Incompressible viscous flow past two circular cylinders of different diameters is analysed by solving the two-dimensional Navier-Stokes equations using finite difference method at two Reynolds numbers of 100 and 1000. The diameter of the secondary cylinder is half of that of the main cylinder. To investigate the effect of the secondary cylinder on the flow, the secondary cylinder is attached with the main cylinder at five positions, where the angles of stagger of the cylinders to the flow direction are 0 °, 45 °, 90 °, 135 °, and 180 °. Compared with the results for the case of a single cylinder, it is found that the drag acting on both cylinders changes considerably at angles of 0 °, 90 ° and 180 °, and does not vary much at angles of 45 ° and 135 °. The mean lift on the main cylinder decreases at angles of 45 °, 90 °, and 135 °, but keeps unaffected at angles of 0 ° and 180 °. The mean lift on the secondary cylinder increases at angles of 45 °, 90 °, and 135 °, and does not change at 0 °, and 180 °. The amplitudes of drag and lift coefficients increase at the angles of 45 °, 90 °, and 135 °, while decrease at the other angles. The frequency of the vortex shedding is different from that of single cylinder at different positions. Because of the asymmetrical flow, there is also a strong flow-induced torsional moment at angle 90 °. The pressure and vorticity distributions along the surface of the cylinders are also studied in detail.
u, Due to the technical requirements, an auxiliary pipeline is often connected with the main pipeline in the offshore engineering.
