Nonlinear Phenomena of Fluid Flow in a Bioinspired Two-Dimensional Geometric Symmetric Channel with Sudden Expansion and Contraction

Liquan Yang, Mo Yang () and Weijia Huang
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Liquan Yang: School of Energy and Power Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China
Mo Yang: School of Energy and Power Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China
Weijia Huang: School of Energy and Power Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China

Mathematics, 2024, vol. 12, issue 4, 1-14

Abstract: Inspired by the airway for phonation, fluid flow in an idealized model within a sudden expansion and contraction channel with a geometrically symmetric structure is investigated, and the nonlinear behaviors of the flow therein are explored via numerical simulations. Numerical simulation results show that, as the Reynolds number (Re = U 0 H/ν) increases, the numerical solution undergoes a pitchfork bifurcation, an inverse pitchfork bifurcation and a Hopf bifurcation. There are symmetric solutions, asymmetric solutions and oscillatory solutions for flows. When the sudden expansion ratio (Er) = 6.00, aspect ratio (Ar) = 1.78 and Re ≤ Rec1 (≈185), the numerical solution is unique, symmetric and stable. When Rec1 < Re ≤ Rec2 (≈213), two stable asymmetric solutions and one symmetric unstable solution are reached. When Rec2 < Re ≤ Rec3 (≈355), the number of numerical solution returns one, which is stable and symmetric. When Re > Rec3, the numerical solution is oscillatory. With increasing Re, the numerical solution develops from periodic and multiple periodic solutions to chaos. The critical Reynolds numbers (Rec1, Rec2 and Rec3) and the maximum return velocity, at which reflux occurs in the channel, change significantly under conditions with different geometry. In this paper, the variation rules of Rec1, Rec2 and Rec3 are investigated, as well as the maximum return velocity with the sudden expansion ratio Er and the aspect ratio Ar.

Keywords: bioinspired channel; sudden expansion and contraction channels; fluid flow; numerical simulation; bifurcation; nonlinearity (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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