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Numerical investigation of the development of three-dimensional wavepackets in a sharp cone boundary layer at Mach 6

Published online by Cambridge University Press:  03 September 2014

Jayahar Sivasubramanian  and
Hermann F. Fasel
Jayahar Sivasubramanian*
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, AZ 85721, USA
Hermann F. Fasel
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, AZ 85721, USA
*
†Email address for correspondence: jayahar@email.arizona.edu
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Abstract

Direct numerical simulations were performed to investigate wavepackets in a sharp cone boundary layer at Mach 6. In order to understand the natural transition process in hypersonic cone boundary layers, the flow was forced by a short-duration (localized) pulse. The pulse disturbance developed into a three-dimensional wavepacket, which consisted of a wide range of disturbance frequencies and wavenumbers. First, the linear development of the wavepacket was studied by forcing the flow with a low-amplitude pulse (0.001 % of the free-stream velocity). The dominant waves within the resulting wavepacket were identified as the second-mode axisymmetric disturbance waves. In addition, weaker first-mode oblique disturbance waves were also observed on the lateral sides of the wavepacket. In order to investigate the nonlinear transition regime, large-amplitude pulse disturbances (0.5 % of the free-stream velocity) were introduced. The response of the flow to the large-amplitude pulse disturbances indicated the presence of a fundamental resonance mechanism. Lower secondary peaks in the disturbance wave spectrum were identified at approximately half the frequency of the high-amplitude frequency band, suggesting the possibility of a subharmonic resonance mechanism. However, the spectrum also indicated that the fundamental resonance was much stronger than the subharmonic resonance. A secondary stability investigation using controlled disturbances confirmed that fundamental resonance is indeed a dominant mechanism compared to subharmonic resonance. Furthermore, strong peaks in the disturbance wave spectrum were also observed for low-azimuthal-wavenumber second-mode oblique waves, hinting at a possible oblique breakdown mechanism. Thus, the wavepacket simulations indicate that the second-mode fundamental resonance and oblique breakdown mechanisms are the strongest for the investigated flow. Hence, both mechanisms are likely to be relevant in the natural transition process for a cone boundary layer at Mach 6.

JFM classification

Boundary Layers: Boundary layer stability Compressible Flows: Compressible boundary layers Aerodynamics: High-speed flow
Type
Papers
Information
Journal of Fluid Mechanics , Volume 756 , 10 October 2014 , pp. 600 - 649
Copyright
© 2014 Cambridge University Press 

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