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    Bifurcations and eddy genesis of Stokes flow within a sectorial cavity
    (Gauthier-Villars/Editions Elsevier, 2013) Gürcan, Fuat; Bilgil, Halis
    This work analyzes the Stokes flow generated in a sectorial driven cavity formed by a pair of curved stationary side walls capped by straight translating lids. The flow is governed by two physical control parameters: the cavity aspect ratio, A = r(2)/r(1) (where r1 and r2 are the radii of the inner and outer curved side walls, respectively) and the ratio (S = U-1/U-2) of the upper to the lower lid speed. A boundary value problem is formulated, which is solved analytically for the streamfunction, psi, expressed as an infinite series of Papkovich-Faddle eigenfunctions. The streamfunction solution is then expanded about any stagnation point to reveal changes in the local flow structure as A and S are varied. At critical values of A and S, stagnation point bifurcations arise and the local flow topology is transformed. For S is an element of [-1, 0) and A is an element of [1.6, 6.5), the various flow transformations are tracked as A is decreased and hence the means is identified by which new eddies appear and become fully developed. The key results are shown in an (5, A) control space diagram which exhibits an intricate structure due to the intersection and confluence of eight bifurcation curves representing flow bifurcations at degenerate critical points. There are eight points where two critical curves intersect and the flow bifurcations are described. It is shown that, for S not equal 0, the number of eddies increases from 1 to 3 via several key flow transformations, which become more complicated as vertical bar S vertical bar is reduced. For S = 0, as A is decreased slowly, the number of eddies also increases, in this case, from 1 to 2 via the development of corner eddies.
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    Effect of the Reynolds number on flow bifurcations and eddy genesis in a lid-driven sectorial cavity
    (Sprınger Japan Kk, 2016) Bilgil, Halis; Gürcan, Fuat
    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 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 . A comparison between the obtained results and some earlier studies is presented.