Flow past a square cylinder at low Reynolds numbers

Abstract

SUMMARYResults 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, s , at Re s are predicted. Also, the variation of 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. s = 180 • at Re = Re s . For Re>5, 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.

Unconfined Unsteady Laminar Flow of a Power-Law Fluid across a Square Cylinder

“…In the same figure results from Franke et al [13], Sen et al [14], Ehsan et al [15], and Zhao [16] Figure 5C it is seen that the large computational domain allows some minor frequencies (superharmonics) to appear, whereas these minor frequencies disappear in the narrow computational domain. After the above comparisons results for the nonNewtonian fluids are presented.…”

“…In the same figure results from Franke et al [13], Sen et al [14], Ehsan et al [15], and Zhao [16] are included for comparison. In the same figure results from the present work are included for the cases H/D = 50,000 and H/D = 20.…”

CFD Analysis of 2D Unsteady Flow Past a Square Cylinder at Low Reynolds Numbers

“…More complex cases are being investigated. The boundary conditions used in this paper are different from the boundary conditions used in [1,2]. There are practical problems following the boundary conditions described in Section 2.…”

“…The flow around a square cylinder has been investigated extensively using different methods in literature [e.g. 1,2].…”

In-chip direct laser writing of a centimeter-scale acoustic micromixer

“…Comparing this estimation with our case of square cylinders placed in a row shows that this value should be taken as a lower estimate, since both a square cross section as placing pillars closely in a row increase the drag compared a single round cylinder. 34,35 Based on the curvatures of the solvent surface surrounding the pillars during evaporation, we estimate a maximum Laplace pressure of −0.8 kPa inside the solvent, corresponding with a peak inward faced capillary force on the outermost pillar of approximately 3 μN.…”