Response of the Blasius boundary layer to free-stream vorticity

Bertolotti, F. P.

doi:10.1063/1.869350

Cited by 69 publications

(56 citation statements)

References 31 publications

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“…The result of Kachanov et al (1979a,b) Influence of localised smooth steps on the instability of a boundary layer 141 was consistent with the theoretical study by Rogler & Reshotko (1975). Considering steady vortices, Kendall (1985Kendall ( , 1990Kendall ( , 1991 obtained the first qualitative data, which was compared with numerical results generated by Bertolotti (1996Bertolotti ( , 2003.…”

Section: Motivation Behind the Study Of Steps In Boundary Layerssupporting

confidence: 70%

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: Motivation Behind the Study Of Steps In Boundary Layerssupporting

confidence: 70%

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

Lombard

Sherwin

2017

J. Fluid Mech.

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“…The perturbations reach a maxinmnl at X -~ 0.02 and then decay. A similar behavior of perturbations generated by streamwise vortices was obtained in [3,4].…”

Section: Obsupporting

confidence: 64%

“…Ttm profile of the low-frequency oscillations of velocity (u' / in the boundary layer in the case of an elevated level of free-stream turbulence, which was measured by Westin et al [6], almost coincides with the velocity profiles of gTowing perturbations for X = 10 -.5 and 0.02. The profile of velocity perturbations coinckling with the experimental oim w~ts also obtained in calculation of the evolution of perturbations generated by streamwise vortices in [3,4]. This circnmstance allows us to assume that the reason for increasing oscillatious in the boundary la.~r may be both streamwise and perpendicular to the leading-edge vortices in the free stream.…”

Section: Obmentioning

confidence: 98%

“…It is ~ussu,ned that these streaky structures appear as a resul: ~ 1)enetration of ~x)rtices from the external flow into the boundary layer and their subsequent amplificat~,,a in it. Th~;refore, the solution of the t)rot)lem of recel)tivity of the 1)oundary layer to vortex disturbances is an important component in developing the theory of the laminar-turbulent transition in the case of an elevated level of t'ree-stream turbulence.This problem ha.s been sol~vd only for the particular case of interaction of streamwise vortices with tile boundary layer on a fiat plate [3,4]. This is tile siml)lest case, since tim free-stream vorticity field is not distorted by tile flow near the leading edge.…”

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confidence: 98%

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Receptivity of the boundary layer on a flat plate with a blunted leading edge to steady nonuniformity of the free stream

Ustinov¹

2000

J Appl Mech Tech Phys

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Introduction. In the case of a high level of free-stream turbulence (0.1% < ~t < 5%). the laminarturbulent transitiou occurs without fornmtion of the Tolhnien-Schlichting waves [1]. Instead of them. the growth of low-frequency perturbations of velocity is observed. Flow visualization shows that these 1)erturbations are narrow streaks exteuded in the streamwise direction [2]. It is ~ussu,ned that these streaky structures appear as a resul: ~ 1)enetration of ~x)rtices from the external flow into the boundary layer and their subsequent amplificat~,,a in it. Th~;refore, the solution of the t)rot)lem of recel)tivity of the 1)oundary layer to vortex disturbances is an important component in developing the theory of the laminar-turbulent transition in the case of an elevated level of t'ree-stream turbulence.This problem ha.s been sol~vd only for the particular case of interaction of streamwise vortices with tile boundary layer on a fiat plate [3,4]. This is tile siml)lest case, since tim free-stream vorticity field is not distorted by tile flow near the leading edge. However, such a deformation involves a(htitional amplification of pertltrbations due to the exi)ansion of vortex filaments [5]. Tile gTeatest amI)lification is experienced by I), :, bations whose vortex lines intersect tile lea(ting edge. Hence, these perturbations (and not tile streamwise vortices) should generate the streaky structure most effectively. It is shown in [5] that vorticity perpendicular to the leading edge (or nonuniformity of tile velocity profile in the spanwise (tirectit)tt) can even lead to a local separation of tile boundary layer. The analysis [5] was made for large-scale disturbances of small but finite amplitu(le. Under tim assumt)tions accel)ted, the development of disturbances is actually inviscid, and tile governing influence is exerted by nonlinear effects. However, it follows from the exl)erimental results of XNestin et al. [6] that the transverse size of the streaky structure is small, and viscosity plays a significant role in the development of this structure. In addition, the aml)litude of perturbations observed in [6] is small for manif'estation of strong nonlinear effects. In the I)resent work, the I)robleIn of interaction of a nonuniform flow with the boundary layer is solved under tile folh)wing ~lssumptions: the characteristic size of disturban('es is assumed to be of the order of the 1)oun(lary-layer thickness and the evolution of (listurbances is linear in terms of their amplitude.

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“…The receptivity process of streaks is considered in detail by Bertolotti [5], who generates an inflow condition for steady vortices by seeking self-similar solutions that satisfy the governing equations to within the desired tolerance in a sufficiently large neighborhood of the leading edge of the plate. This inflow condition is then used in a PSE (Parabolic Stability Equations) solver to find the downstream development of the streaks.…”

Section: Discussionmentioning

confidence: 99%

Optimal Disturbances in Boundary Layers

Andersson

Berggren

Henningson

1998

Computational Methods for Optimal Design and Control

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Streamwise streaks are ubiquitous in transitional boundary layers, particularly when subjected to freestream turbulence. Using the steady boundary-layer approximation, we numerically calculate the upstream disturbances experiencing maximum spatial energy growth. The calculations use techniques commonly employed when solving optimal-control problems for distributed parameter systems. The calculated optimal disturbances consist of streamwise vortices developing into streamwise streaks. The maximum possible energy growth was found to scale linearly with the distance from the leading edge. Based on this result, we propose a simple model for prediction of transition location. Available experiments have been used to correlate the single constant appearing in the model.

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Response of the Blasius boundary layer to free-stream vorticity

Cited by 69 publications

References 31 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

Receptivity of the boundary layer on a flat plate with a blunted leading edge to steady nonuniformity of the free stream

Optimal Disturbances in Boundary Layers

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