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Global stability and nonlinear dynamics of wake flows with a two-fluid interface

Published online by Cambridge University Press:  25 March 2021

Simon Schmidt Open the ORCID record for Simon Schmidt [Opens in a new window] ,
Outi Tammisola Open the ORCID record for Outi Tammisola [Opens in a new window] ,
Lutz Lesshafft Open the ORCID record for Lutz Lesshafft [Opens in a new window]  and
Kilian Oberleithner Open the ORCID record for Kilian Oberleithner [Opens in a new window]
Simon Schmidt*
Affiliation:
Laboratory for Flow Instability and Dynamics, Technische Universität Berlin, 10623Berlin, Germany
Outi Tammisola
Affiliation:
FLOW, Engineering Mechanics, KTH Royal Institute of Technology, SE-100 44Stockholm, Sweden
Lutz Lesshafft
Affiliation:
LadHyX, CNRS/École Polytechnique/Institut Polytechnique de Paris, 91128Palaiseau, France
Kilian Oberleithner
Affiliation:
Laboratory for Flow Instability and Dynamics, Technische Universität Berlin, 10623Berlin, Germany
*
†Email address for correspondence: [email protected]
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Abstract

A framework for the computation of linear global modes, based on time stepping of a linearised Navier–Stokes solver with an Eulerian interface representation, is presented. The method is derived by linearising the nonlinear solver Basilisk, capable of computing immiscible two-phase flows, and offers several advantages over previous, matrix-based, multi-domain approaches to linear global stability analysis of interfacial flows. Using our linear solver, we revisit the study of Tammisola et al. (J. Fluid Mech., vol. 713, 2012, pp. 632–658), who found a counter-intuitive, destabilising effect of surface tension in planar wakes. Since their original study does not provide any validation, we further compute nonlinear results for the studied flows. We show that a surface-tension-induced destabilisation of plane wakes is observable which leads to periodic, quasiperiodic or chaotic oscillations depending on the Weber number of the flow. The predicted frequencies of the linear global modes, computed in the present study, are in good agreement with the nonlinear results, and the growth rates are comparable to the disturbance growth in the nonlinear flow before saturation. The bifurcation points of the nonlinear flow are captured accurately by the linear solver and the present results are as well in correspondence with the study of Tammisola et al. (J. Fluid Mech., vol. 713, 2012, pp. 632–658).

JFM classification

Multiphase and Particle-laden Flows: Gas/liquid flow Mathematical Foundations: Computational methods
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 915 , 25 May 2021 , A96
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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