The evolution of Tollmien-Schlichting waves near a leading edge. Part 2. Numerical determination of amplitudes

Goldstein, M. E.; Sockol, P. M.; Sanz, José María Serrano

doi:10.1017/s0022112083000853

Cited by 114 publications

(203 citation statements)

References 4 publications

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“…on various 2D and 3D streamwise-localised surface roughness elements resulting in excitation of various 2D and 3D non-stationary instability modes (such as TS modes, crossflow modes, Görtler modes, etc.) (Gaster 1965;Murdock 1980;Goldstein 1983;Ruban 1984;Goldstein 1985;Goldstein & Hultgren 1987;Kerschen 1989Kerschen , 1990Hall 1990;Denier, Hall & Seddougui 1991;Bassom & Hall 1994;Choudhari 1994;Saric 1994;Bassom & Seddougui 1995;Duck, Ruban & Zhikharev 1996;Dietz 1999;Wu 2001b;Saric et al 2002;Templelmann 2011). The receptivity mechanism shows that the deviation on the length scale of eigenmodes from a smooth surface can excite TS waves by interacting with free-stream disturbances or acoustic noise.…”

Section: Motivation Behind the Study Of Steps In Boundary Layersmentioning

confidence: 99%

“…Subsequently, the theoretical approach was developed by Choudhari & Streett (1992) and Crouch (1994) for localised and distributed vortex receptivity. Based on asymptotic theory, Goldstein (1983Goldstein ( , 1985, Ruban (1985) and Wu (2001a) carried out the studies for acoustic receptivity and Kerschen (1990), Goldstein & Leib (1993), Choudhari (1994) and Wu (2001a,b) for localised and distributed boundary layer receptivity. A detailed review work was done in the introduction of Borodulin et al (2013).…”

Section: Motivation Behind the Study Of Steps In Boundary Layersmentioning

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: Motivation Behind the Study Of Steps In Boundary Layersmentioning

confidence: 99%

Section: Motivation Behind the Study Of Steps In Boundary Layersmentioning

confidence: 99%

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

Lombard

Sherwin

2017

J. Fluid Mech.

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“…As ξ → ∞ the eigensolutions develop a two-layer behaviour, the inner layer of width O(ξ −1/2 ) and the main layer of O (1). In the inner layer the variables G = (2ξ) 1/2 ϕ 2 and m = (2ξ) 1/2 N are introduced, and the ith eigensolution takes the form,…”

Section: Formulation Of Equations and Body Geometrymentioning

confidence: 99%

“…In the development of the unsteady boundary layer flow there exists two distinct streamwise regions whose solutions overlap [1,2]. In the first region the linearised unsteady boundary layer equation (LUBLE) is satisfied and in the second the motion is governed by the Orr-Sommerfeld equation.…”

Section: Introductionmentioning

confidence: 99%

Receptivity for a Flat Plate with a Rounded Leading-Edge

Nichols

Hammerton

2000

Laminar-Turbulent Transition

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Abstract. The receptivity due to the interaction of an acoustic wave with a body which has a rounded leading edge and a region of low wall shear is considered. The body of interest is formed by a line source in a uniform stream. The nose radius, r * n , of this body is characterised in the theory through a parameter A = 2ω r * n /3U∞ where ω is the frequency of the acoustic wave and U∞ the mean flow speed. By comparing asymptotic and numerical results, the receptivity coefficient, C1, is calculated. The receptivity coefficient is seen to decrease dramatically with a small increase in nose radius, a local rise occurs about A = 0.035 and it then gradually declines to nearly zero when A = 0.1.

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“…His works have been focused on localised disturbances either from the leading edge ( [6]) or from changes in the wall geometry ( [7]) which includes local surface roughness. Goldstein [6] also recognised that three general classes of receptivity regions might exist: (i) the leading-edge region where the basic boundary layer is thinner and grows rapidly, and the motion is governed by the unsteady boundary layer equation, (ii) regions which are much further downstream where the boundary layer is forced to make a rapid adjustment, and the motion is governed by the Orr-Sommerfield equation, and finally (iii) an overlap region where the TS wave solutions of regions 1 and 2 match asymptotically.…”

Section: Introductionmentioning

confidence: 99%

Thermal receptivity of free convective flow from a heated vertical surface: Linear waves

Paul

Rees

Wilson

2008

International Journal of Thermal Sciences

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Numerical techniques are used to study the receptivity to small-amplitude thermal disturbances of the boundary layer flow of air which is induced by a heated vertical flat plate. The fully elliptic nonlinear, time-dependent NavierStokes and energy equations are first solved to determine the steady state boundary-layer flow, while a linearised version of the same code is used to determine the stability characteristics. In particular we investigate (i) the ultimate fate of a localised thermal disturbance placed in the region near the leading edge and (ii) the effect of small-scale surface temperature oscillations as means of understanding the stability characteristics of the boundary layer. We show that there is a favoured frequency of excitation for the time-periodic disturbance which maximises the local response in terms of the local rate of heat transfer. However the magnitude of the favoured frequency depends on precisely how far from the leading edge the local response is measured. We also find that the instability is advective in nature and that the response of the boundary layer consists of a starting transient which eventually leaves the computational domain, leaving behind the large-time time-periodic asymptotic state. Our detailed numerical results are compared with those obtained using parallel flow theory.

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The evolution of Tollmien-Schlichting waves near a leading edge. Part 2. Numerical determination of amplitudes

Cited by 114 publications

References 4 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 for a Flat Plate with a Rounded Leading-Edge

Thermal receptivity of free convective flow from a heated vertical surface: Linear waves

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