Multiple steady and oscillatory solutions in a collapsible channel flow

Wang, D., Luo, X. and Stewart, P. S. (2021) Multiple steady and oscillatory solutions in a collapsible channel flow. International Journal of Applied Mechanics, (doi: 10.1142/S1758825121500587) (Early Online Publication)

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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:Early Online Publication
Refereed:Yes
Glasgow Author(s) Enlighten ID:Luo, Professor Xiaoyu and Wang, Dr Danyang and Stewart, Dr 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

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