Transient growth analysis of hypersonic flow over an elliptic cone

Jr, Quintanilha Helio, Paredes, Pedro, Hanifi, Ardeshir and Theofilis, Vassilis ORCID: 0000-0002-7720-3434 (2022) Transient growth analysis of hypersonic flow over an elliptic cone. JOURNAL OF FLUID MECHANICS, 935. a40-.

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Official URL: http://dx.doi.org/10.1017/jfm.2022.46

Abstract

<jats:p>Non-modal linear stability analysis results are presented for hypersonic flow over an elliptic cone with an aspect ratio of two at zero angle of attack, completing earlier modal instability analysis of flow around the same geometry. The theoretical framework to perform transient growth analysis of compressible flows on a generalized two-dimensional frame of reference is developed for the first time and is then applied to solve the initial-value problem governing non-modal linear instability on planes perpendicular to the cone axis, taken at successive streamwise locations along the elliptic cone. Parameter ranges examined here are chosen so as to model flight of the Hypersonic International Flight Research Experimentation 5 (HIFiRE-5) test geometry at altitudes of 21 km and 33 km, corresponding to Mach numbers 7.45 and 8.05 and unit Reynolds numbers <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112022000465_inline1.png" /> <jats:tex-math>$Re' = 1.07\times 10^7$</jats:tex-math> </jats:alternatives> </jats:inline-formula> and <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112022000465_inline2.png" /> <jats:tex-math>$1.89\times 10^6$</jats:tex-math> </jats:alternatives> </jats:inline-formula>, respectively. Results obtained indicate that the significance of the non-modal growth for laminar–turbulent transition increases with increasing flight altitude (decreasing Reynolds number). At a given set of flow parameters, transient growth is stronger in the vicinity of the tip of the cone and in azimuthal locations away from both of the minor (centreline) and major (attachment line) axes of the cone. Linear optimal disturbances calculated at conditions of maximal transient growth are found to peak in the crossflow region of the elliptic cone. These structures are elongated along the streamwise spatial direction, while being periodic along the spanwise direction with periodicity lengths of the same order of magnitude as the well-known structures identified as crossflow vortices in both experiments and simulations.</jats:p>

Item Type:	Article
Uncontrolled Keywords:	boundary layer stability, transition to turbulence, high-speed flow
Divisions:	Faculty of Science and Engineering > School of Engineering
Depositing User:	Symplectic Admin
Date Deposited:	03 Mar 2022 10:12
Last Modified:	17 Mar 2024 13:27
DOI:	10.1017/jfm.2022.46
Open Access URL:	https://doi.org/10.1017/jfm.2022.46
Related URLs:	Author Publisher
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3150022