Secondary instability of roughness-induced transient growth

Denissen, Nicholas; White, Edward B.

doi:10.1063/1.4829482

Cited by 37 publications

(22 citation statements)

References 33 publications

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“…As can be seen, all the modes are mostly localised along the central low-speed region, differently from the case of non-isolated cylinder analysed in the previous section for which a large part of the mode migrates on the outer streaks downstream of the roughness element. The crucial importance of such low-speed regions in the roughness-induced transition process to turbulence has already been underlined by previous studies such as the experimental work by Asai et al (2002Asai et al ( , 2007, or the numerical investigation by Brandt (2007) and Denissen & White (2013). More recently, several different authors have observed a similar behaviour in the case of roughness-induced compressible boundary layer flows (Bernardini et al 2012;Balakumar & Kegerise 2013;Iyer & Mahesh 2013;de Tullio et al 2013;Subbareddy et al 2014).…”

Section: Influence Of the Aspect Ratiosupporting

confidence: 55%

“…It is worthy to note finally that, relatively far from the roughness element, the shapes of these global modes visualized in different X = constant planes are very similar to that found by Brandt (2007) and more recently by de and Denissen & White (2013) using a local stability approach. Indeed, due the strong predominance of the base flow streamwise component and its nearly parallel nature far from the roughness element, it is expected that the two approaches, global and local, give similar results regarding the shape of the modes in the almost parallel parts of the flow.…”

Section: Analysis Of the Modessupporting

confidence: 51%

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Investigation of the roughness-induced transition: global stability analyses and direct numerical simulations

et al. 2014

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. Investigation of the roughness-induced transition: global stability analyses and direct numerical simulations. Journal of Fluid Mechanics, Cambridge University Press (CUP), 2014, 760, pp.175-211. 10.1017/jfm.2014.589. hal-01086744 Science Arts & Métiers (SAM)is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible. The linear global instability and resulting transition to turbulence induced by an isolated cylindrical roughness element of height h and diameter d immersed within an incompressible boundary layer flow along a flat plate is investigated using the joint application of direct numerical simulations and fully three-dimensional global stability analyses. For the range of parameters investigated, base flow computations show that the roughness element induces a wake composed of a central low-speed region surrounded by a threedimensional shear layer and a pair of low-and high-speed streaks on each of its sides. Results from the global stability analyses highlight the unstable nature of the central low-speed region and its crucial importance in the laminar-turbulent transition process. It is able to sustain two different global instabilities: a sinuous and a varicose one. Each of these globally unstable modes are related to a different physical mechanism. While the varicose mode finds its root in the instability of the whole three-dimensional shear layer surrounding the central low-speed region, the sinuous instability turns out to be similar to the von Kármán instability in the two-dimensional cylinder wake and finds its root in the lateral shear layers of the separated zone. The aspect ratio of the roughness element plays a key role on the selection of the dominant instability. Indeed, whereas the flow over thin cylindrical roughness elements transitions due to a sinuous instability of the near-wake, for larger roughness element the varicose instability of the central low-speed region turns out to be the dominant one. Direct numerical simulations of the flow past an aspect ratio η = 1 (with η = d/h) roughness element sustaining only the sinuous instability have revealed that the bifurcation occurring in this particular case is supercritical. Finally, comparison of the transition thresholds predicted by global linear stability analyses with the von Doenhoff-Braslow transition diagram provides qualitatively good agreements.

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Section: Influence Of the Aspect Ratiosupporting

confidence: 55%

Section: Analysis Of the Modessupporting

confidence: 51%

Investigation of the roughness-induced transition: global stability analyses and direct numerical simulations

et al. 2014

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“…Biglobal stability analysis to investigate roughness wakes in planes perpendicular to the main flow was mainly used in supersonic boundary layers, see, e.g. Groskopf, Kloker & Marxen (2010); recent studies for subsonic boundary-layer flow are reported by Denissen & White (2013) and Shin, Rist & Krämer (2015). The two-dimensional unstable eigenfunctions were either of varicose or sinuous type, where a dominant varicose mode could be connected to the three-dimensional shear layer developing downstream of the roughness.…”

