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Transition to chaos in a two-sided collapsible channel flow

Published online by Cambridge University Press:  07 September 2021

Qiuxiang Huang Open the ORCID record for Qiuxiang Huang [Opens in a new window] ,
Fang-Bao Tian Open the ORCID record for Fang-Bao Tian [Opens in a new window] ,
John Young Open the ORCID record for John Young [Opens in a new window]  and
Joseph C.S. Lai Open the ORCID record for Joseph C.S. Lai [Opens in a new window]
Qiuxiang Huang
Affiliation:
School of Engineering and Information Technology, University of New South Wales, Canberra, ACT 2600, Australia
Fang-Bao Tian*
Affiliation:
School of Engineering and Information Technology, University of New South Wales, Canberra, ACT 2600, Australia
John Young
Affiliation:
School of Engineering and Information Technology, University of New South Wales, Canberra, ACT 2600, Australia
Joseph C.S. Lai
Affiliation:
School of Engineering and Information Technology, University of New South Wales, Canberra, ACT 2600, Australia
*
†Email addresses for correspondence: [email protected]; [email protected]
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Abstract

The nonlinear dynamics of a two-sided collapsible channel flow is investigated by using an immersed boundary-lattice Boltzmann method. The stability of the hydrodynamic flow and collapsible channel walls is examined over a wide range of Reynolds numbers $Re$, structure-to-fluid mass ratios $M$ and external pressures $P_e$. Based on extensive simulations, we first characterise the chaotic behaviours of the collapsible channel flow and explore possible routes to chaos. We then explore the physical mechanisms responsible for the onset of self-excited oscillations. Nonlinear and rich dynamic behaviours of the collapsible system are discovered. Specifically, the system experiences a supercritical Hopf bifurcation leading to a period-1 limit cycle oscillation. The existence of chaotic behaviours of the collapsible channel walls is confirmed by a positive dominant Lyapunov exponent and a chaotic attractor in the velocity-displacement phase portrait of the mid-point of the collapsible channel wall. Chaos in the system can be reached via period-doubling and quasi-periodic bifurcations. It is also found that symmetry breaking is not a prerequisite for the onset of self-excited oscillations. However, symmetry breaking induced by mass ratio and external pressure may lead to a chaotic state. Unbalanced transmural pressure, wall inertia and shear layer instabilities in the vorticity waves contribute to the onset of self-excited oscillations of the collapsible system. The period-doubling, quasi-periodic and chaotic oscillations are closely associated with vortex pairing and merging of adjacent vortices, and interactions between the vortices on the upper and lower walls downstream of the throat.

JFM classification

Biological Fluid Dynamics: Blood flow
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 926 , 10 November 2021 , A15
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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References

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Huang et al. Supplementary Movie 1

Re = 200, M=1, Ks=2400 and Pe=1.95

Download Huang et al. Supplementary Movie 1(Video)
Video 6.8 MB

Huang et al. Supplementary Movie 2

Re = 550, M=1, Ks=2400 and Pe=1.95

Download Huang et al. Supplementary Movie 2(Video)
Video 5.6 MB

Huang et al. Supplementary Movie 3

Re = 600, M=1, Ks=2400 and Pe=1.95

Download Huang et al. Supplementary Movie 3(Video)
Video 6.2 MB

Huang et al. Supplementary Movie 4

Re = 650, M=1, Ks=2400 and Pe=1.95

Download Huang et al. Supplementary Movie 4(Video)
Video 9.7 MB

Huang et al. Supplementary Movie 5

Re = 800, M=1, Ks=2400 and Pe=1.95

Download Huang et al. Supplementary Movie 5(Video)
Video 7.8 MB

Huang et al. Supplementary Movie 6

Re = 250, M=5, Ks=2400 and Pe=1.95

Download Huang et al. Supplementary Movie 6(Video)
Video 7.1 MB

Huang et al. Supplementary Movie 7

Re = 250, M=6, Ks=2400 and Pe=1.95

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Video 7 MB

Huang et al. Supplementary Movie 8

Re = 250, M=7, Ks=2400 and Pe=1.95

Download Huang et al. Supplementary Movie 8(Video)
Video 7.1 MB

Huang et al. Supplementary Movie 9

Re = 250, M=8, Ks=2400 and Pe=1.95

Download Huang et al. Supplementary Movie 9(Video)
Video 7.1 MB