Linearised dynamics and non-modal instability analysis of an impinging under-expanded supersonic jet
File(s)
Published version
Author(s)
Karami, Shahram
Stegeman, Paul C
Theofilis, Vassilis
Schmid, Peter J
Soria, Julio
Type
Conference Paper
Abstract
Non-modal instability analysis of the shear layer near the nozzle of a supersonic under-expanded impinging jet is studied. The shear layer instability is considered to be one of the main components of the feedback loop in supersonic jets. The feedback loop is observed in instantaneous visualisations of the density field where it is noted that acoustic waves scattered by the nozzle lip internalise as shear layer instabilities.
A modal analysis describes the asymptotic limit of the instability disturbances and fails to capture short-time responses. Therefore, a non-modal analysis which allows the quantitative description of the short-time amplification or decay of a disturbance is performed by means of a local far-field pressure pulse. An impulse response analysis is performed which allows a wide range of frequencies to be excited. The temporal and spatial growths of the disturbances in the shear layer near the nozzle are studied by decomposing the response using dynamic mode decomposition and Hilbert transform analysis.
The short-time response shows that disturbances with non-dimensionalised temporal frequencies in the range of 1 to 4 have positive growth rates in the shear layer. The Hilbert transform analysis shows that high non-dimensionalised temporal frequencies (>4) are dampened immediately, whereas low non-dimensionalised temporal frequencies (<1) are neutral. Both dynamic mode decomposition and Hilbert transform analysis show that spatial frequencies between 1 and 3 have positive spatial growth rates. Finally, the envelope of the streamwise velocity disturbances reveals the presence of a convective instability.
A modal analysis describes the asymptotic limit of the instability disturbances and fails to capture short-time responses. Therefore, a non-modal analysis which allows the quantitative description of the short-time amplification or decay of a disturbance is performed by means of a local far-field pressure pulse. An impulse response analysis is performed which allows a wide range of frequencies to be excited. The temporal and spatial growths of the disturbances in the shear layer near the nozzle are studied by decomposing the response using dynamic mode decomposition and Hilbert transform analysis.
The short-time response shows that disturbances with non-dimensionalised temporal frequencies in the range of 1 to 4 have positive growth rates in the shear layer. The Hilbert transform analysis shows that high non-dimensionalised temporal frequencies (>4) are dampened immediately, whereas low non-dimensionalised temporal frequencies (<1) are neutral. Both dynamic mode decomposition and Hilbert transform analysis show that spatial frequencies between 1 and 3 have positive spatial growth rates. Finally, the envelope of the streamwise velocity disturbances reveals the presence of a convective instability.
Editor(s)
Jimenez, J
Date Issued
2018
Date Acceptance
2017-05-29
Citation
Journal of Physics : Conference Series, 2018, 1001 (Conference 1)
ISSN
1742-6588
Publisher
Institute of Physics (IoP)
Journal / Book Title
Journal of Physics : Conference Series
Volume
1001
Issue
Conference 1
Copyright Statement
© 2018 IOP Publishing Ltd. Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence (https://creativecommons.org/licenses/by/3.0/). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000454926900019&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Source
Third Madrid Summer School on Turbulence
Subjects
Science & Technology
Physical Sciences
Physics, Applied
Physics, Multidisciplinary
Physics
LARGE-EDDY SIMULATION
DECOMPOSITION
STABILITY
Publication Status
Published
Start Date
2017-05-29
Finish Date
2017-06-30
Coverage Spatial
Univ Politecnica Madrid, Sch Aeronaut, Madrid, Spain
Date Publish Online
2018-04-12