Numerical simulation of a freely vibrating circular cylinder with different natural frequencies

This paper deals with the numerical simulation of low-Reynolds-number-flow around a freely vibrating circular cylinder in two-degrees-of-freedom. The governing equations are written in a non-inertial system fixed to the moving cylinder and solved using finite difference method. The natural frequency of the cylinder is chosen to be constant, agreeing with the vortex-shedding frequency for a stationary cylinder at Reynolds number Re0. Systematic computations are carried out for Re0=80, 100, 140 and 180 keeping the mass ratio and structural damping coefficient at m*=10 and ζ=0. The effect of Re0 on the root-mean-square (rms) values of cylinder displacements and drag coefficients is analyzed. Plotting the data set belonging to different Re0 values against U*St0 makes comparison easier. Local extreme values are found in the rms of streamwise displacement and drag coefficient in the range U*St0=0.4–0.65. In the vicinity of U*St0=0.5 the rms of drag approaches zero and the phase angle between the x component of the motion and drag changes abruptly from 0° to 180°. The pressure drag coefficient seems to be responsible for the sudden change. The cylinder follows a distorted figure-eight path in most cases investigated and its orientation changes from clockwise to counterclockwise orbit at around U*St0=0.5.

本文针对两自由度自由振动圆柱的低雷诺数绕流数值模拟展开研究。控制方程建立于随运动圆柱固连的非惯性坐标系中，并采用有限差分法求解。选取与雷诺数Re0下静止圆柱的涡脱频率相一致的恒定圆柱固有频率。针对Re0=80、100、140及180开展系统数值计算，保持质量比m*=10与结构阻尼系数ζ=0恒定不变。分析了雷诺数Re0对圆柱位移与阻力系数均方根（root-mean-square, rms）值的影响。将不同Re0对应的数据集以U*St0为横轴绘图，可使对比更为简便。在U*St0=0.4~0.65区间内，流向位移与阻力系数的均方根值出现局部极值。在U*St0≈0.5附近，阻力系数的均方根值趋近于零，且运动x分量与阻力间的相位角从0°突变为180°，该突变似乎由压力阻力系数主导。绝大多数研究工况下，圆柱运动轨迹呈变形的"8"字形，且其运动轨道在U*St0≈0.5处从顺时针转向逆时针。