Onset of shear layer instability in flow past a cylinder

Mittal, Sanjay; Kottaram, Jacob J.; Kumar, B. V. Rathish

doi:10.1063/1.2909587

Cited by 14 publications

(7 citation statements)

References 31 publications

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“…This is in contrast to the trend reported by Shair et al (1963) and Coutanceau & Bouard (1977). In more recent work, Mittal et al (2008) imposed centreline symmetry and studied the onset of shear-layer instability in the flow past a cylinder. They find that the separated shear layer loses stability at low Reynolds numbers with very small growth rates.…”

Section: Introductioncontrasting

confidence: 78%

“…Whilst this may be true in certain contexts, and there are many counter-examples, it is our view that without a detailed and accurate study, one cannot immediately draw such conclusions about the flow in the current context. Careful numerical studies, such as byMittal et al (2008), who investigated the onset of shear layer instability in the flow past a cylinder, show good agreement between simulations and global frequencies predicted. InAbdessemed et al (2009), the computational domain extends to a lateral extent of 12.5 cylinder diameters, and streamwise extent of approximately 100 cylinder diameters and Dirchlet conditions are imposed on the boundaries for the perturbations.…”

supporting

confidence: 57%

“…In Jackson (1987), the finite element method was used to solve an extended set of equations for detecting Hopf bifurcation for a class of bluff bodies. The global stability approach has also been used by Morzyński & Thiele (1991), Morzyński, Afanasiev & Thiele (1999), Chen, Pritchard & Tavener (1995), Kumar & Mittal (2006), Mittal, Kottaram & Kumar (2008), Kumar et al (2009) amongst others, for discussing the instability of the flow past cylinders and related problems. Morzyński et al (1999) was one of the first papers to suggest the use of subspace iteration (see Saad 1989) for solving the eigenvalue problem of the type arising in hydrodynamic stability computations using the global stability approach.…”

Section: Introductionmentioning

confidence: 98%

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Onset of global instability in the flow past a circular cylinder cascade

Boppana

Gajjar

2010

J. Fluid Mech.

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The effect of blockage on the onset of instability in the two-dimensional uniform flow past a cascade of cylinders is investigated. The same techniques as those described in Gajjar & Azzam (J. Fluid Mech., vol. 520, 2004, p. 51) are used to tackle the generalized eigenvalue problem arising from a global stability analysis of the linearized disturbance equations. Results have been obtained for the various mode classes, and our results show that for the odd-even modes, which correspond to anti-phase oscillatory motion about the midplane between the cylinders and are the modes most extensively studied in the literature, the effect of blockage has a marginal influence on the critical Reynolds numbers for instability. This is in sharp contrast to results cited in many studies with a fully developed inlet flow past a cylinder placed between confining walls. We are also able to find other unstable modes and in particular for low blockage ratios, the odd-odd modes which correspond to the in-phase oscillatory motion about the midplane between the cylinders are the first to become unstable as compared with the odd-even modes, and with much lower frequencies.

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Section: Introductioncontrasting

confidence: 78%

supporting

confidence: 57%

Section: Introductionmentioning

confidence: 98%

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Onset of global instability in the flow past a circular cylinder cascade

Boppana

Gajjar

2010

J. Fluid Mech.

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“…The onset of shear layer instability has been studied extensively in the past. Mittal et al (2008) showed, via global convective analysis of the flow past half a cylinder, that the shear layer attached to the cylinder becomes unstable at Re¼54. Bloor (1964) reported that the onset of shear layer instability takes place at Re $ 1300.…”

Section: Introductionmentioning

confidence: 99%

Transition of the boundary layer on a circular cylinder in the presence of a trip

Behara

Mittal

2011

Journal of Fluids and Structures

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“…It was found that the shear layer instability can be excited in a certain range of frequencies and at Re as low as 100. In a very recent study Mittal, Kottaram & Kumar (2008) showed that the origin of these kind of instabilities can be traced down to very low values of Re. However, at these low Re this convective instability has a very low growth rate compared to that of the regular Kármán shedding and, therefore, it cannot be observed in the experiments.…”

Section: Introductionmentioning

confidence: 99%

Global stability of flow past a cylinder with centreline symmetry

et al. 2009

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Global absolute and convective stability analysis of flow past a circular cylinder with symmetry conditions imposed along the centreline of the flow field is carried out. A stabilized finite element formulation is used to solve the eigenvalue problem resulting from the linearized perturbation equation. All the computations carried out are in two dimensions. It is found that, compared to the unrestricted flow, the symmetry conditions lead to a significant delay in the onset of absolute as well as convective instability. In addition, the onset of absolute instability is greatly affected by the location of the lateral boundaries and shows a non-monotonic variation. Unlike the unrestricted flow, which is associated with von Kármán vortex shedding, the flow with centreline symmetry becomes unstable via modes that are associated with low-frequency large-scale structures. These lead to expansion and contraction of the wake bubble and are similar in characteristics to the low-frequency oscillations reported earlier in the literature. A global linear convective stability analysis is utilized to find the most unstable modes for different speeds of the disturbance. Three kinds of convectively unstable modes are identified. The ones travelling at very low streamwise speed are associated with large-scale structures and relatively low frequency. Shear layer instability, with relatively smaller scale flow structures and higher frequency, is encountered for disturbances travelling at relatively larger speed. For low blockage a new type of instability is found. It travels at relatively high speed and resembles a swirling flow structure. As opposed to the absolute instability, the convective instability appears at much lower Re and its onset is affected very little by the location of the lateral boundaries. Analysis is also carried out for determining the convective stability of disturbances that travel in directions other than along the free stream. It is found that the most unstable disturbances are not necessarily the purely streamwise travelling ones. Disturbances that move purely in the cross-stream direction can also be convectively unstable. The results from the linear stability analysis are confirmed by carrying out direct time integration of the linearized disturbance equations. The disturbance field shows transient growth by several orders of magnitude confirming that such flows act as amplifiers. Direct time integration of the Navier–Stokes equation is carried out to track the time evolution of both the large-scale low-frequency oscillations and small-scale shear layer instabilities. The critical Re for the onset of convective instability is compared with earlier results from local analysis. Good agreement is found.

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Onset of shear layer instability in flow past a cylinder

Cited by 14 publications

References 31 publications

Onset of global instability in the flow past a circular cylinder cascade

Onset of global instability in the flow past a circular cylinder cascade

Transition of the boundary layer on a circular cylinder in the presence of a trip

Global stability of flow past a cylinder with centreline symmetry

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