Flow past a square cylinder at low Reynolds numbers

Abstract

Results are presented for the flow past a stationary square cylinder at zero incidence for Reynolds number, Re ⩽ 150. A stabilized finite-element formulation is employed to discretize the equations of incompressible fluid flow in two-dimensions. For the first time, values of the laminar separation Reynolds number, Re_s, and separation angle, θ_s, at Re_s are predicted. Also, the variation of θ_s with Re is presented. It is found that the steady separation initiates at Re = 1.15. Contrary to the popular belief that separation originates at the rear sharp corners, it is found to originate from the base point, i.e. θ_s=180^∘ at Re = Re_s. For Re > 5, θ_s approaches the limit of 135^∘. The length of the separation bubble increases approximately linearly with increasing Re. The drag coefficient varies as Re^−0.66. Flow characteristics at Re ⩽ 40 are also presented for elliptical cylinders of aspect ratios 0.2, 0.5, 0.8 and 1 (circle) having the same characteristic dimension as the square and major axis oriented normal to the free-stream. Compared with a circular cylinder, the flow separates at a much lower Re from a square cylinder leading to the formation of a bigger wake (larger bubble length and width). Consequently, at a given Re, the drag on a square cylinder is more than the drag of a circular cylinder. This suggests that a cylinder with square section is more bluff than the one with circular section. Among all the cylinder shapes studied, the square cylinder with sharp corners generates the largest amount of drag.