Numerical simulation of flow over four identical circular cylinders with various gap ratios and attack angles

Viscous flow past four identical circular cylinders in square arrangement is investigated numerically. The two-dimensional Navier-Stokes equations are solved by using the three-step finite element method. The effects of gap ratio L / D and attack angle β on the wake mode, vortex shedding frequency, pressure distribution and fluid forces are examined at the Reynolds number Re = 200, where L is the minimal center-tocenter distance between two adjacent cylinders, D is the uniform cylinder diameter. Calculations are carried out for various L / D, ranging from 1.25 to 5.0, and three typical attack angles β = 0°, 22.5° and 45°. The numerical examinations identified three wake modes, which are mainly dependent on the gap ratio in contrast to the attack angle. Otherwise the pressure distribution along each cylinder surface is related closely to the attack angle. The variation of mean drag coefficient and RMS lift coefficient with the gap ratio under different attack angles are presented. The comparisons with the isolate cylinder at the same Reynolds number show significant diversities of the hydrodynamic characteristics. The fluid forces from the present 2-D model are compared with the available 3- D results. Good agreements are observed except for the special case involving the wake transition, where the strong threedimensionality of flow is expected.