The Magnus moment characteristics of rotating missiles with Mach numbers of 1.3 and 1.5 at different altitudes and angles of attack were numerically simulated based on the transition SST model. It was found that the Magnus moment direction of the missiles changed with the increase of the angle of attack. At a low altitude, with the increase of the angle of attack, the Magnus moment direction changed from positive to negative; however, at high altitudes, with the increase of the angle of attack, the Magnus moment direction changed from positive to negative and then again to positive. The Magnus force direction did not change with the change of the altitude and the angle of attack at low angles of attack; however, it changed with altitude at an angle of attack of 30°. When the angle of attack was 20°, the interference of the tail fin to the lateral force of the missile body was different from that for other angles of attack, leading to an increase of the lateral force of the rear part of the missile body. With the increasing altitude, the position of the boundary layer with a larger thickness of the missile body moved forward, making the lateral force distribution of the missile body even. Consequently, Magnus moments generated by different boundary layer thicknesses at the front and rear of the missile body decreased and the Magnus moment generated by the tail fin became larger. As lateral force directions of the missile body and the tail were opposite, the Magnus moment direction changed noticeably. Under a high angle of attack, the Magnus moment direction of the missile body changed with the increasing altitude. The absolute value of the pitch moment coefficient of the missile body decreased with the increasing altitude.

中文翻译：

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高空旋转导弹马格努斯力矩气动特性分析

基于过渡SST模型，数值模拟了马赫数为1.3和1.5的旋转导弹在不同高度和攻角下的马格努斯矩特性。发现导弹的马格努斯矩方向随攻角的增加而变化。在低空，随着迎角的增加，马格努斯矩的方向从正变为负；但是，在高海拔地区，随着迎角的增加，马格努斯矩的方向从正变为负，然后又变为正。在低攻角下，马格努斯力的方向不随高度和攻角的变化而变化。但是，它随高度变化（迎角为30°）而变化。当迎角为20°时 尾鳍对导弹主体侧向力的干扰与其他迎角不同，导致导弹主体后部的侧向力增加。随着高度的增加，导弹主体厚度较大的边界层位置向前移动，使得导弹主体的侧向力分布均匀。因此，导弹主体前后边界层厚度不同而产生的马格努斯矩减小，尾鳍产生的马格努斯矩变大。由于导弹主体和机尾的侧向力方向相反，因此马格努斯矩方向发生了明显变化。在高攻角下，导弹主体的马格努斯力矩方向随高度的增加而变化。