Wang, D., Luo, X. and Stewart, P. S. (2021) Multiple steady and oscillatory solutions in a collapsible channel flow. International Journal of Applied Mechanics, 13(6), 2150058. (doi: 10.1142/S1758825121500587)
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Abstract
We study flow driven through a finite-length planar rigid channel by a fixed upstream flux, where a segment of one wall is replaced by a pre-stressed elastic beam subject to uniform external pressure. The steady and unsteady systems are solved using a finite element method. Previous studies have shown that the system can exhibit three steady states for some parameters (termed the upper, intermediate and lower steady branches, respectively). Of these, the intermediate branch is always unstable while the upper and lower steady branches can (independently) become unstable to self-excited oscillations. We show that for some parameter combinations the system is unstable to both upper and lower branch oscillations simultaneously. However, we show that these two instabilities eventually merge together for large enough Reynolds numbers, exhibiting a nonlinear limit cycle which retains characteristics of both the upper and lower branches of oscillations. Furthermore, we show that increasing the beam pre-tension suppresses the region of multiple steady states but preserves the onset of oscillations. Conversely, increasing the beam thickness (a proxy for increasing bending stiffness) suppresses both multiple steady states and the onset of oscillations.
| Item Type: | Articles |
|---|---|
| Additional Information: | We gratefully acknowledge funding from the Chinese Scholarship Council (DYW) and UK Engineering and Physical Sciences Research Council grants EP/S020950, EP/S030875 and EP/N014642 (XYL and PSS) and EP/P024270/1 (PSS). |
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Wang, Dr Danyang and Luo, Professor Xiaoyu and Stewart, Professor Peter |
| Authors: | Wang, D., Luo, X., and Stewart, P. S. |
| College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
| Journal Name: | International Journal of Applied Mechanics |
| Publisher: | World Scientific Publishing |
| ISSN: | 1758-8251 |
| ISSN (Online): | 1758-826X |
| Published Online: | 12 July 2021 |
| Copyright Holders: | Copyright © 2021 The Authors |
| First Published: | First published in International Journal of Applied Mechanics 13(6): 2150058 |
| Publisher Policy: | Reproduced under a Creative Commons License |
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