Nonlinear Development of the Multiple Gortler Modes in Hypersonic Boundary Layer Flows

2021

J. Fluid Mech.

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Section: Methodology and Problem Formulationmentioning

confidence: 99%

Hypersonic attachment-line instabilities with large sweep Mach numbers

2021

J. Fluid Mech.

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“…The trapped-layer mode (mode T) has its disturbances detached from the wall in the upper region of the boundary layer -the temperature adjustment layer. Crossover of the growth rate of the two modes can take place at certain flow conditions [34,35]. The unsteady Görtler mode together with the high turbulence intensity is responsible for the transition in turbomachinery flows, e.g., over the turbine blades [29,36].…”

Section: Introductionmentioning

confidence: 99%

“…It was illustrated that in addition to the conventional Görtler modes in the incompressible flows, there exists the trapped-layer modes [33,34] in compressible boundary layers. The conventional Görtler modes have their disturbances concentrated close to the boundary layer wall, and are hence called the wall-layer modes (mode W).…”

Section: Introductionmentioning

confidence: 99%

Study of the Discrete Spectrum in a Mach 4.5 Görtler Flow

Flow Turbulence Combust

2014

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Evolution of the discrete spectrum in the Ma = 4.5 boundary layer is studied with LST and PSE approaches. Both two-dimensional (2-D) and three-dimensional (3-D) disturbances are considered with streamwise curvature effects. The concave curvature shows a destabilizing effect on the 2-D second/third mode when the fast mode (mode F (1) , mode F (2) ...) synchronizes with the slow mode (mode S). The spectrum branching in the synchronization between the mode F (2) and mode S is also observed. The increase in the spanwise wavenumber(3-D disturbances), on the other hand, suppresses the synchronization between mode F and mode S and reduces the growth rate of the unstable mode. With regard to the 3-D disturbances subjecting to the concave curvature, the mode S originating from the slow acoustic wave amounts to the unsteady Görtler mode while the quasi-steady Görtler mode emanates from the continuous spectrum of the vorticity/entropy wave.

“…The formulation for the primary instability can be found in the authors' previous papers 20, 21 and it will not be repeated here. The secondary instability problem is formulated as follows.…”

Section: Mathematical Formulationmentioning

confidence: 98%

The role of Görtler vortices in the hypersonic boundary layer transition

Liu

44th AIAA Fluid Dynamics Conference

2014

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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.