Section: Introductionmentioning

confidence: 98%

Mechanisms of flow tripping by discrete roughness elements in a swept-wing boundary layer

Kurz

Kloker

2016

J. Fluid Mech.

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The effects of a spanwise row of finite-size cylindrical roughness elements in a laminar, compressible, three-dimensional boundary layer on a wing profile are investigated by direct numerical simulations (DNS). Large elements are capable of immediately tripping turbulent flow by either a strong, purely convective or an absolute/global instability in the near wake. First we focus on an understanding of the steady near-field past a finite-size roughness element in the swept-wing flow, comparing it to a respective case in unswept flow. Then, the mechanisms leading to immediate turbulence tripping are elaborated by gradually increasing the roughness height and varying the disturbance background level. The quasi-critical roughness Reynolds number above which turbulence sets in rapidly is found to be Re kk,qcrit ≈ 560 and global instability is found only for values well above 600 using nonlinear DNS; therefore the values do not differ significantly from two-dimensional boundary layers if the full velocity vector at the roughness height is taken to build Re kk . A detailed simulation study of elements in the critical range indicates a changeover from a purely convective to a global instability near the critical height. Finally, we perform a three-dimensional global stability analysis of the flow field to gain insight into the early stages of the temporal disturbance growth in the quasi-critical and over-critical cases, starting from a steady state enforced by damping of unsteady disturbances.

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“…Alternatively, surface roughness or a wing-fuselage junction may generate perturbations in the boundary layer. While Fransson et al (2004) and White, Rice & Gökhan Ergin (2005) suggest that such perturbations do not have the character of optimal perturbations, they were shown to be even less stable than optimal ones and to exhibit secondary instability for lower streak amplitudes (Denissen & White 2013). Meneghello, Schmid & Huerre (2015) demonstrate that a strong receptivity is observed in particular for perturbations applied in the immediate vicinity of the attachment line.…”

mentioning

confidence: 97%

Secondary instability and subcritical transition of the leading-edge boundary layer

2016

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The leading-edge boundary layer (LEBL) in the front part of swept airplane wings is prone to three-dimensional subcritical instability, which may lead to bypass transition. The resulting increase of airplane drag and fuel consumption implies a negative environmental impact. In the present paper, we present a temporal biglobal secondary stability analysis (SSA) and direct numerical simulations (DNS) of this flow to investigate a subcritical transition mechanism. The LEBL is modelled by the swept Hiemenz boundary layer (SHBL), with and without wall suction. We introduce a pair of steady, counter-rotating, streamwise vortices next to the attachment line as a generic primary disturbance. This generates a high-speed streak, which evolves slowly in the streamwise direction. The SSA predicts that this flow is unstable to secondary, time-dependent perturbations. We report the upper branch of the secondary neutral curve and describe numerous eigenmodes located inside the shear layers surrounding the primary high-speed streak and the vortices. We find secondary flow instability at Reynolds numbers as low as Re ≈ 175, i.e. far below the linear critical Reynolds number Re crit ≈ 583 of the SHBL. This secondary modal instability is confirmed by our three-dimensional DNS. Furthermore, these simulations show that the modes may grow until nonlinear processes lead to breakdown to turbulent flow for Reynolds numbers above Re tr ≈ 250. The three-dimensional mode shapes, growth rates, and the frequency dependence of the secondary eigenmodes found by SSA and the DNS results are in close agreement with each other. The transition Reynolds number Re tr ≈ 250 at zero suction and its increase with wall suction closely coincide with experimental and numerical results from the literature. We conclude that the secondary instability and the transition scenario presented in this paper may serve as a possible explanation for the well-known subcritical transition observed in the leading-edge boundary layer.

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Secondary instability of roughness-induced transient growth

Cited by 37 publications

References 33 publications

Investigation of the roughness-induced transition: global stability analyses and direct numerical simulations

Investigation of the roughness-induced transition: global stability analyses and direct numerical simulations

Mechanisms of flow tripping by discrete roughness elements in a swept-wing boundary layer

Secondary instability and subcritical transition of the leading-edge boundary layer

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