船尾形状对旋成体马格努斯效应的影响

尖头旋成体和船尾形状是子弹、炮弹及火箭弹等抛射体上常用的布局形式。研究表明船尾布局具有减小底部阻力、增大射程的作用，但此时旋成体的马格努斯效应增大，对运动稳定性产生不利影响。为了解释这种流动现象，对三维旋转弹流场进行了数值模拟，对从亚声速到超声速下的旋成体马格努斯力和力矩进行了分析，重点对标准形状和船尾形状两种底部进行了比较。结果表明，相对于标准形状，在所有来流下船尾形状都起到了增大马格努斯效应的作用，并且马格努斯力和力矩与船尾角成正比。为了揭示其流动机理，选择代表性计算状态对两种布局马格努斯力矩系数分布、边界层厚度分布和边界层位移厚度分布进行了对比分析，结果表明，在亚跨声速下船尾马格努斯效应由绕拐角的加速流动引起，使当地压力系数幅值增大；在超声速下船尾马格努斯效应由船尾段的气流膨胀引起，使旋成体左右两侧的边界层位移厚度畸变增大。上述两种效应都使马格努斯力矩增加，对于亚声速流动来说，该效应发生在柱段与船尾段连接位置；对于超声速流动来说，该效应发生在连接点以后的船尾段上。当来流速度在声速点附近时，上述两种效应都可能发挥作用，使船尾形状的旋成体马格努斯效应大幅增加。

Influence of boattail shape on Magnus effects of a spinning rotating body

The pointed rotating body and boattail shape are common layout forms of projectiles such as bullets, cannons and rockets. Studies have shown that the boattail layout has the effect of reducing the bottom resistance and increasing the range, while on the other side it has an adverse effect on the motion stability owing to the increasing Magnus effects of rotating bodies. In order to explain this flow phenomena, the numerical simulation of the flow field of a three-dimensional spinning bullet is carried out to analyze the Magnus forces and moments from subsonic to supersonic, focusing on the comparison between the standard and the boattail bottom shape. The results indicate that the boattail shape has an effect of increasing the Magnus effect relative to the standard shape at all incoming flows, and the Magnus forces and movements are proportional to the boattail angle. In order to reveal the flow mechanism, a comparative analysis of the distributions of Magnus moment coefficients, boundary layer thickness and boundary layer displacement thickness for the two layouts is performed at selected incoming speeds. Results show that the stern Magnus effect at subsonic and transonic speeds is caused by the accelerated flow around the corner, which increases the local pressure coefficient amplitude. For supersonic flow, the Magnus effect is caused by the expansion of the flow at the stern, which increases the boundary layer displacement thickness distortion on both sides of the rotating body. Both of the effects increase the Magnus moment of rotating body, in terms of subsonic flow, this effect occurs at the joint between the column section and the stern section, while in supersonic flow, it occurs at the stern section after the joint. Both effects may play a role when the incoming velocity is around the acoustic velocity point, causing the Magnus effect of the boattail configuration to increase substantially.