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Instability of forced planar liquid jets: mean field analysis and nonlinear simulation

Published online by Cambridge University Press:  25 November 2019

S. Schmidt Open the ORCID record for S. Schmidt [Opens in a new window]  and
K. Oberleithner
S. Schmidt*
Affiliation:
Laboratory for Flow Instability and Dynamics, Technische Universität Berlin, 10623 Berlin, Germany
K. Oberleithner
Affiliation:
Laboratory for Flow Instability and Dynamics, Technische Universität Berlin, 10623 Berlin, Germany
*
†Email address for correspondence: s.schmidt@fdx.de
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Abstract

The stability of forced planar liquid jets in a still gaseous environment is explored using nonlinear simulation and spatial linear stability analysis. Harmonic modulation of the transverse component of the inlet velocity leads to an excitation of sinuous modes in the jet. Two forcing amplitudes, 1 % and 5 %, are investigated. While for 1 % forcing, the interfacial disturbance retains a sinuous shape throughout the domain, for 5 % forcing, an increasing downstream deviation from the sinuous wave shape is found. Both forcings lead to sufficient mean flow correction to render linear stability analysis on a base flow unfeasible. Hence, an analysis on the time-averaged mean flow is performed. A correction scheme is introduced, to account for the spreading of the interface position in the mean flow. Comparison of eigenfunctions and growth rates with their counterparts from the nonlinear simulation shows an excellent agreement for 1 % forcing. For 5 % forcing, agreement of the eigenfunctions deteriorates significantly and growth rates are falsely predicted, resulting in a breakdown of the stability model. Subsequent analysis reveals a strong interaction of the fundamental wave with the second higher harmonic wave for 5 % forcing and a reversed energy flow from the coherent motion to the mean flow. These findings provide an explanation for the failure of the linear stability model for large forcing amplitudes. The study extends the applicability of mean flow stability analysis to convectively unstable planar liquid/gas jets and supports previous findings on the limits of mean flow stability, involving pronounced influence of higher harmonic modes.

JFM classification

Instability: Absolute/convective instability Instability: Nonlinear instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 883 , 25 January 2020 , A7
Copyright
© 2019 Cambridge University Press

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