On the origins of unsteadiness and three-dimensionality in a laminar separation bubble

By V. Theofilis, S. Hein, U. Dallmann. Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 2000

230 citations recorded by the source corpus.

We analyse the three–dimensional non–parallel instability mechanisms responsible for transition to turbulence in regions of recirculating steady laminar two–dimensional incompressible separation bubble flow in a twofold manner. First, we revisit the problem of Tollmien–Schlichting (TS)–like disturbances and we demonstrate, for the first time for this type of flow, excellent agreement between the parabolized stability equation results and those of independently performed direct numerical simulations. Second, we perform a partial–derivative eigenvalue problem stability analysis by discretizing the two spatial directions on which the basic flow depends, precluding TS–like waves from entering the calculation domain. A new two–dimensional set of global amplified instability modes is thus discovered. In order to prove earlier topological conjectures about the flow structural changes occurring prior to the onset of bubble unsteadiness, we reconstruct the total flowfield by linear superposition of the steady two–dimensional basic flow and the new most–amplified global eigenmodes. In the parameter range investigated, the result is a bifurcation into a three–dimensional flowfield in which the separation line remains unaffected while the primary reattachment line becomes three dimensional, in line with the analogous result of a multitude of experimental observations.

Subfields: Applied Mathematics, Computational Mechanics

View Paper: https://www.semanticscholar.org/paper/ab108997531b05183f5f5501904653dac57abe78

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Citations in the corpus

On the origin of the inflectional instability of a laminar separation bubble (2009, background): “Theofilis et al. (2000) have theoretically shown that a two-dimensional separation line with all the oncoming streamlines normal to it gives rise to an infinite sequence of saddle points.”
Modal Analysis of Fluid Flows: An Overview (2017, background): “[178] is amplified more than the Kelvin–Helmholtz mode and stall cells may arise through this primary modal linear amplification mechanism [179].”
Dynamics and Control of Global Instabilities in Open-Flows: A Linearized Approach (2010, background): “The same tendency was observed [123] for the three-dimensional non-oscillating marginal global mode that destabilizes a recirculation bubble in a Cartesian setting [37, 38, 125].”
Direct numerical simulations of forced and unforced separation bubbles on an airfoil at incidence (2008, methodology): “absolute instability. Theofilis (2000) performed global linear stability analysis of a laminar separation bubble, specifying a spanwise wavenumber, β, and computing the resultant two-dimensional disturbance eigenvectors.”
Advances in global linear instability analysis of nonparallel and three-dimensional flows (2003, methodology): “[35] that the BiGlobal instability mechanism discovered is related with and sheds light to the phenomenon of vortex-shedding by separation bubbles; the mechanism is also schematically depicted in Fig.”
Issues in active flow control: theory, control, simulation, and experiment (2004, background): “Interestingly, in two-dimensional basic flows where the assumptions of classic instability analysis of onedimensional basic states approximately hold, as the case is in separated boundary layer flow, both classic Kelvin–Helmholtz (KH)/Tollmien–Schlichting (TS)type and BiGlobal instability are concur”
On the onset of nonlinear oscillations in a separating boundary-layer flow (2003, methodology): “It has been argued that they are due to a global instability manifested in the reattachment region (Theofilis et al. 2000; Häggmark et al. 2000), triggered by topological flow changes generating secondary recirculation zones (Dallmann et al. 1995).”