Linear modal instabilities around post-stall swept finite wings at low Reynolds numbers

Burtsev, Anton ORCID: 0000-0002-8268-9088, He, Wei ORCID: 0000-0002-2633-6114, Zhang, Kai ORCID: 0000-0001-6097-7217, Theofilis, Vassilios, Taira, Kunihiko ORCID: 0000-0002-3762-8075 and Amitay, Michael ORCID: 0000-0003-1366-0406 (2022) Linear modal instabilities around post-stall swept finite wings at low Reynolds numbers. Journal of Fluid Mechanics, 944.

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Abstract

<jats:p>Linear modal instabilities of flow over untapered wings with aspect ratios <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112022004207_inline1.png" /> <jats:tex-math>$AR=4$</jats:tex-math> </jats:alternatives> </jats:inline-formula> and 8, based on the NACA 0015 profile, have been investigated numerically over a range of angles of attack, <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112022004207_inline2.png" /> <jats:tex-math>$\alpha$</jats:tex-math> </jats:alternatives> </jats:inline-formula>, and angles of sweep, <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112022004207_inline3.png" /> <jats:tex-math>$\varLambda$</jats:tex-math> </jats:alternatives> </jats:inline-formula>, at chord Reynolds numbers <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112022004207_inline4.png" /> <jats:tex-math>$100\le Re\le 400$</jats:tex-math> </jats:alternatives> </jats:inline-formula>. Laminar base flows have been generated using direct numerical simulation and selective frequency damping, as appropriate. Several families of unstable three-dimensional linear global (TriGlobal) eigenmodes have been identified and their dependence on geometric parameters has been examined in detail at <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112022004207_inline5.png" /> <jats:tex-math>$Re=400$</jats:tex-math> </jats:alternatives> </jats:inline-formula>. The leading global mode A is associated with the peak recirculation in the three-dimensional laminar separation bubble formed on the wing and becomes unstable when recirculation reaches <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112022004207_inline6.png" /> <jats:tex-math>$\textit {O}(10\,\%)$</jats:tex-math> </jats:alternatives> </jats:inline-formula>. On unswept wings, this mode peaks in the midspan region of the wake and moves towards the wing tip with increasing <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112022004207_inline7.png" /> <jats:tex-math>$\varLambda$</jats:tex-math> </jats:alternatives> </jats:inline-formula>, following the displacement of peak recirculation; its linear amplification leads to wake unsteadiness. Additional amplified modes exist at nearly the same and higher frequencies compared to mode A. The critical <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112022004207_inline9.png" /> <jats:tex-math>$Re$</jats:tex-math> </jats:alternatives> </jats:inline-formula> has been identified and it is shown that amplification increases with increasing sweep, up to <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112022004207_inline10.png" /> <jats:tex-math>$\varLambda \approx 10^\circ$</jats:tex-math> </jats:alternatives> </jats:inline-formula>. At higher <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112022004207_inline11.png" /> <jats:tex-math>$\varLambda$</jats:tex-math> </jats:alternatives> </jats:inline-formula>, all global modes become less amplified and are ultimately stable at <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112022004207_inline12.png" /> <jats:tex-math>$\varLambda =30^\circ$</jats:tex-math> </jats:alternatives> </jats:inline-formula>. An increase in amplification of the leading mode with sweep was not observed over the <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0022112022004207_inline13.png" /> <jats:tex-math>$AR=4$</jats:tex-math> </jats:alternatives> </jats:inline-formula> wing, where tip vortex effects were shown to dominate.</jats:p>

Item Type:	Article
Divisions:	Faculty of Science and Engineering > School of Engineering
Depositing User:	Symplectic Admin
Date Deposited:	12 Jul 2022 15:13
Last Modified:	18 Jan 2023 20:56
DOI:	10.1017/jfm.2022.420
URI:	https://livrepository.liverpool.ac.uk/id/eprint/3158297