小振幅振动翼型升力迟滞环变向的成因分析

在低雷诺数条件下研究了SD7037翼型小振幅强迫振动时，振动轴位置和减缩频率对翼型气动特性的影响。通过升力系数随时间变化曲线与迎角随时间变化曲线的对比，发现引起升力系数随迎角变化的迟滞环变向的原因主要是升力系数随时间变化曲线的相位发生变化，并从数学上证明了这个相位是关于减缩频率的函数。而且，当升力系数随时间变化曲线的相位变大时，会使得对应的升力系数随迎角变化的迟滞环曲线从逆时针向顺时针方向变化，这中间必然会经历一个"直线"过程，就好像迟滞现象消失了一样。进一步通过对比流场，发现振动轴位置和减缩频率对此相位的影响机制不同，振动轴位置主要改变翼型的有效迎角，而减缩频率的增大则影响了周围流场结构，使得附加质量带来的反作用力变大，进而提高升力，振动轴向前移动和减缩频率的增大都会增大升力系数曲线的相位。

Factors analysis of lift hysteresis loop direction changing for small amplitude oscillating airfoils

This paper studies the effects of the pivot location and the reduction frequency on the aerodynamic characteristics of the SD7037 airfoil under small amplitude forced oscillation at low Reynolds number. By comparing lift coefficient-time curve with angle of attack-time curve, it is found that the hysteresis loop direction changing of the lift coefficient varies with the angle of attack is mainly due to the change of the phase of the lift coefficient-time curve. It is proved mathematically that the phase is a function of reduction frequency. What's more, when the phase of the lift coefficient-time curve increases, the hysteresis loop of the corresponding lift coefficient-angle of attack curve will change from counterclockwise to clockwise. In this process, the lift coefficient-angle of attack curve inevitably shows a straight line shape, as if the hysteresis phenomenon "disappears". In addition, by comparing the flow field structure, it is found that the pivot location and reduction frequency have different impact on this phase. While the pivot location mainly changes the effective angle of attack of the airfoil, the increase of reduction frequency affects the structure of the surrounding flow field, so that the reaction force brought by the added mass becomes stronger, and thus the lift is improved. Both the forward movement of the pivot location and the increase of reduction frequency will increase the phase of the lift coefficient curve.