Structural sensitivity of the secondary instability in the wake of a circular cylinder

Giannetti, Flavio; Camarri, Simone; Luchini, Paolo

doi:10.1017/s0022112009993946

Cited by 54 publications

(62 citation statements)

References 32 publications

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“…In figure 7(a,c,e), the solid and dashed lines denote positive and negative spanwise vorticity of the corresponding base flow, respectively, whereas temporal accumulation of the streamwise vorticity contours on the line x = 2.5 is shown in figure 7(b,d,f ). It is seen in figure 7 and the strong localization of the core of modes A and B in the near wake (Giannetti, Camarri & Luchini 2010). The present Floquet stability analysis does not reveal any other instability mode, confirming the affirmation of Marques et al (2004).…”

Section: Secondary Instability 341 Floquet Stability Analysissupporting

confidence: 82%

Flow instabilities in the wake of a rounded square cylinder

Park

Yang

2016

J. Fluid Mech.

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Instabilities in the flow past a rounded square cylinder have been numerically studied in order to clarify the effects of rounding the sharp edges of a square cylinder on the primary and secondary instabilities associated with the flow. Rounding the edges was done by inscribing a quarter circle of radius r in each edge of a square cylinder of height d. Nine cases of rounding were considered, ranging from a square cylinder (r/d = 0) to a circular cylinder (r/d = 0.5) with an increment of 0.0625. Each cross-section was numerically implemented in a Cartesian grid system by using an immersed boundary method. The key parameters are the Reynolds number (Re) and the edge-radius ratio (r/d). For low Re, the flow is steady and symmetric with respect to the centreline. Over the first critical Reynolds number (Re c1 ), the flow undergoes a Hopf bifurcation to a time-periodic flow, termed the primary instability. As Re further increases, the onset of the secondary instability of three-dimensional (3D) nature is detected beyond the second critical Reynolds number (Re c2 ). Rounding the sharp edges of a square cylinder significantly affects the flow topology, leading to noticeable changes in both instabilities. By employing the Stuart-Landau equation, we investigated the criticality of the primary instability depending upon r/d. The onset of the 3D secondary instability was detected by using Floquet stability analysis. The temporal and spatial characteristics of the dominant modes (A, B, QP) were described. The neutral stability curves of each mode were computed depending upon r/d.

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Section: Secondary Instability 341 Floquet Stability Analysissupporting

confidence: 82%

Flow instabilities in the wake of a rounded square cylinder

Park

Yang

2016

J. Fluid Mech.

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“…Consistent with this mode A mechanism is a recent study by [19] which investigates the spatial origins of the mode A and mode B instabilities by determining the locations in the flow where a perturbation force-velocity feedback is maximized. This study corroborates the Floquet analysis done on successively reduced domains by [20] and shows that the mode A instability is formed in a relatively small region very close to the back of the cylinder (within 1.5D of the rear stagnation point).…”

Section: Mode a Stabilization Mechanismmentioning

confidence: 92%

Floquet stability analysis of viscoelastic flow over a cylinder

Richter¹,

Shaqfeh²,

Iaccarino³

2011

Journal of Non-Newtonian Fluid Mechanics

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“…Following on from a series of papers characterising the structural stability of stationary and rotating cylinder wakes (Giannetti & Luchini 2007;Giannetti, Camarri & Luchini 2010;Pralits, Brandt & Giannetti 2010), Pralits et al (2013) investigated the nature of the instability causing the transition from two-to three-dimensional steady flow for a rotating cylinder at the high rotation rate of α = 5 at Re = 100. Middle column: structure of the adjoint mode for matching rotation rates, again depicted as coloured contours of spanwise perturbation vorticity.…”

Section: Structural Stability Of Mode Ementioning

confidence: 99%

A universal three-dimensional instability of the wakes of two-dimensional bluff bodies

2016

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Linear stability analysis of a wide range of two-dimensional and axisymmetric bluff-body wakes shows that the first three-dimensional mode to became unstable is always mode E. From the studies presented in this paper, it is speculated to be the universal primary 3D instability, irrespective of the flow configuration. However, since it is a transition from a steady two-dimensional flow, whether this mode can be observed in practice does depend on the nature of the flow set-up. For example, the mode E transition of a circular cylinder wake occurs at a Reynolds number of Re 96, which is considerably higher than the steady to unsteady Hopf bifurcation at Re 46 leading to Bénard-von-Kármán shedding. On the other hand, if the absolute instability responsible for the latter transition is suppressed, by rotating the cylinder or moving it towards a wall, then mode E may become the first transition of the steady flow. A well-known example is flow over a backward-facing step, where this instability is the first global instability to be manifested on the otherwise two-dimensional steady flow. Many other examples are considered in this paper. Exploring this further, a structural stability analysis (Pralits et al. J. Fluid Mech., vol. 730, 2013, pp. 5-18) was conducted for the subset of flows past a rotating cylinder as the rotation rate was varied. For the non-rotating or slowly rotating case, this indicated that the growth rate of the instability mode was sensitive to forcing between the recirculation lobes, while for the rapidly rotating case, it confirmed sensitivity near the cylinder and towards the hyperbolic point. For the non-rotating case, the perturbation, adjoint and structural stability fields, together with the wavelength selection, show some similarities with those of a Crow instability of a counter-rotating vortex pair, at least within the recirculation zones. On the other hand, at much higher rotation rates, Pralits et al. (J. Fluid Mech., vol. 730, 2013, pp. 5-18) have suggested that hyperbolic instability may play a role. However, both instabilities lie on the same continuous solution branch in Reynolds number/rotation-rate parameter space. The results suggest that this particular flow transition at least, and probably others, may have a number of different physical mechanisms supporting their development.

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Structural sensitivity of the secondary instability in the wake of a circular cylinder

Cited by 54 publications

References 32 publications

Flow instabilities in the wake of a rounded square cylinder

Flow instabilities in the wake of a rounded square cylinder

Floquet stability analysis of viscoelastic flow over a cylinder

A universal three-dimensional instability of the wakes of two-dimensional bluff bodies

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