Splitting and merging of Görtler vortices

Mitsudharmadi, Hatsari; Winoto, S. H.; Shah, D. A.

doi:10.1063/1.2151227

Cited by 17 publications

(6 citation statements)

References 31 publications

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“…One single mushroom structure is seen to emerge from the two low-speed streaks marked by the arrows in figures 17(b) and 17(c). This merging of streaks during the nonlinear stage was also observed in the experiments by Mitsudharmadi, Winoto & Shah (2005). The mushrooms to the left of figure 17(e) have already broken down to smaller scales, whereas the midspan structures are still intact.…”

Section: Boundary-layer Response To Free-stream Turbulencesupporting

confidence: 50%

Receptivity, instability and breakdown of Görtler flow

2011

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Receptivity, disturbance growth and breakdown to turbulence in Görtler flow are studied by spatial direct numerical simulation (DNS). The boundary layer is exposed to free-stream vortical modes and localized wall roughness. We propose a normalization of the roughness-induced receptivity coefficient by the square root of the Görtler number. This scaling removes the dependence of the receptivity coefficient on wall curvature. It is found that vortical modes are more efficient at generating Görtler vortices than localized roughness. The boundary layer is most receptive to zeroand low-frequency free-stream vortices, exciting steady and slowly travelling Görtler modes. The associated receptivity mechanism is linear and involves the generation of boundary-layer streaks, which soon evolve into unstable Görtler vortices. This connection between transient and exponential amplification is absent on flat plates and promotes transition to turbulence on curved walls. We demonstrate that the Görtler boundary layer is also receptive to high-frequency free-stream vorticity, which triggers steady Görtler rolls via a nonlinear receptivity mechanism. In addition to the receptivity study, we have carried out DNS of boundary-layer transition due to broadband free-stream turbulence with different intensities and frequency spectra. It is found that nonlinear receptivity dominates over the linear mechanism unless the free-stream fluctuations are concentrated in the low-frequency range. In the latter case, transition is accelerated due to the presence of travelling Görtler modes.

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Section: Boundary-layer Response To Free-stream Turbulencesupporting

confidence: 50%

Receptivity, instability and breakdown of Görtler flow

2011

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“…In the validation test case the parameters used were those of the experiment of 17,18 . They considered a boundary layer on a concave plate withR = 2 m and free-stream velocityŪ ∞ = 3 m/s.…”

Section: Resultsmentioning

confidence: 99%

“…The parameters adopted for the simulations were based in the experiment of Winoto and collaborators 17,18 and the Prandtl number adopted was Pr = 0.72. The results showed that the primary instability (Görtler vortices) increases the heat transfer rate to values above the turbulent values in the nonlinear development region.…”

Section: Resultsmentioning

confidence: 99%

Heat Transfer Analysis in a Flow Over Concave Wall With Primary and Secondary Instabilities

et al. 2015

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The centrifugal instability mechanism in boundary layers over concave surfaces is responsible for the development of counterrotating vortices, aligned in the streamwise direction, known as Görtler vortices. These vortices create two regions in the spanwise direction, the upwash and downwash regions. The downwash region is responsible for compressing the boundary layer towards the wall, increasing the drag coefficient and the heat transfer rate. The upwash region does the opposite. The Görtler vortices distort the streamwise velocity profile in the spanwise and the wall-normal directions. These distortions generate inflections in the distribution of streamwise velocity that are unstable to unsteady disturbances giving rise to secondary instabilities. In these flows the secondary instabilities can be of varicose or sinuous mode. The present paper analyses the heat transfer in a flow over a concave wall subjected to primary and secondary instabilities. The research is carried out by a Spatial Direct Numerical Simulation. The adopted parameters mimic the experimental parameters of Winoto and collaborators 17,18 and the Prandtl number adopted was Pr = 0.72. The results show that the varicose mode is the dominant secondary instability for the adopted parameters and that the spanwise average heat transfer rates can reach higher values than the turbulent ones. The higher heat transfer is caused by the mean flow distortion induced by the vortices, and this is present before high-frequency secondary instability sets in. Hence there is no direct connection to secondary instability. Possibly low-frequency modes undergo instability earlier.

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“…Splitting and merging of the vortices is thus observed when the imposed disturbances deviate from the most amplified wavelength. 4 In the incompressible flows, this single mode analysis has been proved to be successful in different stages of the disturbance development. The readers may refer to Goulpié et al 5 for the linear analysis, Hall, 6 Lee & Liu, 7 Sabry & Liu, 8 Benmalek & Saric, 9 Cunff & Zebib 10 for the nonlinear development and Hall & Horseman, 11 Li & Malik 1 for the secondary instability.…”

Section: Introductionmentioning

confidence: 97%

The role of Görtler vortices in the hypersonic boundary layer transition

Liu

Ren

2014

44th AIAA Fluid Dynamics Conference

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The Görtler vortices which manifest as the counter-rotating streamwise vortices in highspeed boundary layers are studied. Four groups of M a numbers (M a = 1.5, 3.0, 4.5 and 6.0) and three groups of wavenumbers (B = 0.5, 1.0 and 2.0×10 −3 ) are specified to investigate the parametric effect of M a numbers and the spanwise wavenumbers on the spatial development and the interrelated secondary instability of Görtler vortices. The Görtler vortices in moderate supersonic flows (Ma=1.5, 3.0) are governed by the conventional wall-layer mode (mode W). In hypersonic flows (Ma=4.5, 6.0), it is the trapped-layer mode (mode T) that becomes dominating. The linear and nonlinear development of Görtler vortices are studied using the LST and the direct marching of the nonlinear parabolic equations. The secondary instabilities of Görtler vortices are then analyzed on the saturated state of the Görtler vortices with Floquet theory. The conclusion that "the dominating secondary modes (odd or even) depend on the spanwise wavenumbers of the Görtler vortices 1 " is shown to be unapplicable in compressible cases. The relationship between the primary Görtler instability and the corresponding secondary instability are clarified. In the Görtler-dominated transition process, the most dangerous wavelength of the primary Görtler instability give rise to the largest growth rate of the secondary instability. The role of the Görtler vortices on the blunt compression/flared cone 2 is shown to be minor compared with the Mack mode. For the blunt compression wedge, it is the Görtler mode that becomes responsible for the flow transition as the Mack mode is considerably suppressed.

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Splitting and merging of Görtler vortices

Cited by 17 publications

References 31 publications

Receptivity, instability and breakdown of Görtler flow

Receptivity, instability and breakdown of Görtler flow

Heat Transfer Analysis in a Flow Over Concave Wall With Primary and Secondary Instabilities

The role of Görtler vortices in the hypersonic boundary layer transition

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