基于计算流体力学与刚体动力学耦合的高速旋转弹丸弹道计算方法

为了模拟高速旋转弹丸真实飞行弹道，基于弹轴运动附加于控制体表面、自转运动附加于壁面边界的思想，采用三维有限体积法，改进型简单低耗散迎风矢通量分裂格式、双时间步和Spalart-Allmaras湍流模型等计算流体力学（CFD）方法，建立具有任意拉格朗日-欧拉形式的流动模型。结合高速旋转弹丸刚体运力学（RBD）弹道方程组，推导出弹丸运动和控制体表面运动耦合的数学模型，提出一种CFD与RBD弹道耦合计算方法，实现了4阶龙格-库塔法中流动方程和弹道方程联立计算。研究结果表明：气动耦合方法和时间步长对弹道耦合计算结果影响较大；所提紧耦合方法在时间步长0.5 ms下M549旋成体弹丸仿真弹道结果与采用气动模型法计算结果基本吻合；旋转稳定二维弹道修正弹仿真弹道具有抬头力矩使弹丸低头的特性，该特性与文献［29］的研究结果一致。

Calculation of Trajectory of High-speed Spinning Projectile Based on Computational Fluid Dynamics/Rigid Body Dynamics Coupling

To study the real flight trajectory of high-speed spinning projectile, a computational fluid dynamics/rigid body dynamics (CFD/RBD) couping computational methodology is developed using improved simple low-dissipation advection upstream splitting method (SLAU2), dual time-stepping method and Spalart-Allmaras (S-A) turbulence model based on the ideas of adding the motion of projectile axis to the surfaces of control volumes and adding the spin motion to the wall boundary. A flow model with ALE form is established. An arbitrary Lagrangian-Eulerian (ALE) flow model is established. A coupled mathematical model of the projectile motion and the surfaces of control volume motion is developed, and the simultaneous calculation of flow equations and trajectory equations based on 4th order Runge-Kutta method is achieved. The research results show that the aerodynamic coupling method and time step have great influence on the trajectory coupling calculation results. The trajectory of M549 spinning projectile at 0.5 ms timesteps was simulated using the tighting coupling method. The simulated results are basically consistent with the results calculated by the aerodynamic model. The trajectory simulation result of a spin stabilized two-dimensional trajectory correction projectile shows that the characteristic of that rising moment causes the projectile nose drop, which is consistent with the result in Ref. \29\]. Key