Nonlinear self-sustained structures and fronts in spatially developing wake flows

Pier, Benoı̂t; Huerre, Patrick

doi:10.1017/s0022112001003652

Cited by 109 publications

(102 citation statements)

References 50 publications

(79 reference statements)

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“…This suggests that no stagnation point is associated with the vortex breakdown in this experiment and that a direct transition from columnar to single helical flow occurs. In addition, the predicted frequencies of the m ¼ À1 spiral that can be argued to be selected by the value of x (Pier et al 2001), are seen to be in reasonable qualitative agreement with the frequencies n that could be measured by image analysis, as seen in Table 4.…”

Section: Local Stability Analysissupporting

confidence: 73%

Obstacle-induced spiral vortex breakdown

et al. 2014

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An experimental investigation on vortex breakdown dynamics is performed. An adverse pressure gradient is created along the axis of a wing-tip vortex by introducing a sphere downstream of an elliptical hydrofoil. The instrumentation involves high-speed visualizations with air bubbles used as tracers and 2D Laser Doppler Velocimeter (LDV). Two key parameters are identified and varied to control the onset of vortex breakdown: the swirl number, defined as the maximum azimuthal velocity divided by the free-stream velocity, and the adverse pressure gradient. They were controlled through the incidence angle of the elliptical hydrofoil, the free-stream velocity and the sphere diameter. A single helical breakdown of the vortex was systematically observed over a wide range of experimental parameters. The helical breakdown coiled around the sphere in the direction opposite to the vortex but rotated along the vortex direction. We have observed that the location of vortex breakdown moved upstream as the swirl number or the sphere diameter was increased. LDV measurements were corrected using a reconstruction procedure taking into account the so-called vortex wandering and the size of the LDV measurement volume. This allows us to investigate the spatio-temporal linear stability properties of the flow and demonstrate that the flow transition from columnar to single helical shape is due to a transition from convective to absolute instability.

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Section: Local Stability Analysissupporting

confidence: 73%

Obstacle-induced spiral vortex breakdown

et al. 2014

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“…It is quite possible that the global mode period is set by conditions at a 'front' located at the upstream edge of the absolutely unstable region of the wake. Such fronts have been shown to exist at least for some classes of spatially developing wakes, and it is the frequency of the dominant mode at the front which determines that of the global mode (Pier & Huerre 2001). This issue remains open and requires further work.…”

Section: Concluding Discussionmentioning

confidence: 99%

“…The frequency (and nature) of such global modes can be explored by analysing the complex, nonlinear GinzburgLandau equation as a model of the flow (e.g. Pier et al 1998;Pier & Huerre 2001). 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.…”

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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“…Note, however, that this does not imply that absolute instability is not involved in transition. Pierre and Huerre [23] have shown that when non-linear effects are included a self-sustained non-linear oscillator will always be generated when there is a region of local linear absolute instability. On the rotating disk, Pier [24] has shown that this oscillator will undergo secondary instability close to the absolute instability boundary, providing a possible route to transition.…”

Section: Discussionmentioning

confidence: 99%

The absolute instability of the boundary layer on a rotating cone

Garrett

Peake

2007

European Journal of Mechanics - B/Fluids

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This paper is concerned with the existence of local absolute instability in the boundary-layer flow over the outer surface of a rotating cone, thereby extending earlier work by Lingwood who considered the rotating disk. Both still outer fluids and non-zero axial flow are considered, viscous and streamline-curvature effects are included, and the analysis is conducted for a wide range of cone half-angles, ψ. In still outer fluid our predicted local Reynolds numbers at the onset of absolute instability is relatively insensitive to the value of ψ, and is in reasonable agreement with experimental data for the onset of turbulence when ψ > 50 • . For ψ < 50 • the discrepancy increases, suggesting that some other mechanism may be responsible for transition on more slender cones. The introduction of axial flow is found to significantly increase the Reynolds number for local absolute instability for each half-angle. Crown

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Nonlinear self-sustained structures and fronts in spatially developing wake flows

Cited by 109 publications

References 50 publications

Obstacle-induced spiral vortex breakdown

Obstacle-induced spiral vortex breakdown

The stability of laminar symmetric separated wakes

The absolute instability of the boundary layer on a rotating cone

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