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Multiplicity of Steady State Solutions in 2-D Incompressible Viscous Wall Driven Arc-Shaped Cavity ‎Flow
Author(s): Ercan Erturk
Keywords: Arc-shaped cavity flow; Multiple steady state solutions; Bifurcation Reynolds number; 2-D ‎incompressible viscous flow; Arc length ratio‎.
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 ( <1/2). Multiple steady state solutions of the arc-shaped cavity flow with different arc length ratios ( =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 ( =2/5, 1/3, 1/4, 1/5 and 1/6), the minimum bifurcation Reynolds number occurs at 1/3 arc length ratio with =5164. Detailed results are presented‎.

Journal of Applied Fluid Mechanics

The Journal of Applied Fluid Mechanics (JAFM) is an international, peer-reviewed journal which covers a wide range of theoretical, numerical and experimental aspects in fluid mechanics. The emphasis is on the applications in different engineering fields rather than on pure mathematical or physical aspects in fluid mechanics. Although many high quality journals pertaining to different aspects of fluid mechanics presently exist, research in the field is rapidly escalating.

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