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Nonlinear transition mechanism on a blunt cone at Mach 6: oblique breakdown

Published online by Cambridge University Press:  15 March 2021

Andrew B. Hartman Open the ORCID record for Andrew B. Hartman [Opens in a new window] ,
Christoph Hader Open the ORCID record for Christoph Hader [Opens in a new window]  and
Hermann F. Fasel
Andrew B. Hartman*
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, AZ85721, USA
Christoph Hader
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, AZ85721, USA
Hermann F. Fasel
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, AZ85721, USA
*
†Email address for correspondence: andrewmach1@arizona.edu
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Abstract

Direct numerical simulations (DNS) were carried out to investigate laminar-turbulent transition for a blunt (right) cone ($7^\circ$ half-angle) at Mach 5.9 and zero angle of attack. First, (linear) stability calculations were carried out by employing a high-order Navier–Stokes solver and using very small disturbance amplitudes in order to capture the linear disturbance development. Contrary to standard linear stability theory (LST) results, these investigations revealed a strong ‘linear’ instability in the entropy-layer region for a very short downstream distance for oblique disturbance waves with spatial growth rates far exceeding those of second-mode disturbances. This linear instability behaviour was not captured with conventional LST and/or the parabolized stability equations (PSE). Secondly, a nonlinear breakdown simulation was performed using high-fidelity DNS. The DNS results showed that linearly unstable oblique disturbance waves, when excited with large enough amplitudes, lead to a rapid breakdown and complete laminar-turbulent transition in the entropy layer just upstream of the second-mode instability region.

JFM classification

Aerodynamics: High-speed flow Boundary Layers: Boundary layer stability Instability: Transition to turbulence
Type
JFM Rapids
Information
Journal of Fluid Mechanics , Volume 915 , 25 May 2021 , R2
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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