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Self-excited primary and secondary instability of laminar separation bubbles

Published online by Cambridge University Press:  13 November 2020

Daniel Rodríguez Open the ORCID record for Daniel Rodríguez [Opens in a new window] ,
Elmer M. Gennaro Open the ORCID record for Elmer M. Gennaro [Opens in a new window]  and
Leandro F. Souza Open the ORCID record for Leandro F. Souza [Opens in a new window]
Daniel Rodríguez*
Affiliation:
ETSIAE-UPM (School of Aeronautics), Universidad Politécnica de Madrid, Plaza del Cardenal Cisneros 3, 28040Madrid, Spain
Elmer M. Gennaro
Affiliation:
São Paulo State University (UNESP), Campus of São João da Boa Vista, São João da Boa Vista-SP 13876-750, Brazil
Leandro F. Souza
Affiliation:
Institute of Mathematical and Computer Sciences, University of São Paulo, São Carlos-SP13566-590, Brazil
*
†Email address for correspondence: daniel.rodriguez@upm.es
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Abstract

The self-excited instabilities acting on laminar separation bubbles in the absence of external forcing are studied by means of linear stability analysis and direct numerical simulation. Previous studies demonstrated the existence of a three-dimensional modal instability, that becomes active for bubbles with peak reversed flow of approximately $7\,\%$ of the free-stream velocity, well below the ${\approx } 16\,\%$ required for the absolute instability of Kelvin–Helmholtz waves. Direct numerical simulations are used to describe the nonlinear evolution of the primary instability, which is found to correspond to a supercritical pitchfork bifurcation and results in fully three-dimensional flows with spanwise inhomogeneity of finite amplitude. An extension of the classic weakly non-parallel analysis is then applied to the bifurcated flows, that have a strong dependence on the cross-stream planes and a mild dependence on the streamwise direction. The spanwise distortion of the separated flow induced by the primary instability is found to strongly destabilize the Kelvin–Helmholtz waves, leading to their absolute instability and the appearance of a global oscillator-type instability. This sequence of instabilities triggers the laminar–turbulent transition without requiring external disturbances or actuation. The characteristic frequency and streamwise and spanwise wavelengths of the self-excited instability are in good agreement with those reported for low-turbulence wind-tunnel experiments without explicit forcing. This indicates that the inherent dynamics described by the self-excited instability can also be relevant when external disturbances are present.

JFM classification

Boundary Layers: Boundary layer stability Instability: Absolute/convective instability Instability: Transition to turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 906 , 10 January 2021 , A13
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© The Author(s), 2020. Published by Cambridge University Press

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