Wang, D., Luo, X. , Liu, Z. and Stewart, P. S. (2023) Flow-induced surface instabilities in a flexible-walled channel with a heavy wall. Journal of Fluid Mechanics, 956, A1. (doi: 10.1017/jfm.2022.1086)
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Abstract
We consider the stability of laminar high-Reynolds-number flow through a planar channel formed by a rigid wall and a heavy compliant wall under longitudinal tension with motion resisted by structural damping. Numerical simulations indicate that the baseline state (with Poiseuille flow and a flat wall) exhibits two unstable normal modes: the Tollmien–Schlichting (TS) mode and a surface-based mode which manifests as one of two flow-induced surface instabilities (FISI), known as travelling wave flutter (TWF) and static divergence (SD), respectively. In the absence of wall damping the system is unstable to TWF, where the neutrally stable wavelength becomes shorter as the wall mass increases. With wall damping, TWF is restricted to long wavelengths through interaction with the most unstable centre mode, while for wall damping greater than a critical value the system exhibits an SD mode with a two branch neutral stability curve; the critical conditions along the upper and lower branches are constructed in the limit of large wall damping. We compute the Reynolds–Orr and activation energy descriptions of these neutrally stable FISI by continuing the linear stability analysis to the following order in perturbation amplitude. We find that both FISI are primarily driven by the working of normal stress on the flexible wall, lower-branch SD has negative activation energy, while upper-branch SD approaches zero activation energy in the limit of large wall damping. Finally, we elucidate interaction between TS and TWF modes for large wall mass, resulting in stable islands within unstable regions of parameter space.
| Item Type: | Articles |
|---|---|
| Additional Information: | We acknowledge funding from the Chinese Scholarship Council (DYW), the National Natural Science Foundation of China grant number 11820101001 (DYW, ZSL), Royal Society International Exchanges grant IEC/NSFC/170202 (ZSL, XYL) and UK Engineering and Physical Sciences Research Council grants EP/P024270/1, EP/S020950, EP/S030875 and EP/N014642 (XYL, PSS). |
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Luo, Professor Xiaoyu and Wang, Dr Danyang and Stewart, Professor Peter |
| Authors: | Wang, D., Luo, X., Liu, Z., and Stewart, P. S. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | Journal of Fluid Mechanics |
| Publisher: | Cambridge University Press |
| ISSN: | 0022-1120 |
| ISSN (Online): | 1469-7645 |
| Published Online: | 25 January 2023 |
| Copyright Holders: | Copyright © The Author(s), 2023 |
| First Published: | First published in Journal of Fluid Mechanics 956:A1 |
| Publisher Policy: | Reproduced under a Creative Commons license |
| Data DOI: | 10.5525/gla.researchdata.1232 |
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