Global stability of the two-dimensional flow over a backward-facing step

Lanzerstorfer, Daniel; Kuhlmann, Hendrik C.

doi:10.1017/jfm.2011.399

Cited by 51 publications

(72 citation statements)

References 42 publications

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“…the smallest Re for which one global mode becomes unstable, Re{σ} 0) and corresponding spanwise wavenumber β c . Results are given in table 1 and show an excellent agreement with those of Barkley et al (2002) and Lanzerstorfer & Kuhlmann (2012), with differences smaller than 0.5%. We also looked at the positions of reattachment and separation points (x lr , x us , x ur ) (characterised by zero wall shear stress, see fig.…”

Section: Numerical Methods and Validationmentioning

confidence: 54%

“…Barkley et al (2002) performed a three-dimensional linear stability analysis for a stepto-outlet expansion ratio Γ = 0.5 and showed the three-dimensional character of the first globally unstable mode at Re c = 748, the flow remaining globally stable to twodimensional perturbations due to the convective nature of the shear layer instability. Lanzerstorfer & Kuhlmann (2012) found Re c = 714 for Γ = 0.5, and extended the stability analysis to smaller and larger expansion ratios. Blackburn et al (2008) studied convective instabilities for Γ = 0.5.…”

Section: Introductionmentioning

confidence: 65%

“…Table 1. Critical Reynolds number and spanwise wavenumber (Rec, βc) for different expansion ratios Γ and entrance lengths Lin: (a) Barkley et al (2002), (b) Lanzerstorfer & Kuhlmann (2012), (c) present study.…”

Section: Sensitivity Of Harmonic and Stochastic Gainmentioning

confidence: 91%

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Sensitivity and open-loop control of stochastic response in a noise amplifier flow: the backward-facing step

Boujo

Gallaire

2014

J. Fluid Mech.

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The two-dimensional backward-facing step flow is a canonical example of noise amplifier flow: global linear stability analysis predicts that it is stable, but perturbations can undergo large amplification in space and time as a result of non-normal effects. This amplification potential is best captured by optimal transient growth analysis, optimal harmonic forcing, or the response to sustained noise. In view of reducing disturbance amplification in these globally stable open flows, a variational technique is proposed to evaluate the sensitivity of stochastic amplification to steady control. Existing sensitivity methods are extended in two ways to achieve a realistic representation of incoming noise: (i) perturbations are time-stochastic rather than time-harmonic, (ii) perturbations are localised at the inlet rather than distributed in space. This allows for the identification of regions where small-amplitude control is the most effective, without actually computing any controlled flows. In particular, passive control by means of a small cylinder and active control by means of wall blowing/suction are analysed for Reynolds number Re = 500 and step-to-outlet expansion ratio Γ = 0.5. Sensitivity maps for noise amplification appear largely similar to sensitivity maps for optimal harmonic amplification at the most amplified frequency. This is observed at other values of Re and Γ too, and suggests that the design of steady control in this noise amplifier flow can be simplified by focusing on the most dangerous perturbation at the most dangerous frequency.Key words: Authors should not enter keywords on the manuscript, as these must be chosen by the author during the online submission process and will then be added during the typesetting process (see http://journals.cambridge.org/data/relatedlink/jfm-keywords.pdf for the full list)

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Section: Numerical Methods and Validationmentioning

confidence: 54%

Section: Introductionmentioning

confidence: 65%

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Sensitivity and open-loop control of stochastic response in a noise amplifier flow: the backward-facing step

Boujo

Gallaire

2014

J. Fluid Mech.

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“…The BiGlobal stability analysis method is proposed to take the advantage of this feature by assuming the perturbation in the form of a normal mode in the spanwise direction, thus the primary perturbation characteristics in the cross-sectional (x-y) plane are preserved and the computational cost is significantly reduced. The BiGlobal linear stability analysis has been employed for a number of physical problems, such as the flow in a channel, [19][20][21][22] over a backward-facing step [23][24][25] or a bluff body. 26 It has also been employed for the problem of flow past an isolated airfoil.…”

Section: Introductionmentioning

confidence: 99%

BiGlobal linear stability analysis on low-Re flow past an airfoil at high angle of attack

