The influence of density gradient of driving gas on projectile launching velocity
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摘要: 为进一步提升轻气炮的发射能力，提出采用梯度气体替代单一氢气或氦气作为驱动气体的方法，通过对等直径发射器进行分析，建立了弹丸在梯度气体驱动下的加速运动模型，对比了氖-氦梯度气体驱动与单一氦气驱动的发射能力差异，分析了梯度气体参数对发射性能的影响。结果表明，与单一氦气驱动相比，氖-氦梯度气体驱动能够提升0.4～1.4 km/s的发射速度或降低0.2～0.9 GPa的发射过载；气体的密度和活塞的运动速度对发射速度和过载的影响最大，气体压力和多方气体指数的影响次之；梯度气体中，高密度气体应选择多方气体指数和密度较高的气体（如氖气、氩气等）；梯度气体界面位置（高密度气体占比）对发射速度的影响不大，但高密度气体占比少有利于降低弹底压力。Abstract: The most common hypervelocity propulsion systems are light gas guns. Especially, the ability of two-stage light gas guns is suitable to accelerate projectile at velocities ranging from 2 km/s to 9 km/s. However, velocities higher than 10 km/s are demanded eagerly for ballistic limit equations on on-orbit impacts and meteoroids. In order to enhance the launch performance of the light-gas guns, a concept of using density-gradient gas as the driving gas instead of single helium or hydrogen gas has been proposed. An analytical acceleration model of the projectile in the launch tube with constant cross-sectional area is deduced. The launch process can be divided into three stages. The first stage is the projectile driven by the first shock wave. The second stage is the projectile driven by shock waves reflected on the gas interface. The last stage is the projectile caught up by the rarefaction wave created by the suddenly stop of the piston. The comparison in launch performance between neon-helium density-gradient driving gas and helium driving gas is made, and the influences of parameters of the gradient gas on the launch performance are studied. Results show that the neon-helium density-gradient driving gas can improve the launch velocity by about 0.4−1.4 km/s or lower the maximum base pressure by about 0.2−0.9 GPa. The biggest influential factors for the launch velocity and the maximum base pressure are the density of high density gas and the piston velocity, following by the initial gas pressure and the gaseous polytrophic index. High density gas with both high density and high gaseous polytrophic index would be the prior choice due to the reason that higher gaseous polytrophic index could make the maximum base pressure lower. The launch velocity has little correlation with the ratio of high density gas. However, low ratio of high density gas could lower the maximum base pressure.
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图 2 发射器作用过程的波系图
Figure 2. Wave structure of the constant cross-sectional area launch tube
图 4 不同初始压力下弹丸的加速过程对比
Figure 4. Velocity-time histories of launchers with different initial pressures
图 5 不同界面位置下弹丸底部的压力对比
Figure 5. Pressure-time histories of launchers with different initial gas interfaces
图 6 发射速度结果与单一氦气驱动对比（相同过载）
Figure 6. Muzzle velocities compared with the launchers with only helium driven gas (under the same pb,max)
图 7 发射过载结果与单一氦气驱动对比（相同过载）
Figure 7. Maximum base pressures compared with the launchers with only helium driven gas (under the same ub)
图 8 界面位置和初始填充压力对速度的影响
Figure 8. Muzzle velocities of launchers with different initial pressure and position of gas interface
图 9 界面位置和初始填充压力对过载的影响
Figure 9. Maximum base pressures of launchers with different initial pressure and position of gas interface
图 10 活塞运动距离与活塞速度对速度的影响
Figure 10. Muzzle velocities of launchers with different D and displacement of the piston
图 11 活塞运动距离与活塞速度对过载的影响
Figure 11. Maximum base pressures of launchers with different D and displacement of the piston
图 13 气体1参数对过载的影响
Figure 13. Maximum base pressures of launchers with different ρ10 and γ1
表 1 理论模型与数值计算结果
Table 1. Muzzle velocities obtained from simulation and analytical equation
算例
编号初始压力/
MPa[L1/（L1+L2）]/
%弹丸速度/（km·s−1） 相对误差/
%有限元 式(14) 1 1.00 75 6.04 5.55 8.1 2 1.72 75 8.32 7.75 6.9 3 2.50 75 9.91 9.36 5.6 4 1.72 65 8.07 7.69 4.7 5 1.72 55 7.58 7.63 0.7 
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表 2 发射能力对各参数的敏感性分析
Table 2. The sensitivity of parameters in affecting launch performance
参数 参数变化范围 发射速度提升/（km·s−1） 发射过载增加/GPa 气体压力 1～2 MPa 2.54～3.08 0.98～2.06 界面位置 50%～90% 0～0.46 0.47～1.55 活塞运动距离 40%～80% 1.28～1.4 ～0 活塞运动速度 5～8 km/s 4.38～4.48 ～2.85 气体密度 2.5ρ20～10ρ20 4.08～6.02 3.62～3.79 多方气体指数 1.2～1.67 −0.14～1.80 −1.24～−1.07
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