Dynamics of a hydrofoil free to oscillate in the wake of a fixed, constantly rotating or periodically rotating cylinder

Abstract We present the dynamics of a hydrofoil free to oscillate in a plane as it interacts with vortices that are shed from a cylinder placed upstream. We consider cases where the cylinder is (i) fixed, (ii) forced to rotate constantly in one direction or (iii) forced to rotate periodically. When the upstream cylinder is fixed, at lower reduced velocities, the hydrofoil oscillates with a frequency equal to the frequency of vortices shed from the cylinder, and at higher reduced velocities with a frequency equal to half of the shedding frequency. When we force the cylinder to rotate in one direction, we control its wake and directly influence the response of the hydrofoil. When the rotation rate goes beyond a critical value, the vortex shedding in the cylinder's wake is suppressed and the hydrofoil is moved to one side and remains mainly static. When we force the cylinder to rotate periodically, we control the frequency of vortex shedding, which will be equal to the rotation frequency. Then at lower rotation frequencies, the hydrofoil interacts with one of the vortices in its oscillation path in the positive crossflow (transverse) direction, and with the second vortex in the negative crossflow direction, resulting in a 2:1 ratio between its inline and crossflow oscillations and a figure-eight trajectory. At higher rotation frequencies, the hydrofoil interacts with both shed vortices on its positive crossflow path and again in its negative crossflow path, resulting in a 1:1 ratio between its inline and crossflow oscillations and a linear trajectory.

摘要：我们阐述了一个水翼在一个平面内自由振荡的动力学过程，此时它与放置在上游的圆柱所脱落的涡旋相互作用。我们考虑了圆柱（i）固定、（ii）被强制在一个方向上持续旋转或（iii）被强制周期性旋转的情况。当上游圆柱固定时，在较低的折合速度下，水翼以等于圆柱脱落涡旋频率的频率振荡，在较高的折合速度下，以等于脱落频率一半的频率振荡。当我们强制圆柱在一个方向上旋转时，我们控制了它的尾流并直接影响水翼的响应。当旋转速率超过一个临界值时，圆柱尾流中的涡旋脱落被抑制，水翼被移向一侧并主要保持静止。当我们强制圆柱周期性旋转时，我们控制了涡旋脱落的频率，该频率将等于旋转频率。然后在较低的旋转频率下，水翼在正向横流（横向）方向的振荡路径中与其中一个涡旋相互作用，并在负向横流方向与第二个涡旋相互作用，导致其顺流向和横流向振荡呈2∶1的比例以及呈现出“8”字形轨迹。在较高的旋转频率下，水翼在其正向横流路径以及再次在负向横流路径中都与两个脱落的涡旋相互作用，导致其顺流向和横流向振荡呈1∶1的比例以及呈现出直线轨迹。