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Nonlinear behaviour of the Mack mode in a hypersonic boundary layer

Published online by Cambridge University Press:  07 June 2019

Stuart A. Craig Open the ORCID record for Stuart A. Craig [Opens in a new window] ,
Raymond A. Humble ,
Jerrod W. Hofferth  and
William S. Saric
Stuart A. Craig*
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, AZ 85721, USA
Raymond A. Humble
Affiliation:
Department of Aerospace Engineering, Texas A&M University, College Station, TX 77843, USA
Jerrod W. Hofferth
Affiliation:
Aerospace Systems Directorate, Air Force Research Laboratory, Arnold AFB, TN 37389, USA
William S. Saric
Affiliation:
Department of Aerospace Engineering, Texas A&M University, College Station, TX 77843, USA
*
†Email address for correspondence: sacraig@email.arizona.edu
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Abstract

Mack-mode waves are measured in a hypersonic boundary layer using high-frequency focusing schlieren deflectometry. Experiments are performed using a $5^{\circ }$ flared cone at $0^{\circ }$ angle of attack in the low-disturbance Mach 6 Quiet Tunnel at Texas A&M University across a free-stream unit Reynolds number range of $7.8\times 10^{6}~\text{m}^{-1}\leqslant \mathit{Re}^{\prime }\leqslant 11.0\times 10^{6}~\text{m}^{-1}$. The high-frequency response of the measurement system allows harmonics and other nonlinear behaviour to be measured. Mack-mode waves and several harmonics are clearly observed at a frequency of $f_{0}\approx 250~\text{kHz}$. Bispectral analysis is used to show that these waves undergo several quadratic phase-coupled sum and difference interactions with themselves to produce harmonics, as well interact with a relatively low-frequency wave that results in amplitude modulation. Bispectral analysis is used to highlight these interactions.

JFM classification

Boundary Layers: Boundary layer stability Aerodynamics: High-speed flow Instability: Nonlinear instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 872 , 10 August 2019 , pp. 74 - 99
Copyright
© 2019 Cambridge University Press 

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