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Acoustic resonance in the potential core of subsonic jets

Published online by Cambridge University Press:  27 July 2017

Aaron Towne Open the ORCID record for Aaron Towne [Opens in a new window] ,
André V. G. Cavalieri ,
Peter Jordan ,
Tim Colonius ,
Oliver Schmidt Open the ORCID record for Oliver Schmidt [Opens in a new window] ,
Vincent Jaunet  and
Guillaume A. Brès
Aaron Towne*
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA
André V. G. Cavalieri
Affiliation:
Divisão de Engenharia Aeronáutica, Instituto Tecnológico de Aeronáutica, São José dos Campos, SP, Brazil
Peter Jordan
Affiliation:
Département Fluides, Thermique, Combustion, Institut PPrime, CNRS–Université de Poitiers–ENSMA, UPR3346 Poitiers, France
Tim Colonius
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA
Oliver Schmidt
Affiliation:
Division of Engineering and Applied Science, California Institute of Technology, Pasadena, CA 91125, USA
Vincent Jaunet
Affiliation:
Département Fluides, Thermique, Combustion, Institut PPrime, CNRS–Université de Poitiers–ENSMA, UPR3346 Poitiers, France
Guillaume A. Brès
Affiliation:
Cascade Technologies Inc., Palo Alto, CA 94303, USA
*
†Email address for correspondence: atowne@stanford.edu
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Abstract

The purpose of this paper is to characterize and model waves that are observed within the potential core of subsonic jets and relate them to previously observed tones in the near-nozzle region. The waves are detected in data from a large-eddy simulation of a Mach 0.9 isothermal jet and modelled using parallel and weakly non-parallel linear modal analysis of the Euler equations linearized about the turbulent mean flow, as well as simplified models based on a cylindrical vortex sheet and the acoustic modes of a cylindrical soft duct. In addition to the Kelvin–Helmholtz instability waves, three types of waves with negative phase velocities are identified in the potential core: upstream- and downstream-propagating duct-like acoustic modes that experience the shear layer as a pressure-release surface and are therefore radially confined to the potential core, and upstream-propagating acoustic modes that represent a weak coupling between the jet core and the free stream. The slow streamwise contraction of the potential core imposes a frequency-dependent end condition on the waves that is modelled as the turning points of a weakly non-parallel approximation of the waves. These turning points provide a mechanism by which the upstream- and downstream-travelling waves can interact and exchange energy through reflection and transmission processes. Paired with a second end condition provided by the nozzle, this leads to the possibility of resonance in limited frequency bands that are bound by two saddle points in the complex wavenumber plane. The predicted frequencies closely match the observed tones detected outside of the jet. The vortex-sheet model is then used to systematically explore the Mach number and temperature ratio dependence of the phenomenon. For isothermal jets, the model suggests that resonance is likely to occur in a narrow range of Mach number, $0.82<M<1$.

JFM classification

Instability: Absolute/convective instability Acoustics: Acoustics Wakes/Jets: Jets
Type
Papers
Information
Journal of Fluid Mechanics , Volume 825 , 25 August 2017 , pp. 1113 - 1152
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Copyright
© 2017 Cambridge University Press 

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Footnotes

‡

Present address: Center for Turbulence Research, Stanford University, Stanford, CA 94305, USA.

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