated including direct waves, refracted arrival waves, and instability waves. Green's functions of direct waves, refracted arrival waves, and diffracted waves are derived based on the third order convective wave equation using asymptotic theories, i.e. low and high frequency limits as well as far field asymptotes. Green's functions of instability waves and channeled waves are formulated using the adjoint operator of the third order convective wave equation and the corresponding bi-orthogonal system. In the third problem the interaction between a weak shock wave and a supersonic unsteady vortex-laden mixing layer is studied. The shock leakage across a mixing layer is analyzed based on geometrical acoustics, and the wave-front evolution of the leaked shock noise and its amplitude are predicted. These theoretical predictions show fairly good agreement with DNS in most cases.

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