Three-dimensional instability in flow over a 
backward-facing step

Barkley, Dwight; Gomes, M. Gabriela M.; Henderson, Ronald D.

doi:10.1017/s002211200200232x

Cited by 298 publications

(298 citation statements)

References 31 publications

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“…With increasing Re steady two-dimensional laminar separated backward-facing step flow with a 2:1 longitudinal-to-transversal aspect ratio first becomes unstable to a steady 3D bifurcation at critical Reynolds number about 750, as discovered by Barkley et al [1], essentially following the same modal scenario predicted by Theofilis et al [21] in the adverse-pressure-gradient laminar separation bubble flow on a flat plate. The mesh and geometry are represented in Fig.…”

Section: Backward-facing Step: Real and Complex Shift-invertsupporting

confidence: 68%

“…Three different problems have been considered in this section in order to validate the present exponential shift-invert method described above: (i) stenosis flow [19], (ii) backward-facing step flow [1] and (iii) lid-driven swirling flow [13]. In all cases, the base solution was obtained using Newton-Raphson iteration started from a numerical solution previously generated with Semtex, see Blackburn [4] for details.…”

Section: Real Shift-invertmentioning

confidence: 99%

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On the use of matrix-free shift-invert strategies for global flow instability analysis

Gómez

Pérez

Blackburn

et al. 2015

Aerospace Science and Technology

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A novel time-stepping shift-invert algorithm for linear stability analysis of laminar flows in complex geometries is presented. This method, based on a Krylov subspace iteration, enables the solution of complex non-symmetric eigenvalue problems in a matrix-free framework. Validations and comparisons to the classical exponential method have been performed in three different cases: (i) stenotic flow, (ii) backward-facing step and (iii) lid-driven swirling flow. Results show that this new approach speeds Keywords-U P tne re Q u i re d Krylov subspace iterations and has the capability of converging to specific parts of the Global linear instability analysis global spectrum. It is shown that, although the exponential method remains the method of choice if Large-scale eigenvalue problems leading eigenvalues are sought, the performance of the present method could be dramatically improved Krylov subspace with the use of a preconditioner. In addition, as opposed to other methods, this strategy can be directly Jacobian-free methods applied to any time-stepper, regardless of the temporal or spatial discretization of the latter.

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Section: Backward-facing Step: Real and Complex Shift-invertsupporting

confidence: 68%

Section: Real Shift-invertmentioning

confidence: 99%

On the use of matrix-free shift-invert strategies for global flow instability analysis

Gómez

Pérez

Blackburn

et al. 2015

Aerospace Science and Technology

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“…Independent investigations using linear instability theory and/or direct numerical simulations (DNS) (Rist & Maucher 2002;Fasel & Postl 2004) agree reasonably well with this threshold for the onset of absolute instability of wave-like disturbances of the LSB. However, it was Theofilis (2000) and Theofilis, Hein & Dallmann (2000) who first unequivocally demonstrated the self-excitation potential of LSB flows, by solving the partial-derivative-based eigenvalue problem pertinent to the (twodimensional DNS obtained) separated boundary layer ensuing Howarth's freestream linear deceleration on a flat plate (Briley 1971), without the need to invoke the assumption of weak non-parallelism of the basic state; at about the same time, an analogous conclusion was independently reached by Barkley, Gomes & Henderson (2002) in the LSB formed in the laminar backward-facing step flow.…”

Section: Introductionmentioning

confidence: 94%

Structural changes of laminar separation bubbles induced by global linear instability

