Numerical Simulation Of VIV Of Two Rigidly Connected Circular Cylinders In Tandem At A Low Reynolds Number

When water flows around an elastically installed cylinder,it will cause vortex-induced vibration of the structure,which will lead to fatigue damage of the structure and reduce its life.In structures such as offshore oil platforms and Submerged Floating Tunnels,two pipes or risers are connected at a certain distance to form a rigid double-pipe structure.Due to the interaction between adjacent pipelines,the vortex-induced vibration response of this structure is quite different from that of an isolated cylinder.It is of great scientific significance and engineering application value to study the vortex-induced vibration response of two rigidly connected cylinders under the action of water flow.Based on the finite difference method(FDM),a numerical model for solving the problems of flow around cylinders and vortex-induced vibration of cylinders at a low Reynolds number is established.The governing equation of fluid motion is the Navier-Stokes equation,the governing equation of structural motion is solved by the fourth-order Runge-Kutta method,and the boundary of the structure is treated by the virtual boundary force method(VBF).The numerical model is verified by the calculation results of flow around isolated and tandem cylinders and vortex-induced vibration of isolated and tandem cylinders:(1)In the numerical simulation of flow around two tandem cylinders at Re=200,the lift coefficients,drag coefficients,and Strouhal number of the structure at different spacing ratios are calculated.(2)In the numerical simulation of vortex-induced vibration of isolated and tandem cylinders at Re=200,the response amplitude,response frequency,and force of the structure at different reduced velocities are calculated.The calculated results of the above examples are in good agreement with those of the predecessors.The validated numerical model is used to calculate one-versus two-degree-of-freedom vortex-induced vibrations of the two rigidly connected cylinders in tandem under the conditions of Re=150,mass ratio m~*=2,and damping ratioζ=0.The response amplitude,response frequency,lift coefficients,drag coefficients,and wake field of the structure at two spacing ratios L~*=2,4 are analyzed,and the calculation results of vortex-induced vibration of the structure with one degree of freedom and two degrees of freedom are compared.The range of reduced velocities is U_r=0.5～10 with an interval of 0.5.The calculation results of one-degree-of-freedom vortex-induced vibration of two rigidly connected circular cylinders in tandem show that:(1)In the range of U_r=4.5～6(L~*=2)and U_r=7.5～8.5(L~*=4),the time histories of the transverse displacement of the structure show the characteristic of"beat";In the range of U_r=4.5～6,the"beat"period increases with the increase of U_r(L~*=2);In the range of U_r=7.5～8.5,with the increase of U_r,the"beat"period reaches its maximum at U_r=8.(2)In each"beat"period,the positive and negative vortices in the wake of the structure merge once(L~*=2,4).(3)In the range of U_r=0.5～10,the transverse response frequency f_y of the structure is not locked with the natural frequency f_n,which is different from f_y/f_n≈1 in the lock-in range of the vortex-induced vibration of an isolated cylinder(L~*=2,4).Compared with the calculation results of one-degree-of-freedom vortex-induced vibration,the calculation results of two-degree-of-freedom vortex-induced vibration of two rigidly connected circular cylinders in tandem show that:(1)In the range U_r=4.5～6,the time histories of the transverse displacement of the structure also shows the characteristic of"beat",while the difference is that with the increase of U_r,the"beat"period reaches its maximum at U_r=5(L~*=2).The beat phenomenon occurs in a wider range of reduced velocities,the time histories of the transverse displacement of the structure show the characteristic of"beat"at U_r=5.5,6,7,8.5,9(L~*=4).(2)In the range U_r=4.5～6,the shape and merging period of the vortex in the wake of the structure change(L~*=2);In the range U_r=5～6,the shedding behavior of the positive and negative vortices in the wake of the structure is inconsistent,and the motion trajectories of the structure are"oblique ellipse"(L~*=4).The changes in the wake field mentioned above are related to the obvious increase of the amplitude of the structure along the flow direction in those reduced velocities range(L~*=2,4).