Instabilität laminarer Grenzschichten an konkaven Wänden gegenüber gewissen dreidimensionalen Störungen

Görtler, Henry

doi:10.1002/zamm.19410210408

Cited by 141 publications

(70 citation statements)

References 2 publications

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“…Another aspect is their short integration time, which might not capture lowfrequency modulations of such flow structures. In accordance with experimental observations (Görtler 1941;Floryan 1991;Schülein & Trofimov 2011) as well as numerical findings (Loginov et al 2006;Grilli et al 2013), the spanwise width of each vortex pair is approximately 2 δ 0 . The spanwise width of our computational domain of L z = 4.5 δ 0 in combination with periodic boundary conditions allows flow structures with a spanwise wavelength of at most 4.5 δ 0 to be captured.…”

Section: Instantaneous and Mean Flow Organisationsupporting

confidence: 89%

“…Note that our short time LES shows a significantly lower variation of ±5.0 ⋅ 10 −5 . They found two pairs of possibly steady counter-rotating streamwise vortices originating in the proximity of the compression corner and termed them Görtler-like vortices, bearing similarities with the instability mechanism found experimentally for laminar boundary layers developing on sufficiently concave surfaces (Görtler 1941;Floryan 1991). We will resume this discussion later in this section and show that a similar mechanism exists for the current SWBLI.…”

Section: Instantaneous and Mean Flow Organisationmentioning

confidence: 58%

“…Indeed, at z δ 0 ≈ −0.4 such a flow configuration can be observed. Vortex- Smits & Dussauge (2006) and Görtler (1941).…”

Section: Instantaneous and Mean Flow Organisationmentioning

confidence: 99%

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Unsteady effects of strong shock-wave/boundary-layer interaction at high Reynolds number

2017

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We analyse the low-frequency dynamics of a high-Reynolds-number impinging shockwave/turbulent boundary-layer interaction (SWBLI) with strong mean-flow separation. The flow configuration for our grid-converged large-eddy simulations (LES) reproduces recent experiments for the interaction of a Mach 3 turbulent boundary layer with an impinging shock that nominally deflects the incoming flow by 19.6○ . The Reynolds number based on the incoming boundary layer thickness of Re δ0 ≈ 203 ⋅ 10 3 is considerably higher than in previous LES studies. The very long integration time of 3805 δ 0 U 0 allows for an accurate analysis of low-frequency unsteady effects. Experimental wallpressure measurements are in good agreement with the LES data. Both datasets exhibit the distinct plateau within the separated-flow region of a strong SWBLI. The filtered three-dimensional flow field shows clear evidence of counter-rotating streamwise vortices originating in the proximity of the bubble apex. Contrary to previous numerical results on compression ramp configurations, these Görtler-like vortices are not fixed at a specific spanwise position, but rather undergo a slow motion coupled to the separationbubble dynamics. Consistent with experimental data, power spectral densities (PSD) of wall-pressure probes exhibit a broadband and very energetic low-frequency component associated with the separation-shock unsteadiness. Sparsity-promoting dynamic mode decompositions (SPDMD) for both spanwise-averaged data and wall-plane snapshots yield a classical and well-known low-frequency breathing mode of the separation bubble, as well as a medium-frequency shedding mode responsible for reflected and reattachment shock corrugation. SPDMD of the two-dimensional skin-friction coefficient further identify streamwise streaks at low frequencies that cause large-scale flapping of the reattachment line. The PSD and SPDMD results of our impinging SWBLI support the theory that an intrinsic mechanism of the interaction zone is responsible for the lowfrequency unsteadiness, in which Görtler-like vortices might be seen as a continuous (coherent) forcing for strong SWBLI.

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Section: Instantaneous and Mean Flow Organisationsupporting

confidence: 89%

Section: Instantaneous and Mean Flow Organisationmentioning

confidence: 58%

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Unsteady effects of strong shock-wave/boundary-layer interaction at high Reynolds number

2017

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“…This Rayleigh circulation criterion states that boundary layers on concave walls and wall jets on convex walls can become unstable [25]. In 1941, Görtier showed the solution of the disturbance equations to be in the form of stream wise-oriented, counter-rotating vortices [26]. The Görtier number is defined as G~ v yRRe lR' (3.11) where ß is the local momentum thickness and v is the kinematic viscosity, and the spanwise…”

Section: Görtier Instabilitymentioning

confidence: 99%

Longitudinal Vortices in Turbulent Boundary Layers Subjected to Wall Curvature and Strong Adverse Pressure Gradients: Numerical Investigations Using LES and DNS

Fasel¹,

Groß²,

Postl³

2001

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“…Various analyses on the instability mechanism have been reported since a century ago, such as by Rayleigh [3] in the case of rotating fluid, by Taylor [4] for the Taylor-Couette instability in parallel flow between concentric cylinders, by Dean [5] for fully developed flow in curved pipe or duct, and by Görtler [6] for laminar boundary layer flow over a concave surface.…”

Section: Introductionmentioning

confidence: 99%

Development of pre-set counter-rotating streamwise vortices in wavy channel

Budiman

Mitsudharmadi

Bouremel

et al. 2016

Experimental Thermal and Fluid Science

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Development of counter-rotating streamwise vortices in a rectangular channel with onesided wavy surface has been experimentally quantified using hot-wire anemometry. The wavy surface has fixed amplitude of 3.75 mm. The counter-rotating vortices are pre-set by means of a sawtooth pattern cut at the leading edge of the wavy surface. Variations of the central streamwise velocity U c with a channel gap H = 35 mm and 50 mm (corresponding to a Reynolds number from 1600 to 4400) change the instability of the flow which can be distinguished from the velocity contours at a certain spanwise plane. The streamwise velocity contours and turbulence intensity for Reynolds number Re = 3100 and H = 35 mm show the disappearance of the mushroom-like vortices prior to turbulence near the second peak of the wavy surface, while for higher Re, this phenomenon occurs earlier. Under certain conditions, for example, for Re = 4400 and H = 50 mm, the splitting of the vortices can also be observed.

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Instabilität laminarer Grenzschichten an konkaven Wänden gegenüber gewissen dreidimensionalen Störungen

Cited by 141 publications

References 2 publications

Unsteady effects of strong shock-wave/boundary-layer interaction at high Reynolds number

Unsteady effects of strong shock-wave/boundary-layer interaction at high Reynolds number

Longitudinal Vortices in Turbulent Boundary Layers Subjected to Wall Curvature and Strong Adverse Pressure Gradients: Numerical Investigations Using LES and DNS

Development of pre-set counter-rotating streamwise vortices in wavy channel

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