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Mode selection and resonant phase locking in unstable axisymmetric jets

Published online by Cambridge University Press:  26 April 2006

T. C. Corke ,
F. Shakib  and
H. M. Nagib
T. C. Corke
Affiliation:
Fluid Dynamics Center, Mechanical and Aerospace Engineering Department, Illinois Institute of Technology, Chicago, IL 60616, USA
F. Shakib
Affiliation:
Fluid Dynamics Center, Mechanical and Aerospace Engineering Department, Illinois Institute of Technology, Chicago, IL 60616, USA
H. M. Nagib
Affiliation:
Fluid Dynamics Center, Mechanical and Aerospace Engineering Department, Illinois Institute of Technology, Chicago, IL 60616, USA
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Abstract

This paper presents experimental results on the nonlinear phase locking present in the resonant growth of unstable modes in the shear layer of an axisymmetric jet. The initial instability modes scale with the exiting shear layer and grow convectively with downstream distance. Because of the special condition at the exit lip of the jet, the initial growth of modes is very sensitive to local unsteady pressure fields. A part of the unsteady field is stochastic in nature. To a larger extent, the pressure field at the lip of the jet contains the imprint of the downstream-developing instability modes, in particular the first unstable axisymmetric mode and its subharmonic. These are felt at the lip of the jet as a result of the energetic processes of the first vortex rollup and vortex pairing. As a result, a resonant feedback exists which under special conditions makes the initial region of this flow in some sense absolutely unstable. The features of this process are brought out by the normalized crossbispectrum or cross-bicoherence between the instantaneous unsteady pressure at the lip of the jet and velocity time series measured at the same azimuthal position for different downstream locations. These give a measure of the nonlinear phase locking between the principle modes and their sum and difference modes. Analysis of these show a perfect nonlinear phase locking at the fundamental axisymmetric and subharmonic frequencies between the pressure field at the lip and the velocity field at the downstream locations corresponding to the energy saturations of the fundamental and subharmonic modes. This resonance process can be suppressed or enhanced by low-amplitude axisymmetric mode forcing at the natural preferred frequency of slightly detuned cases. Contrasted to this is the behaviour of the fundamental m = ± 1 helical mode. This mode was found to have the same spatial growth rate as the axisymmetric mode and a streamwise frequency approximately 20 % higher, in agreement with theoretical predictions. However, short-time spectral estimates showed that these two fundamental modes do not exist at the same time or space. This suggests that each is a basin of attraction which suppresses the existence of the other. The apparent non-deterministic switching observed between these modes is probably the result of the response of the jet to stochastic input of axisymmetric or non-axisymmetric disturbances. This scenario may lead to a low-dimensional temporal model based on the interaction between these two modes which captures most of the early random nature seen in our experiments.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 223 , February 1991 , pp. 253 - 311
Copyright
© 1991 Cambridge University Press

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