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Spatial stability analysis of subsonic corrugated jets

Published online by Cambridge University Press:  08 August 2019

F. C. Lajús Jr. Open the ORCID record for F. C. Lajús Jr. [Opens in a new window] ,
A. Sinha ,
A. V. G. Cavalieri Open the ORCID record for A. V. G. Cavalieri [Opens in a new window] ,
C. J. Deschamps Open the ORCID record for C. J. Deschamps [Opens in a new window]  and
T. Colonius Open the ORCID record for T. Colonius [Opens in a new window]
F. C. Lajús Jr.*
Affiliation:
Universidade Federal de Santa Catarina, Eng. Mecânica, Florianópolis, SC 88040-900, Brazil Intituto Tecnológico de Aeronáutica, São José dos Campos, SP 12228-900, Brazil
A. Sinha
Affiliation:
Aerospace Engineering, Indian Institute of Technology Bombay, Mumbai 400076, India
A. V. G. Cavalieri
Affiliation:
Intituto Tecnológico de Aeronáutica, São José dos Campos, SP 12228-900, Brazil
C. J. Deschamps
Affiliation:
Universidade Federal de Santa Catarina, Eng. Mecânica, Florianópolis, SC 88040-900, Brazil
T. Colonius
Affiliation:
Mechanical Engineering, California Institute of Technology, Pasadena, CA 91125, USA
*
†Email address for correspondence: francisco.lajus.jr@gmail.com
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Abstract

The linear stability of high-Reynolds-number corrugated jets is investigated by solving the compressible Rayleigh equation linearized about the time-averaged flow field. A Floquet ansatz is used to account for periodicity of this base flow in the azimuthal direction. The origin of multiple unstable solutions, which are known to appear in these non-circular configurations, is traced through gradual perturbations of a parametrized base-flow profile. It is shown that all unstable modes are corrugated jet continuations of the classical Kelvin–Helmholtz modes of circular jets, highlighting that the same instability mechanism, modified by corrugations, leads to the growth of disturbances in such flows. It is found that under certain conditions the eigenvalues may form saddles in the complex plane and display axis switching in their eigenfunctions. A parametric study is also conducted to understand how penetration and number of corrugations impact stability. The effect of these geometric properties on growth rates and phase speeds of the multiple unstable modes is explored, and the results provide guidelines for the development of nozzle configurations that more effectively modify the Kelvin–Helmholtz instability.

JFM classification

Acoustics: Jet noise Flow Control: Instability control Instability: Absolute/convective instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 876 , 10 October 2019 , pp. 766 - 791
Copyright
© 2019 Cambridge University Press 

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Supplementary material: Image

Lajús et al. supplementary movie

Spatial stability behavior of deformed Kelvin-Helmholtz modes, with gradual increase of corrugation (indicated by P arrows), at St=0.15 to 0.35 (animation steps of 0.1) near a saddle point. In the left, growth rates and phase speeds are displayed, with solid and dashed lines indicating the solution paths of two interacting modes along the complex plane. Colors indicate the solutions branch at low St level, while (i,ii) stands for the current St branch of increasing P. In the right, the behavior of some indicated eigenfunctions are displayed. For P=0.7, an axis-switching of eigenfunctions is observed. Beyond a certain P magnitude, this behavior is not verified, but then these modes change their solution path, and exchange positions in the current branch of increasing P. Black lines indicate the base-flow velocity profile, while contours indicate normalized absolute values of the eigenfunctions.

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