Wang, D.Y., Luo, X.Y. and Stewart, P.S. (2021) Energetics of collapsible channel flow with a nonlinear fluid-beam model. Journal of Fluid Mechanics, 926, A2. (doi: 10.1017/jfm.2021.642)
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Abstract
We consider flow along a finite-length collapsible channel driven by a fixed upstream flux, where a section of one wall of a planar rigid channel is replaced by a plane-strain elastic beam subject to uniform external pressure. A modified constitutive law is used to ensure that the elastic beam is energetically conservative. We apply the finite element method to solve the fully nonlinear steady and unsteady systems. In line with previous studies, we show that the system always has at least one static solution and that there is a narrow region of the parameter space where the system simultaneously exhibits two stable static configurations: an (inflated) upper branch and a (collapsed) lower branch, connected by a pair of limit point bifurcations to an unstable intermediate branch. Both upper and lower static configurations can each become unstable to self-excited oscillations, initiating either side of the region with multiple static states. As the Reynolds number increases along the upper branch the oscillatory limit cycle persists into the region with multiple steady states, where interaction with the intermediate static branch suggests a nearby homoclinic orbit. These oscillations approach zero amplitude at the upper branch limit point, resulting in a stable tongue between the upper and lower branch oscillations. Furthermore, this new formulation allows us to calculate a detailed energy budget over a period of oscillation, where we show that both upper and lower branch instabilities require an increase in the work done by the upstream pressure to overcome the increased dissipation.
| Item Type: | Articles |
|---|---|
| Additional Information: | Funding. We gratefully acknowledge funding from the Chinese Scholarship Council (D.Y.W.), UK Engineering and Physical Sciences Research Council grants EP/S020950, EP/S030875 and EP/N014642 (X.Y.L. and P.S.S.). |
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | Wang, Dr Danyang and Luo, Professor Xiaoyu and Stewart, Professor Peter |
| Authors: | Wang, D.Y., Luo, X.Y., 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: | 09 September 2021 |
| Copyright Holders: | Copyright © The Author(s) 2021 |
| First Published: | First published in Journal of Fluid Mechanics 926: A2 |
| Publisher Policy: | Reproduced under a Creative Commons licence |
| Related URLs: | |
| Data DOI: | 10.5525/gla.researchdata.1112 |
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