Fundamental Study on Unsteady Aerodynamics of Macroscopic Particles

本研究的主要目的是了解旋转和平移速度阶跃变化的宏观颗粒所受的气动力，特别是研究非线性相互作用对流体动力的影响，这可能在颗粒的非定常运动中起到重要作用。在理论研究中，主要采用作者提出的匹配渐近展开的方法来处理二维圆柱体，该圆柱体是以旋转运动为脉冲开始的。最重要的结果是，升力是由非线性相互作用产生的，其运动开始时的渐近行为取决于雷诺数的阶数，即对于低雷诺数，它表现出t^&lt；-1/2&gt；奇异性，对于中等雷诺数，它是一个常数，对于高雷诺数，它具有t^&lt；1/2&gt；，其中t是从开始调谐的。为了验证涡旋法的有效性，对上述理论问题进行了处理，并对理论结果进行了验证。在三维流动中，拉伸项对流动行为起着重要的作用，因此在本文的涡旋法中，将PSE方法的概念应用到这一项上，并计算了球体周围的流动。数值结果表明，用PSE方法计算拉伸项是可行的。

The primary purpose of the present study is to know the aerodynamic forces acting on a macroscopic particle which undergoes a step change in its rotating and translating velocities, in particular, to investigate the effect of nonlinear interaction to the hydrodynamic forces, which may play an important role in the unsteady motion of the particle.In the theoretical study, a two-dimensional circular cylinder, which starts impulsively with rotational motion, is mainly treated, using the method of the matched asymptotic expansion, which was proposed by the present investigator. The most important result is that the lift force is generated by the nonlinear interaction and its asymptotic behavior for the beginning of motion is dependent on the order of Reynolds number, that is, for the low Reynolds number it exhibits t^<-1/2> singularity, for the moderate Reynolds number it is a constant, and for the high Reynolds number it has t^<1/2>, where t is tune from the start.In the numerical study, the vortex method is used in the present study, which may be powerful for the unsteady flow, and is developed to the extremely low Reynolds number flow. To confirm the validity of the vortex method the above mentioned theoretical problems are treated and the theoretical results are confirmed. In the three-dimensional flow, the stretching term plays an important role to the flow behavior, so in the present vortex method the concept of the PSE method is applied to this term and the flow around a sphere is calculated. The numerical results show that the PSE method for the stretching term is available.