Impact of Forward-Facing Steps on Laminar-Turbulent Transition in Transonic Flows

Edelmann, Christopher A.; Rist, Ulrich

doi:10.2514/1.j053529

Cited by 42 publications

(28 citation statements)

References 10 publications

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“…The results from the linear analysis, and more generally the results from the DNS presented in § 4, underline the attractiveness of replacing a forward-facing sharp step (γ = 1) with largê h by a smooth one (γ < 1) because the smooth step with the sameĥ does not lead to a separation bubble. We attribute the discrepancy between the current findings and the work of Edelmann & Rist (2015) to a step-induced separation bubble that has a strong destabilising effect on the TS mode. Furthermore, for a forward-facing smooth step of fixed height, the position of the global maximum value of a contour varies with respect to the given frequency, which is consistent with the relative position of the step with respect to the position of the upper branch when changing frequency in the neutral curve diagram (figure 7(g,i,k) for example).…”

Section: 3contrasting

confidence: 99%

“…In contrast, a strong destabilisation of the TS wave by the sharp step (γ = 1) for low frequency is reported by Edelmann & Rist (2015), where the separation bubble induces a strong increase in N-factor from N = 4 to N = 6 because of the existence of separation bubbles in front of the step. This contrasts with the weak destabilisation influence of a smooth step on the TS wave in a boundary layer, where negligible variation of the N-factor can be seen in figure 13 even for a largeĥ > 20 % step height.…”

Section: 3mentioning

confidence: 91%

“…Recently, through further numerical calculations, Edelmann & Rist (2015) observed that, for subsonic Mach numbers and larger height (h/δ * = 0.94 orĥ = 33 %), two separation bubbles, in front and on top of the step, were observed and strong amplification of the disturbances was found in front of and behind the step. The results from the linear analysis, and more generally the results from the DNS presented in § 4, underline the attractiveness of replacing a forward-facing sharp step (γ = 1) with largê h by a smooth one (γ < 1) because the smooth step with the sameĥ does not lead to a separation bubble.…”

Section: 3mentioning

confidence: 99%

“…Ability of smooth steps to amplify the very low-frequency TS waves at F = 42 The studies by Wörner et al (2003) and Edelmann & Rist (2015) considered the effect of low-frequency TS modes for a long range from the leading edge of the flat plate with Re δ * = 2200. In Edelmann & Rist (2015), the N-factor, defined as N = ln(A/A 0 ), got close to the transition criterion of N = 8.…”

Section: 3mentioning

confidence: 99%

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Influence of localised smooth steps on the instability of a boundary layer

Lombard

Sherwin

2017

J. Fluid Mech.

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We consider a smooth, spanwise-uniform forward-facing step defined by a Gauss error function of height 4 %-30 % and four times the width of the local boundary layer thickness δ 99 . The boundary layer flow over a smooth forward-facing stepped plate is studied with particular emphasis on stabilisation and destabilisation of the twodimensional Tollmien-Schlichting (TS) waves and subsequently on three-dimensional disturbances at transition. The interaction between TS waves at a range of frequencies and a base flow over a single or two forward-facing smooth steps is conducted by linear analysis. The results indicate that for a TS wave with a frequency F ∈ [140, 160] (F = ων/U 2 ∞ × 10 6 , where ω and U ∞ denote the perturbation angle frequency and free-stream velocity magnitude, respectively, and ν denotes kinematic viscosity), the amplitude of the TS wave is attenuated in the unstable regime of the neutral stability curve corresponding to a flat plate boundary layer. Furthermore, it is observed that two smooth forward-facing steps lead to a more acute reduction of the amplitude of the TS wave. When the height of a step is increased to more than 20 % of the local boundary layer thickness for a fixed width parameter, the TS wave is amplified, and thereby a destabilisation effect is introduced. Therefore, the stabilisation or destabilisation effect of a smooth step is typically dependent on its shape parameters. To validate the results of the linear stability analysis, where a TS wave is damped by the forward-facing smooth steps direct numerical simulation (DNS) is performed. The results of the DNS correlate favourably with the linear analysis and show that for the investigated frequency of the TS wave, the K-type transition process is altered whereas the onset of the H-type transition is delayed. The results of the DNS suggest that for the perturbation with the non-dimensional frequency parameter F = 150 and in the absence of other external perturbations, two forward-facing smooth steps of height 5 % and 12 % of the boundary layer thickness delayed the H-type transition scenario and completely suppressed for the K-type transition. By considering Gaussian white noise with both fixed and random phase shifts, it is demonstrated by DNS that transition is postponed in time and space by two forward-facing smooth steps.

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Section: 3contrasting

confidence: 99%

Section: 3mentioning

confidence: 91%

Section: 3mentioning

confidence: 99%

Section: 3mentioning

confidence: 99%

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Influence of localised smooth steps on the instability of a boundary layer

Lombard

Sherwin

2017

J. Fluid Mech.

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“…Further studies on surface deformations have examined the effect of humps [29][30][31][32], dimples [33], corrugation [34], steps [35][36][37][38][39], roughness distributions [40,41], and deep gaps [42]. More recently, Xu et al [43] studied the impact of three-dimensional surface indentations on the destabilization of TS disturbances, where separation bubbles could form within sufficiently deformed indentations.…”

Section: Introductionmentioning

confidence: 99%

Effect of Small Surface Deformations on the Stability of Tollmien–Schlichting Disturbances

et al. 2018

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The effect of a small Gaussian shaped deformation on the development and growth of Tollmien-Schlichting disturbances on an unswept airfoil is investigated. A broad range of gap depths and widths is modeled that can be sufficient to generate localized pockets of reverse flow. Boundary-layer profiles are computed using a Navier-Stokes solver, permitting a thorough investigation of all configurations considered. The linear stability of Tollmien-Schlichting waves is then examined using parabolized stability equations and linearized Navier-Stokes formulations, with the former method giving excellent agreement with the latter for all disturbances studied, including within separated boundary layers. Tollmien-Schlichting disturbances are amplified by deeper and wider gaps, with a correlation derived by relating the increase in the N factor with the gap dimensions and freestream Reynolds number.

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Direct Numerical Simulations of Tollmien-Schlichting Disturbances in the Presence of Surface Irregularities

Tocci

Chauvat

Hein

et al. 2021

IUTAM Laminar-Turbulent Transition

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A realistic aircraft wing is not expected to be an ideally smooth surface: the influence of junctions or wing panels must be taken into account in the laminar wing design. The presence of these spanwise invariant two-dimensional surface irregularities further amplifies the boundary-layer streamwise instabilities existing on a smooth surface, potentially causing an early transition to turbulence. In the present work, the effect of steps, gaps and humps on the development of Tollmien-Schlichting (TS) waves in an incompressible boundary layer is studied using direct numerical simulations (DNS). For a specific height we investigated several shapes of the geometric irregularity. Depending on their shape the surface imperfections give rise to a local separation bubble which interacts with the oncoming TS waves: for the frequency considered, all the surface irregularities have a destabilizing effect, with the rectangular hump case being the most dangerous one.

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Impact of Forward-Facing Steps on Laminar-Turbulent Transition in Transonic Flows

Cited by 42 publications

References 10 publications

Influence of localised smooth steps on the instability of a boundary layer

Influence of localised smooth steps on the instability of a boundary layer

Effect of Small Surface Deformations on the Stability of Tollmien–Schlichting Disturbances

Direct Numerical Simulations of Tollmien-Schlichting Disturbances in the Presence of Surface Irregularities

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