Zhang

Samtaney

2016

Physics of Fluids

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CitationBiGlobal linear stability analysis on low-Re flow past an airfoil at high angle of attack 2016, 28 (4) We perform BiGlobal linear stability analysis on flow past a NACA0012 airfoil at 16• angle of attack and Reynolds number ranging from 400 to 1000. The steady-state two-dimensional base flows are computed using a well-tested finite difference code in combination with the selective frequency damping method. The base flow is characterized by two asymmetric recirculation bubbles downstream of the airfoil whose streamwise extent and the maximum reverse flow velocity increase with the Reynolds number. The stability analysis of the flow past the airfoil is carried out under very small spanwise wavenumber β = 10 −4 to approximate the two-dimensional perturbation, and medium and large spanwise wavenumbers ( β = 1-8) to account for the three-dimensional perturbation. Numerical results reveal that under small spanwise wavenumber, there are at most two oscillatory unstable modes corresponding to the near wake and far wake instabilities; the growth rate and frequency of the perturbation agree well with the two-dimensional direct numerical simulation results under all Reynolds numbers. For a larger spanwise wavenumber β = 1, there is only one oscillatory unstable mode associated with the wake instability at Re = 400 and 600, while at Re = 800 and 1000 there are two oscillatory unstable modes for the near wake and far wake instabilities, and one stationary unstable mode for the monotonically growing perturbation within the recirculation bubble via the centrifugal instability mechanism. All the unstable modes are weakened or even suppressed as the spanwise wavenumber further increases, among which the stationary mode persists until β = 4. C 2016 AIP Publishing LLC. [http://dx

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“…In stability analyses, the two-dimensional flow was reported to be absolutely stable up to a Reynolds number of at least Re = 600 and convectively unstable for at least Re > 525 (Kaiktsis et al 1996). The dependence of instabilities on the expansion ratio has been studied and centrifugal instability, elliptic instability and lift-up mechanisms are identified when reducing the expansion ratio from 0.972 to 0.25 (Lanzerstorfer & Kuhlmann 2012). In the current work, the Reynolds number is defined using the upstream centreline velocity and the step height and all cited results are converted to this definition.…”

Section: Flow Past a Backward-facing Stepmentioning

confidence: 99%

Effects of base flow modifications on noise amplifications: flow past a backward-facing step

Mao

2015

J. Fluid Mech.

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Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. Amplifications of flow past a backward-facing step to optimal inflow and initial perturbations are investigated at Reynolds number 500. Two mechanisms of receptivity to inflow noise are identified: the bubble-induced inflectional point instability and the misalignment effect downstream of the secondary bubble. The further development of the misalignment results in decay of perturbations from x = 28 (the step is located at x = 0), as has been observed in previous non-normality studies , and eventually limits the receptivity. The receptivity is found to maximise at inflow perturbation frequency ω = 0.50 and spanwise wavenumber β = 0, where the inflow noise takes full advantage of both mechanisms and is amplified over two orders in terms of the velocity magnitude. In direct numerical simulations (DNS) of the flow perturbed by optimal or random inflow noise, vortex shedding, flapping of bubbles, three-dimensionality and turbulence are observed in succession as the magnitude of the inflow noise increases. Similar features of linear and nonlinear receptivity are observed at higher Reynolds number. The Strouhal number of the bubble flapping is 0.08, at which the receptivity to inflow noise reaches maximum. This Strouhal number is close to reported values extracted from DNS or large eddy simulations at larger Reynolds number (Le et al. 1997;Kaiktsis et al. 1996;Métais 2001;Wee et al. 2004). Methodologies to further clarify the mechanisms of receptivity and suppress the noise amplifications by modifying the base flow using a linearly optimal body force is proposed. It is noticed that the mechanisms of optimal noise amplifications are fully revealed in the distribution of the base flow modification, which weakens the bubble instabilities and the misalignment effects and subsequently reduces receptivity significantly. Comparing the base flow modifications with respect to amplifications to inflow and initial perturbations, it is found that the maximum receptivity to initial perturbations is highly correlated with the receptivity to inflow noise at the optimal frequency ω = 0.50 while the correlation reduces as the inflow frequency deviates from this optimal value.

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Global stability of the two-dimensional flow over a backward-facing step

Cited by 51 publications

References 42 publications

Sensitivity and open-loop control of stochastic response in a noise amplifier flow: the backward-facing step

Sensitivity and open-loop control of stochastic response in a noise amplifier flow: the backward-facing step

BiGlobal linear stability analysis on low-Re flow past an airfoil at high angle of attack

Effects of base flow modifications on noise amplifications: flow past a backward-facing step

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