On the görtler instability of boundary layers

Floryan, J. M.

doi:10.1016/0376-0421(91)90006-p

Cited by 237 publications

(130 citation statements)

References 71 publications

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“…Previous measurements (Barlow & Johnston 1984) suggest a 40% increase in wall shear stress owing to Görtler vortices on a concave smooth wall (Floryan 1991). The increase will, of course, depend on the strength of the Görtler vortices and, to some extent, on whether the wall is rough or smooth.…”

Section: Instantaneous Flow Structure and Turbulence Quantitiesmentioning

confidence: 88%

Near-field flow structure of a confined wall jet on flat and concave rough walls

Albayrak¹,

Hopfinger²,

Lemmin³

2008

J. Fluid Mech.

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Experimental results are presented of the mean flow and turbulence characteristics in the near field of a plane wall jet issuing from a nozzle onto flat and concave walls consisting of fixed sand beds. This is a flow configuration of interest for sediment erosion, also referred to as scouring. The measurements were made with an acoustic profiler that gives access to the three components of the instantaneous velocities. For the flat-wall flow, it is shown that the outer-layer spatial growth rate and the maxima of the Reynolds stresses approach the values accepted for the far field of a wall jet at a downstream distance x/b 0 ≈ 8. These maxima are only about half the values of a plane free jet. This reduction in Reynolds stresses is also observed in the shear-layer region, x/b 0 < 6, where the Reynolds shear stress is about half the value of a free shear layer. At distances x/b 0 > 11, the maximum Reynolds shear stress approaches the value of a plane free jet. This change in Reynolds stresses is related to the mean vertical velocity that is negative for x/b 0 < 8 and positive further downstream. The evolution of the inner region of the wall jet is found to be in good agreement with a previous model that explicitly includes the roughness length.On the concave wall, the mean flow and the Reynolds stresses are drastically changed by the adverse pressure gradient and especially by the development of Görtler vortices. On the downslope side of the scour hole, the flow is nearly separating with the wall shear stress tending to zero, whereas on the upslope side, the wall-friction coefficient is increased by a factor of about two by Görtler vortices. These vortices extend well into the outer layer and, just above the wall, cause a substantial increase in Reynolds shear stress.

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Section: Instantaneous Flow Structure and Turbulence Quantitiesmentioning

confidence: 88%

Near-field flow structure of a confined wall jet on flat and concave rough walls

Albayrak¹,

Hopfinger²,

Lemmin³

2008

J. Fluid Mech.

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“…14(a) and 15(a). The formation of high shear layer initiates the development of horseshoe vortices as the initiation of the secondary instability [18]. As these horseshoe vortices propagate downstream and breakdown, the turbulence spreads out in the boundary-layer resulting in the decay of the second peak near the boundary-layer edge until the turbulence near the wall becomes dominant in the flow.…”

Section: Resultsmentioning

confidence: 99%

“…Alternatively, the start of non-linear region can be located by the formation of an inflection point in the boundary-layer velocity profile at upwash. The horseshoe vortices as the secondary instability of Görtler vortices are known to be caused by the high shear layer near the edge of the boundary-layer [18], which is a consequence of the formation of the inflection point in the velocity profile. The plots of U/U ∞ against η at upwash and downwash are shown in Figs.…”

Section: Resultsmentioning

confidence: 99%

“…(αθ is called dimensionless wave number and α (= 2π/λ) is called wave number). Luchini and Bottaro [17] found that the most amplified wavelengths are for Λ = 220 to 270, while Floryan [18], Smith [2], and Meksyn [19] respectively proposed Λ = 210, 272, and 227. Since the wavelengths of naturally developed Görtler vortices are not uniform, experimental investigations were biased due to the choice of "good" pair of Görtler vortices.…”

Section: Introductionmentioning

confidence: 99%

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Concave Surface Boundary Layer Flows in the Presence of Streamwise Vortices

Winoto¹,

Tandiono²,

Shah³

et al. 2011

International Journal of Fluid Machinery and Systems

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Concave surface boundary-layer flows are subjected to centrifugal instability which results in the formation of streamwise counter-rotating vortices. Such boundary layer flows have been experimentally investigated on concave surfaces of 1 m and 2 m radius of curvature. In the experiments, to obtain uniform vortex wavelengths, thin perturbation wires placed upstream and perpendicular to the concave surface leading edge, were used to pre-set the wavelengths. Velocity contours were obtained from hot-wire anemometer velocity measurements. The most amplified vortex wavelengths can be pre-set by the spanwise spacing of the thin wires and the free-stream velocity. The velocity contours on the cross-sectional planes at several streamwise locations show the growth and breakdown of the vortices. Three different vortex growth regions can be identified. The occurrence of a secondary instability mode is also shown as mushroom-like structures as a consequence of the non-linear growth of the streamwise vortices. Wall shear stress measurements on concave surface of 1 m radius of curvature reveal that the spanwise-averaged wall shear stress increases well beyond the flat plate boundary layer values. By pre-setting much larger or much smaller vortex wavelength than the most amplified one, the splitting or merging of the streamwise vortices will respectively occur.

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“…A simple sinusoidal wavy channel can be used as a passive control for these vortices. The vortex instability in a wavy channel, which is caused by the centrifugal force field, is very similar to the so called Görtler instability [13]. Numerous experimental and analytical studies on flow over wavy surface, such as Nishimura et al [14,15], Gschwind et al [16], and Cabal et al [17] suggested stability criteria to control the vortices generated, while Floryan [18] suggested a neutral stability region as a function of the Reynolds number Re (= U c H / 2ν) and the wavy surface geometry based on the linear stability analysis.…”

Section: Introductionmentioning

confidence: 96%

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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On the görtler instability of boundary layers

Cited by 237 publications

References 71 publications

Near-field flow structure of a confined wall jet on flat and concave rough walls

Near-field flow structure of a confined wall jet on flat and concave rough walls

Concave Surface Boundary Layer Flows in the Presence of Streamwise Vortices

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

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