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Linear and nonlinear processes in two-dimensional mixing layer dynamics and sound radiation

Published online by Cambridge University Press:  14 April 2009

LAWRENCE C. CHEUNG  and
SANJIVA K. LELE
LAWRENCE C. CHEUNG*
Affiliation:
Department of Mechanical Engineering, Stanford University, Stanford, CA 94305-3030, USA
SANJIVA K. LELE
Affiliation:
Department of Mechanical Engineering, Stanford University, Stanford, CA 94305-3030, USA Department of Aeronautics and Astronautics, Stanford University, Stanford, CA 94305-3030, USA
*
†Email address for correspondence: l.cheung@imperial.ac.uk
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Abstract

In this study, we consider the effects of linear and nonlinear instability waves on the near-field dynamics and aeroacoustics of two-dimensional laminar compressible mixing layers. Through a combination of direct computations, linear and nonlinear stability calculations, we demonstrate the significant role of nonlinear mechanisms in accurately describing the behaviour of instability waves. In turn, these processes have a major impact on sound generation mechanisms such as Mach wave radiation and vortex pairing sound. Our simulations show that the mean flow correction, which is required in order to accurately describe the dynamics of large-scale vortical structures, is intrinsically tied to the nonlinear modal interactions and accurate prediction of saturation amplitudes of instability waves. In addition, nonlinear interactions are largely responsible for the excitation and development of higher harmonics in the flow which contribute to the acoustic radiation. Two flow regimes are considered: In supersonic shear layers, where the far-field sound is determined by the instability wave solution at sufficiently high Mach numbers, it is shown that these nonlinear effects directly impact the Mach wave radiation. In subsonic shear layers, correctly capturing the near-field vortical structures and the interactions of the subharmonic and fundamental modes become critical due to the vortex pairing sound generation process. In this regime, a method is proposed to combine the instability wave solution with the Lilley–Goldstein acoustic analogy in order to predict far-field sound.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 625 , 25 April 2009 , pp. 321 - 351
Copyright
Copyright © Cambridge University Press 2009

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