NUMERICAL STUDY OF SLOW VISCOUS-FLOW WITH SHEAR PAST A CIRCULAR-CYLINDER

Steady two-dimensional flow of a viscous incompressible fluid at low Reynolds numbers past a circular cylinder is considered in this investigation. The flow at sufficiently large distances is considered as simple shear in problem 1 and variable shear in problem 2. The derivatives in the r.h.s. of the governing equations are approximated by backward - differences of order h or k. The resulting algebraic equations are solved by 'Block SLOR' method and equations in each block are solved by 'Method of Sweeps'. The parameters that enter the flow are the Reynolds number Re = Ua/v and G = velocity curvature factor. For both simple shear problem and variable shear problem (here after called as problem 1 and problem 2), the velocity curvature factor is considered as G = 0.1. The equations are solved for Re = 0. 7, 0.1 and Re = .08 in problems 1 and 2 respectively. The iterations are stopped when the values of the two successive iterates in absolute value are less than 10(-5). The number of iterations for Re = 0. 1 is 1569, for Re = 0.7 is 1501 in problem 1 and in problem 2 the number of iterations are taken for Re = 0.08 is 1807. For Re > 0.7 in problem 1 and for Re > 0.08 in problem 2 there is no convergence. Graphs are drawn for stream lines, vorticity lines. The drag, lift and torque on the cylinder are also given.