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

Published online by Cambridge University Press:  19 February 2019

X. Chen Open the ORCID record for X. Chen [Opens in a new window] ,
G. L. Huang  and
C. B. Lee Open the ORCID record for C. B. Lee [Opens in a new window]
X. Chen
Affiliation:
State Key Laboratory of Turbulence and Complex Systems, Collaborative Innovation Center for Advanced Aero-Engines, Peking University, Beijing 100871, PR China
G. L. Huang
Affiliation:
State Key Laboratory of Turbulence and Complex Systems, Collaborative Innovation Center for Advanced Aero-Engines, Peking University, Beijing 100871, PR China
C. B. Lee*
Affiliation:
State Key Laboratory of Turbulence and Complex Systems, Collaborative Innovation Center for Advanced Aero-Engines, Peking University, Beijing 100871, PR China
*
†Email address for correspondence: [email protected]
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Abstract

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.

JFM classification

Boundary Layers: Boundary layer stability Instability: Transition to turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 865 , 25 April 2019 , pp. 1 - 40
Copyright
© 2019 Cambridge University Press 

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Footnotes

‡

Present address: Computational Aerodynamics Institute, China Aerodynamics Research and Development Center, Mianyang 621000, China

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Chen et al. supplementary movie 1

Normalized temperature contour for case L3

Download Chen et al. supplementary movie 1(Video)
Video 8.7 MB

Chen et al. supplementary movie 2

Normalized temperature contour for case L6

Download Chen et al. supplementary movie 2(Video)
Video 8.2 MB

Chen et al. supplementary movie 3

Normalized temperature contour for case L9

Download Chen et al. supplementary movie 3(Video)
Video 9 MB