Multiplicity of Steady State Solutions in 2-D Incompressible Viscous Wall Driven Arc-Shaped Cavity Flow

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Erturk E.

JOURNAL OF APPLIED FLUID MECHANICS, vol.14, no.4, pp.1147-1163, 2021 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 4
  • Publication Date: 2021
  • Doi Number: 10.47176/jafm.14.04.32281
  • Journal Indexes: Science Citation Index Expanded, Scopus, Aerospace Database, Applied Science & Technology Source, Aqualine, Aquatic Science & Fisheries Abstracts (ASFA), Communication Abstracts, Computer & Applied Sciences, INSPEC, Metadex, Directory of Open Access Journals, Civil Engineering Abstracts
  • Page Numbers: pp.1147-1163


Numerical simulations of the steady 2-D incompressible viscous flow in an arc-shaped cavity are presented. The Navier-Stokes equations in streamfunction and vorticity formulation are solved numerically using a body fitted mesh obtained by a conformal mapping. Our numerical results reveal that the arc-shaped cavity flow has multiple steady solutions above a bifurcation Reynolds number when the arc length ratio is less than 1/2 (r <1/2). Multiple steady state solutions of the arc-shaped cavity flow with different arc length ratios (r =2/5, 1/3, 1/4, 1/5 and 1/6) are presented at a variety of Reynolds numbers. Our results show that the bifurcation Reynolds number at which a second solution starts to exist changes as the arc length ratio of the arc-shaped cavity changes. Among the considered different arc length ratios (r =2/5, 1/3, 1/4, 1/5 and 1/6), the minimum bifurcation Reynolds number occurs at 1/3 arc length ratio with Re=5164. Detailed results are presented.