Interactions between Görtler vortices and the second mode in hypersonic boundary layer

2021 ◽  
Vol 33 (11) ◽  
pp. 111701
Author(s):  
Ganglei Huang
Keyword(s):  
Boundary Layer ◽  
Hypersonic Boundary Layer ◽  
Görtler Vortices ◽  
Second Mode ◽  
Gortler Vortices

Crossflow effects on the growth rate of inviscid Görtler vortices in a hypersonic boundary layer

1994 ◽  
Vol 276 ◽  
pp. 343-367 ◽  
Author(s):  
Yibin Fu ◽  
Philip Hall
Keyword(s):  
Boundary Layer ◽  
Growth Rate ◽  
Exact Solution ◽  
Eigenvalue Problem ◽  
Hypersonic Boundary Layer ◽  
Minimum Order ◽  
Görtler Vortices ◽  
Neutral Mode ◽  
Gortler Vortices ◽  
The Relationship

The effects of crossflow on the growth rate of inviscid Görtler vortices in a hypersonic boundary layer with pressure gradient are studied in this paper. Attention is focused on the inviscid mode trapped in the temperature adjustment layer; this mode has greater growth rate than any other mode at the minimum order of the Görtler number at which Görtler vortices may exist. The eigenvalue problem which governs the relationship between the growth rate, the crossflow amplitude and the wavenumber is solved numerically, and the results are then used to clarify the effects of crossflow on the growth rate of inviscid Görtler vortices. It is shown that crossflow effects stabilize Görtler vortices in different manners for incompressible and hypersonic flows. The neutral mode eigenvalue problem is found to have an exact solution, and as a byproduct, we have also found the exact solution to a neutral mode eigenvalue problem which was formulated, but unsolved before, by Bassom & Hall (1991).

Hypersonic boundary layer transition on a concave wall: stationary Görtler vortices

2019 ◽  
Vol 865 ◽  
pp. 1-40 ◽  
Author(s):  
X. Chen ◽  
G. L. Huang ◽  
C. B. Lee
Keyword(s):  
Boundary Layer ◽  
Numerical Simulations ◽  
Stability Theory ◽  
Direct Numerical Simulations ◽  
Boundary Layer Transition ◽  
Hypersonic Boundary Layer ◽  
Mode Instability ◽  
Görtler Vortices ◽  
Gortler Vortices ◽  
The Stability

This study investigates the stability and transition of Görtler vortices in a hypersonic boundary layer using linear stability theory and direct numerical simulations. In the simulations, Görtler vortices are separately excited by wall blowing and suction with spanwise wavelengths of 3, 6 and 9 mm. In addition to primary streaks with the same wavelength as the blowing and suction, secondary streaks with half the wavelength also emerge in the 6 and 9 mm cases. The streaks develop into mushroom structures before breaking down. The breakdown processes of the three cases are dominated by a sinuous-mode instability, a varicose-mode instability and a combination of the two, respectively. Both fundamental and subharmonic instabilities are relevant in all cases. Multiple modes are identified in the secondary-instability stage, some of which originate from the primary instabilities (first and second Mack modes). We demonstrate that the first Mack mode can be destabilized to either a varicose-mode or sinuous-mode streak instability depending on its frequency and wavelength, whereas the second Mack mode undergoes a stabilizing stage before turning into a varicose mode in the 6 and 9 mm cases. An energy analysis reveals the stabilizing and destabilizing mechanisms of the primary instabilities under the influence of Görtler vortices, highlighting the role played by the spanwise production based on the spanwise gradient of the streamwise velocity in both varicose and sinuous modes. The effects introduced by the secondary streaks are examined by filtering the secondary streaks in two new simulations with nominally identical conditions to those of the 6 and 9 mm cases. Remarkably, the secondary streaks can destabilize the Görtler vortices, therefore advancing the transition. The stability theory results are in good agreement with those from direct numerical simulations.

Effects of Görtler vortices, wall cooling and gas dissociation on the Rayleigh instability in a hypersonic boundary layer

1993 ◽  
Vol 247 ◽  
pp. 503-525 ◽  
Author(s):  
Yibin Fu ◽  
Philip Hall
Keyword(s):  
Boundary Layer ◽  
Growth Rate ◽  
Large Amplitude ◽  
Hypersonic Boundary Layer ◽  
Rayleigh Instability ◽  
Variable Curvature ◽  
Görtler Vortices ◽  
Gortler Vortices

In a hypersonic boundary layer over a wall of variable curvature, the region most susceptible to Görtler vortices is the temperature adjustment layer sitting at the edge of the boundary layer. This temperature adjustment layer is also the most dangerous site for Rayleigh instability. In this paper, we investigate how the existence of large-amplitude Görtler vortices affects the growth rate of Rayleigh instability. The effects of wall cooling and gas dissociation on this instability are also studied. We find that all these mechanisms increase the growth rate of Rayleigh instability and are therefore destabilizing.

Secondary instabilities of Görtler vortices in high-speed boundary layer flows

2015 ◽  
Vol 781 ◽  
pp. 388-421 ◽  
Author(s):  
Jie Ren ◽  
Song Fu
Keyword(s):  
Boundary Layer ◽  
High Speed ◽  
Incompressible Flows ◽  
Hypersonic Flows ◽  
Type I ◽  
Görtler Vortices ◽  
Layer Mode ◽  
Threshold Amplitude ◽  
Gortler Vortices ◽  
Secondary Instabilities

Görtler vortices developed in laminar boundary layer experience remarkable changes when the flow is subjected to compressibility effects. In the present study, five $\mathit{Ma}$ numbers, covering incompressible to hypersonic flows, at $\mathit{Ma}=0.015$, 1.5, 3.0, 4.5 and 6.0 are specified to illustrate these effects. Görtler vortices in subsonic and moderate supersonic flows ($\mathit{Ma}=0.015$, 1.5 and 3.0) are governed by the conventional wall-layer mode (mode W). In hypersonic flows ($\mathit{Ma}=4.5$, 6.0), the trapped-layer mode (mode T) becomes dominant. This difference is maintained and intensifies downstream leading to different scenarios of secondary instabilities. The linear and nonlinear development of Görtler vortices which are governed by dominant modal disturbances are investigated with direct marching of the nonlinear parabolic equations. The secondary instabilities of Görtler vortices set in when the resulting streaks are adequately developed. They are studied with Floquet theory at multiple streamwise locations. The secondary perturbations become unstable downstream following the sequence of sinuous mode type I, varicose mode and sinuous mode type II, indicating an increasing threshold amplitude. Onset conditions are determined for these modes. The above three modes can each have the largest growth rate under the right conditions. In the hypersonic cases, the threshold amplitude $A(u)$ is dramatically reduced, showing the significant impact of the thermal streaks. To investigate the parametric effect of the spanwise wavenumber, three global wavenumbers ($B=0.5$, 1.0 and $2.0\times 10^{-3}$) are specified. The relationship between the dominant mode (sinuous or varicose) and the spanwise wavenumber of Görtler vortices found in incompressible flows (Li & Malik, J. Fluid Mech., vol. 297, 1995, pp. 77–100) is shown to be not fully applicable in high-speed cases. The sinuous mode becomes the most dangerous, regardless of the spanwise wavelength when $\mathit{Ma}>3.0$. The subharmonic type can be the most dangerous mode while the detuned type can be neglected, although some of the sub-dominant secondary modes reach their peak growth rates under detuned states.

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