This research continues the research of Deng et al. (2022) [1], using Discrete Element Method (DEM) coupled with Finite Element Analysis to solve shotgun exterior ballistics. The simulation examples in this research are using an Italian-made 24 gm #9½ birdshot with 433 pellets fired from 30” long, 12-gauge cylinder and full choke barrels. The simulations of shotgun exterior ballistics of this research included pellet swarm velocity and the pellet dispersion at different distances until 50 yards away from the muzzle. The ballistics simulation of the pellet swarm is completed from interior to exterior consecutively after the shotshell is fired inside the chamber so all ballistics performances can be calculated at one time. Three forces were applied to the pellets for exterior ballistics simulation: the contact force between pellets, the aerodynamic separation force between pellets, and the drag force. Because of the complexity of the aerodynamic forces exerted on pellets, this research used an equivalent aerodynamic force to simulate this complex phenomenon. Two birdshot models with different pellet formations were created; the first one was simulated to calibrate the separation scale factor defined in aerodynamic separation force, and the second one was used for validation and sensitivity of the model. The simulation results show that for #9½ birdshots fired by cylinder barrel, the average Effective Shot Dispersion (ESD) of pellet dispersion of both birdshots inside the 30” diameter of the target circle at 40 yards from the muzzle is 398.53, which is remarkably close to 396.98 of the experiment result. The simulation of the average pellets' target hit rate is 77.14% (inside the 30” diameter of the target circle), which is also remarkably close to the experiment hit rate of 77.57%. The same birdshot fired from a full choke barrel shows that ESD and hit rate rose to 406.34 and 83.14%, respectively. These results demonstrate the effectiveness of using the discrete element method in conjunction with the proposed equivalent aerodynamic force to predict the shotgun's interior and exterior ballistics.

中文翻译：

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等效气动力离散元法霰弹枪外弹道分析

这项研究延续了 Deng 等人的研究。(2022) [1]，使用离散元法 (DEM) 结合有限元分析来求解霰弹枪外弹道。本研究中的模拟示例使用意大利制造的 24 克 #9½ 鸟弹，从 30 英寸长、12 号气缸和全阻流筒发射 433 颗弹丸。本研究对霰弹枪外弹道的模拟包括弹丸群速度和不同距离的弹丸散布，直至距离枪口 50 码。弹丸在室内发射后，从内到外依次完成弹丸群的弹道模拟，可一次性计算出所有弹道性能。对弹丸施加三种力进行外弹道模拟：弹丸之间的接触力、弹丸之间的空气动力分离力和阻力。由于弹丸所受的气动力的复杂性，本研究采用等效气动力来模拟这种复杂现象。创建了两种具有不同弹丸结构的鸟弹模型；第一个模型用于校准气动分离力中定义的分离比例因子，第二个模型用于模型的验证和灵敏度。模拟结果表明，对于通过圆筒发射的#9½鸟弹，两颗鸟弹在距枪口 40 码处的 30” 直径目标圆内的弹丸散布的平均有效散弹散布 (ESD) 为 398.53，非常接近实验结果为396.98。模拟的平均弹丸目标命中率为77.14%（目标圆直径30英寸内），这也非常接近实验的77.57%命中率。从全阻流管发射的相同鸟弹显示，ESD 和命中率分别上升至 406.34 和 83.14%。这些结果证明了使用离散元方法结合所提出的等效空气动力来预测霰弹枪的内部和外部弹道的有效性。