On the inviscid energetics of Mack’s first mode instability

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Author(s)Liang, Tony
Author(s)Kafle, Sulav
Author(s)Khan, Arham Amin
Author(s)Paredes, Pedro
Author(s)Kuehl, Joseph
Date Accessioned2023-03-08T15:15:09Z
Date Available2023-03-08T15:15:09Z
Publication Date2022-12-22
DescriptionThis version of the article has been accepted for publication in Theoretical and Computational Fluid Dynamics, after peer review (when applicable) and is subject to Springer Nature’s AM terms of use, but is not the Version of Record and does not reflect post-acceptance improvements, or any corrections. The Version of Record is available online at: https://doi.org/10.1007/s00162-022-00636-9. This article will be embargoed until 12/22/2023.
AbstractHigh-speed boundary layer transition is dominated by the modal, exponential amplification of the oblique Mack’s first mode waves in two-dimensional boundary layers from Mach 1 up to freestream Mach numbers of 4.5 to 6.5 depending on the wall-to-adiabatic temperature ratio. At higher Mach numbers, the acoustic, planar Mack’s second mode waves become dominant. Although many theoretical, computational and experimental studies have focused on the supersonic boundary layer transition due to the oblique Mack’s first mode, several fundamental questions about the source of this instability and the reasons for its obliqueness remain unsolved. Here, we perform an inviscid energetics investigation and classify disturbances based on their energetics signature on a Blasius boundary layer for a range of Mach numbers. This approach builds insight into the fundamental mechanisms governing various types of instability. It is shown that first mode instability is distinct from Tollmien–Schlichting instability, being driven by a phase shifting between streamwise velocity and pressure perturbations in the vicinity of the generalized inflection point and insensitive to the viscous no-slip condition. Further, it is suggested that the obliqueness of the first mode is associated with an inviscid flow invariant.
SponsorThe authors gratefully acknowledges support from the AFOSR via Grants FA9550-20-1-0047 and FA9550-20-1-0023 and to the AFRL via Grant 21A01107.
CitationLiang, T., Kafle, S., Khan, A.A. et al. On the inviscid energetics of Mack’s first mode instability. Theor. Comput. Fluid Dyn. (2022). https://doi.org/10.1007/s00162-022-00636-9
ISSN1432-2250
URLhttps://udspace.udel.edu/handle/19716/32389
Languageen_US
PublisherTheoretical and Computational Fluid Dynamics
Keywordshypersonic boundary layer stability
KeywordsMack’s first mode
KeywordsMack’s second mode
KeywordsTollmien–Schlichting instability
TitleOn the inviscid energetics of Mack’s first mode instability
TypeArticle
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