风沙运动中MAGNUS效应的数值研究

Numerical Study on Magnus Effect in Wind-blown Sand Movement

：在风沙运动中，跃移沙粒一般都会伴随高速旋转，同时引起一种升力效应，即Magnus效应。采用数值模拟的方法计算了0．1〈Re〈400，转速ω为100～1000rev·s^-1范围时均匀来流中单个球形沙粒受到的Magnus力，并与Rubinow和Keller推导的Magnus力公式进行了比较。计算结果表明，在0．1〈Re〈200范围内，升力和沙粒的旋转速度成正比，随雷诺数的增大而减小。同时，Magnus效应和固定沙粒在均匀来流中的流动结构也有关系，即计算结果和Magnus力公式的升力系数比K在沙粒流动是附体的时随Re数增加逐渐减小，在Re=20～30时达到最小值，然后在沙粒流动是对称分离的时K随着Re数增加逐渐增大。当雷诺数继续增大到超过200时，沙粒本身流动状态非对称所引起的升力超过Magnus效应产生的升力，但Magnus效应的作用也不可以忽略。根据计算结果，对Magnus力公式进行了修正。另外，还发现流场速度梯度与Magnus效应并没有耦合作用，速度梯度对升力的影响可以和Magnus效应线性叠加。

In the course of wind-blown sand movement, sand particles usually leap with high-speed rotation, which generates lift force called Magnus effect. The Magnus force upon a single rotating sphere was investigated by means of numerical simulation for Re （Reynolds number） from 0. 1 to 400 and rotational speeds from 100 to 1 000 rev· s^-1 . Results were compared with Magnus Force Formula deduced by Rubinow ＆ Keller. For Re between 0. 1 and 200, lift was in proportion with rotating speed, and it declined with the increase of Re. Meanwhile, Magnus effect has relation with the flow field patterns of a fixed sphere in a uniform flow： for attached flows, the lift coefficient ratio K by numerical simulation result and the Magnus Force Formula result declined with the increase of Re, and it reached a minimum value at Re=20-30; for symmetrically separated flows, however, K ascended with the increase of Re. At a higher Re of over 200, lift force caused by asymmetrical flow becomes greater than the Magnus force, but the Magnus effect can not be neglected. According to the numerical simulation results, an amending to the Magnus Force Formula was obtained. Since velocity gradient and Magnus force have no coupling effect, the impact of Magnus effect and velocity gradient on lift force can be linear superposed.