Rodríguez

Theofilis

2010

J. Fluid Mech.

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The topology of the composite flow fields reconstructed by linear superposition of a two-dimensional boundary layer flow with an embedded laminar separation bubble and its leading three-dimensional global eigenmodes has been studied. According to critical point theory, the basic flow is structurally unstable; it is shown that in the presence of three-dimensional disturbances the degenerate basic flow topology is replaced by a fully three-dimensional pattern, regardless of the amplitude of the superposed linear perturbations. Attention has been focused on the leading stationary eigenmode of the laminar separation bubble discovered by Theofilis et al. (Phil. Trans. R. Soc. Lond. A, vol. 358, 2000, pp. 3229-3324); the composite flow fields have been fully characterized with respect to the generation and evolution of their critical points. The stationary global mode is shown to give rise to a three-dimensional flow field which is equivalent to the classical U-shaped separation, defined by Hornung & Perry (Z. Flugwiss. Weltraumforsch., vol. 8, 1984, pp. 77-87), and induces topologies on the surface streamlines that are resemblant to the characteristic stall cells observed experimentally. IntroductionThe instability of a laminar separation bubble (LSB), embedded inside a boundary layer and arising as a consequence of an adverse free-stream pressure gradient on a flat surface, or induced by changes of the surface curvature, constitutes a problem of prime technological significance: in an aeronautical context related applications include lifting surfaces, low-pressure turbines and wind-turbine blades. The presence of a separated shear layer as an integral part of the LSB suggests that the instability properties of the shear layer should play a decisive role in the reattachment of the separated boundary layer. The one-dimensionality of the model shear-layer profile and its resulting amenability to classic, ordinary-differential-equation-based analysis (Michalke 1964; Blumen 1970 and subsequent work in this 'local' vein) has generated a wealth of knowledge on the problem of shear-layer instability perse and as applied to the LSB flow. On the other hand, Gaster postulated (H. Fasel, private communication November 2004) that, besides paying attention to the amplification of incoming disturbances by solution of the local instability problem, analysis of LSB flows 'in the true sense' should also be performed, by which a global instability analysis of the entire separated boundary layer flow is implied.

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“…Alternatively, it is possible to undertake (usually numerically) a linear stability analysis of full pre-computed solutions of spatially developing flows, to identify their stability and the frequency of any global mode which might result (e.g. Barkley & Henderson 1996;Barkley, Gomes & Henderson 2002). This has not yet been done for spatially developing versions of the wakes and mixing layers discussed earlier.…”

Section: Introductionmentioning

confidence: 99%

The stability of laminar symmetric separated wakes

Castro

2005

J. Fluid Mech.

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Time-dependent computations of the two-dimensional incompressible uniformvelocity laminar flow past a normal flat plate (of unit half-width) in a channel are presented. Attention is restricted to cases in which the well-known anti-symmetric (von Kármán-type) vortex shedding is suppressed by the imposition of a symmetry plane on the downstream plate centreline. With a further symmetry plane at the channel's upper boundary, the only two governing parameters in the problem are the channel half-width, H , and the Reynolds number, Re (based on the body half-width and the upstream velocity, U ). The former is restricted to the range 3 6 H 6 30 and the interest lies in determining the nature of the initial instability which occurs in the separated wake as Re is gradually increased. It is found that for sufficiently large H and at a critical Re, a long-time-scale global (supercritical) instability is initiated, which in its saturated (limit) state takes the form of 'lumps' of vorticity being periodically shed from the tail end of the separated bubble. Stability calculations of corresponding mean flow profiles (typical of those found in the separated wake) are undertaken by examining the impulse response of particular profiles via appropriate solution of the Orr-Sommerfeld equation. The results of this analysis extend those available from related published work and are consistent with the behaviour found from the numerical computations. Taken together, all the results suggest that this type of global instability may be generic to many kinds of separated wakes and, indeed, may provide the fundamental explanation for the very low-frequency oscillations often noticed in fully turbulent wake bubbles.

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Three-dimensional instability in flow over a backward-facing step

Cited by 298 publications

References 31 publications

On the use of matrix-free shift-invert strategies for global flow instability analysis

On the use of matrix-free shift-invert strategies for global flow instability analysis

Structural changes of laminar separation bubbles induced by global linear instability

The stability of laminar symmetric separated wakes

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