Stabilization of absolute instability in spanwise wavy two-dimensional wakes

Hwang, Yongyun; Kim, Jin-Sung; Choi, Haecheon

doi:10.1017/jfm.2013.270

Cited by 51 publications

(80 citation statements)

References 64 publications

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“…We did not separate the effects of modifying any specific term in Navier-Stokes equations. Our arguments for spanwise wavelength selection are hence slightly different than the ones described in the local analysis of Hwang et al (2013), detailing the stabilising mechanism of a fixed velocity profile. However, the two analysis are not contradictory, as these two mechanisms might co-exist in a real flow.…”

Section: B For Illustration)contrasting

confidence: 56%

“…This corresponds to a wavelength of around 6. The observed optimal wavelengths for a cylinder flow are longer: Kim & Choi (2005) obtained 10-12 in our nondimensional coordinates, and Hwang et al (2013) 12 in our coordinates. The physical reason for the difference between optimal wavelengths in these two configurations could be the confinement.…”

Section: B For Illustration)mentioning

confidence: 56%

“…In the earlier works (Kim & Choi 2005;Hwang et al 2013), in-phase distribution was observed to be much more efficient in stabilizing the flow than out-of-phase distribution, but this effect was not explained. The σ 2 derived in the present work (Eq.…”

Section: B For Illustration)mentioning

confidence: 81%

“…For the purpose of this test, we have chosen the same artificially modified 1D base flow profile as Hwang et al (2013), multiplied by a Gaussian in the streamwise direction:…”

Section: Verification Of Quadratic Behaviourmentioning

confidence: 99%

“…In order to explain these effects, Hwang et al (2013) examined the local absolute instability of a fixed streamwise base flow profile (a wake profile), modified sinusoidally in the spanwise direction. The absolute instability was suppressed by spanwise wavy modifications at medium to long wavelengths, while short wavelengths had a strongly destabilizing effect, the latter not observed in the DNS (Kim & Choi 2005).…”

Section: Introductionmentioning

confidence: 99%

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Second-order perturbation of global modes and implications for spanwise wavy actuation

et al. 2014

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Sensitivity analysis has successfully located the most efficient regions in which to apply passive control in many globally unstable flows. As is shown here and in previous studies, the standard sensitivity analysis, which is linear (1 st order) with respect to the actuation amplitude, predicts that steady spanwise wavy alternating actuation/modification has no effect on the stability of planar flows, because the eigenvalue change integrates to zero in the spanwise direction. In experiments however, spanwise wavy modification has been shown to stabilize the flow behind a cylinder quite efficiently.In this paper, we generalize sensitivity analysis by examining the eigenvalue drift (including stabilization/destabilization) up to 2 nd order in the perturbation, and show how the 2 nd order eigenvalue changes can be computed numerically by overlapping the adjoint eigenfunction with the 1 st order global eigenmode correction, shown here for the first time. We confirm the prediction against a direct computation, showing that the eigenvalue drift due to a spanwise wavy base flow modification is of 2 nd order. Further analysis reveals that the 2 nd order change in the eigenvalue arises through a resonance of the original (2D) eigenmode with other unperturbed eigenmodes that have the same spanwise wavelength as the base flow modification. The eigenvalue drift due to each mode interaction is inversely proportional to the distance between the eigenvalues of the modes (which is similar to resonance), but also depends on mutual overlap of direct and adjoint eigenfunctions (which is similar to pseudoresonance). By this argument, and by calculating the most sensitive regions identified by our analysis, we explain why an in-phase actuation/modification is better than an out-of-phase actuation for control of wake flows by spanwise wavy suction and blowing. We also explain why wavelengths several times longer than the wake thickness are more efficient than short wavelengths.

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Section: B For Illustration)contrasting

confidence: 56%

Section: B For Illustration)mentioning

confidence: 56%

Section: B For Illustration)mentioning

confidence: 81%

“…For the purpose of this test, we have chosen the same artificially modified 1D base flow profile as Hwang et al (2013), multiplied by a Gaussian in the streamwise direction:…”

Section: Verification Of Quadratic Behaviourmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Second-order perturbation of global modes and implications for spanwise wavy actuation

et al. 2014

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The Role of Spanwise Forcing on Vortex Shedding Suppression in a Flow Past a Cylinder

Rocco

Sherwin

2015

Fluid Mechanics and Its Applications

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Flow control design inspired by linear stability analysis

Camarri

2015

Acta Mech

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In the recent literature, a growing number of research papers have been dedicated to applying the techniques of global stability and sensitivity analysis to the design of flow controls. The controls that are designed in this way are mainly passive or open-loop controls. Among those, we consider here controls that are aimed at linearly stabilizing flow configurations which would be otherwise globally unstable. In particular, a review of the literature on flow controls designed on the basis of stability and sensitivity analysis is presented. The mentioned methods can be rigorously applied to relatively simple flow regimes, typically observed at low values of the Reynolds number. In this respect, the recent literature also demonstrates a large interest in the application of the same methods for the control of coherent large-scale flow structures in turbulent flows, as, for instance, the quasiperiodic shedding of vortices in turbulent wakes. The papers dedicated to this subject are also reviewed here. Finally, all the described methods imply the solution of eigenvalue problems which are at the state-of-the-art for computational complexity. On the one hand, there are attempts to reduce the complexity of the involved computational problems by applying local stability analysis, and some examples are illustrated. On the other hand, recent advances in numerical methods, also concisely reviewed here, allow the manipulation of large eigenvalue problems and greatly simplify the development of numerical tools for stability and sensitivity analysis of complex flow models, often built using existing fluid dynamics codes

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Stabilization of absolute instability in spanwise wavy two-dimensional wakes

Cited by 51 publications

References 64 publications

Second-order perturbation of global modes and implications for spanwise wavy actuation

Second-order perturbation of global modes and implications for spanwise wavy actuation

The Role of Spanwise Forcing on Vortex Shedding Suppression in a Flow Past a Cylinder

Flow control design inspired by linear stability analysis

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