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Numerical investigation of the nonlinear transition regime in a Mach 2 boundary layer

Published online by Cambridge University Press:  26 November 2010

CHRISTIAN S. J. MAYER ,
STEFAN WERNZ  and
HERMANN F. FASEL
CHRISTIAN S. J. MAYER*
Affiliation:
Department of Aerospace and Mechanical Engineering, The University of Arizona, Tucson, AZ 85721, USA
STEFAN WERNZ
Affiliation:
Department of Aerospace and Mechanical Engineering, The University of Arizona, Tucson, AZ 85721, USA
HERMANN F. FASEL
Affiliation:
Department of Aerospace and Mechanical Engineering, The University of Arizona, Tucson, AZ 85721, USA
*
†Present address: ExxonMobil Upstream Research Company, Houston, TX 77252, USA. Email address for correspondence: christian.s.mayer@exxonmobil.com
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Abstract

The transition process in a supersonic flat-plate boundary layer at Mach 2 is investigated numerically using linear stability theory (LST) and direct numerical simulations (DNS). The experimental investigations by Kosinov and his co-workers serve as a reference and provide the physical conditions for the numerical set-up. In these experiments, the weakly nonlinear regime of transition was studied. This led to the discovery of asymmetric subharmonic resonance triads, which appear to be relevant for transition in a Mach 2 boundary layer. These triads were composed of one primary oblique wave of frequency 20kHz and two oblique subharmonic waves of frequency 10kHz. While the experimentalists have focused on this new breakdown mechanism, we have found that the experimental data also indicate the presence of another mechanism related to oblique breakdown. This might be the first experimental evidence of the oblique breakdown mechanism in a supersonic boundary layer. With the simulations presented here, the possible presence of oblique breakdown mechanisms in the experiments is explored by deliberately suppressing subharmonic resonances in the DNS and by comparing the numerical results with the experimental data. The DNS results show excellent agreement with the experimental measurements for both linear and nonlinear transition stages. Most importantly, the results clearly show the characteristic features of oblique breakdown. In addition, we also investigated the subharmonic transition route using LST and DNS. When forcing both the subharmonic and the fundamental frequencies in the DNS, a subharmonic resonance mechanism similar to that in the experiments can be observed.

JFM classification

Boundary Layers: Boundary layer stability Compressible Flows: Compressible boundary layers Instability: Transition to turbulence
Type
Papers
Information
Journal of Fluid Mechanics , Volume 668 , 10 February 2011 , pp. 113 - 149
Copyright
Copyright © Cambridge University Press 2010

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