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The secondary instabilities of stationary cross-flow vortices in a Mach 6 swept wing flow

Published online by Cambridge University Press:  28 June 2019

Guoliang Xu Open the ORCID record for Guoliang Xu [Opens in a new window] ,
Jianqiang Chen ,
Gang Liu ,
Siwei Dong  and
Song Fu Open the ORCID record for Song Fu [Opens in a new window]
Guoliang Xu
Affiliation:
China Aerodynamics Research and Development Center, Mianyan 621000, China
Jianqiang Chen
Affiliation:
China Aerodynamics Research and Development Center, Mianyan 621000, China
Gang Liu
Affiliation:
China Aerodynamics Research and Development Center, Mianyan 621000, China
Siwei Dong
Affiliation:
China Aerodynamics Research and Development Center, Mianyan 621000, China
Song Fu*
Affiliation:
School of Aerospace Engineering, Tsinghua University, Beijing 100084, China
*
†Email address for correspondence: fs-dem@tsinghua.edu.cn
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Abstract

The secondary instabilities of stationary cross-flow vortices in a Mach 6 swept wing flow are studied using Floquet theory. High-frequency secondary instability modes of ‘y’ mode on top of stationary cross-flow vortices, and ‘z’ mode concentrating on the shoulder of the stationary cross-flow vortex are found. The most unstable secondary instability mode is always the ‘z’ mode as in incompressible swept wing flows. A new secondary instability mode concentrating on the trough of the stationary cross-flow vortex is found. The balance analysis of disturbance kinetic energy shows that the new mode belongs to the class of ‘y’ mode. The growth rate of the new ‘y’ mode located on the trough of the stationary cross-flow vortex is significantly larger than that of the ‘y’ mode on top of the stationary cross-flow vortex, and is comparable with the growth rate of the ‘z’ mode. It is also found that the new ‘y’ mode with higher frequency can evolve into the ‘z’ mode further downstream. The role of the pressure fluctuation term, including the pressure diffusion and pressure dilatation, in the energy production of secondary instability modes, is also investigated. It is shown that the pressure diffusion will only enhance the growth rate of the ‘z’ mode with higher frequency, but has little influence on other types of secondary instability mode. However, the pressure dilatation term arising from non-vanishing velocity divergence will reduce the growth rates of all secondary instability modes.

JFM classification

Boundary Layers: Boundary layer stability Aerodynamics: High-speed flow Instability: Transition to turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 873 , 25 August 2019 , pp. 914 - 941
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Copyright
© 2019 Cambridge University Press 

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