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Effect of the Reynolds number on flow bifurcations and eddy genesis in a lid-driven sectorial cavity

  • Halis BilgilEmail author
  • Fuat Gürcan
Original Paper Area 1
  • 212 Downloads

Abstract

This paper presents the two-dimensional (2D) steady incompressible flow in a lid-driven sectorial cavity. In order to analyze the flow structures, the 2D Navier–Stokes equations are solved by using the finite element method. Different cases of the cavity aspect ratio A and three cases of the speed ratios \((S=-1,0,1)\) of the upper and the lower lids are considered. The finite element formulation for the governing equations is adopted via the velocity-pressure formulation. By varying A for each S, the effect of the Reynolds number on the streamline patterns and their bifurcations are investigated in range \(Re\in [0,200]\). A comparison between the obtained results and some earlier studies is presented.

Keywords

Bifurcation Eddy Finite element Flow structure Stagnation point Streamline 

List of symbols

\(r_{1},r_{2}\)

radius of the inner and outer circles respectively

A

cavity aspect ratio = \(r_{2}/r_{1}\)

\(2{\alpha }\)

angle of the sector

u

dimensionless fluid velocity

\(U_{1},U_{2}\)

speed of the upper and lower lids respectively

S

speed ratio of the moving lids = \(U_{2}/U_{1}\)

\(\psi \)

streamfunction

Re

Reynolds number

Mathematics Subject Classification

35Q35 74S05 00A69 

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Copyright information

© The JJIAM Publishing Committee and Springer Japan 2016

Authors and Affiliations

  1. 1.Department of MathematicsAksaray UniversityAksarayTurkey
  2. 2.Faculty of Engineering and Natural SciencesInternational University of SarajevoSarajevoBosnia and Herzegovina

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