Instability of the separated shear layer in flow past a cylinder: Forced excitation

Mittal, Sanjay

doi:10.1002/fld.1548

Cited by 5 publications

(3 citation statements)

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“…He observed the shear layer instability to occur as low as Re = 350. Through computations, Mittal (2008) investigated the receptivity of the separated shear layer for the Re = 300 flow past a cylinder to pulsatile inflow. It was found that the shear layer instability can be excited in a certain range of frequencies and at Re as low as 100.…”

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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Section: Introductionmentioning

confidence: 99%

Global stability of flow past a cylinder with centreline symmetry

et al. 2009

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“…The computed eigenvalue with the largest real part corresponds to the primary instability of the flow, and its imaginary part is the frequency through which the disturbance periodically grows over time. Such numerical eigenvalue analysis has recently been applied to a number of flow problems to find global stability limits, where the cylinder problem generally served as a benchmark test [10,13,14].…”

Section: Recent Workmentioning

confidence: 99%

“…A number of instability modes have been identified with cylinder flow associated with its wake, separated shear layer, boundary layer, and three-dimensional instabilities along its span [11][12][13]. Each mode adds a time varying component to the flow and can generally be observed above a critical Reynolds number (Re).…”

Section: Introductionmentioning

confidence: 99%

Numerical Investigation of the Evolution of Vortex Instability in a 2-D Compressible Flow over a Cylinder

Rohde¹

2011

20th AIAA Computational Fluid Dynamics Conference

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This paper presents a computational fluid dynamics (CFD) study of 2-D flow over a cylinder at a Mach number of 0.3 and diameter based Reynolds numbers ranging between 50 and 1000. The flow simulation was marched in time from an impulsive start and reveals the evolution of vortex instability. After the cylinder has traveled between 100 and 1000 diameters, alternate vortex shedding begins, and a von Karman vortex street develops in the wake. Throughout the initial transient of the flow, the lift coefficient shows periodic oscillation with steady amplitude growth rates from machine precision until periodic vortex shedding is reached, and a distinct frequency shift is observed at the onset of vortex shedding at higher Reynolds numbers. The numerical algorithm is based on a finite volume description of the unsteady, compressible Navier Stokes equations. The inviscid subset of the equations is modeled according to the total variation diminishing (TVD) principle with the numerical viscosity control parameter set to zero. No turbulence modeling was implemented, since the flow is below the transition Reynolds number of 300,000. The accuracy of the scheme is second order in space and first order in time.

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