二级轻气炮发射过程数学模型和计算方法

Mathematical Model and Computing Method for Launch Process of Two-stage Light-gas Gun

建立起模拟二级轻气炮发射过程的数值方法。运用经典内弹道学理论描述药室内火药燃烧状况和活塞运动过程,可压缩流体一维变截面非定常无粘流动数学模型描述轻气室内气体流动状态和弹丸运动过程,并通过活塞运动状态将两者耦合到一起,建立起二级轻气炮发射过程的数学模型。运用经典Runge-Kutta方法求解药室方程,二阶MacCormack格式和Harten二阶TVD格式求解轻气室方程,通过两部分计算的交替进行,实现了二级轻气炮发射过程的数值模拟。分析不同差分格式对计算结果的影响,MacCormack格式具有较高的整体计算精度,而TVD格式可以更好地捕捉流场中的激波。

A numerical method for simulating launch process of two-stage light-gas gun is established. The classical theory of interior ballistics is employed to describe the combustion of powder in chamber and the movement of piston, and the mathematical model for compressible unsteady inviscid quasi-one-dimensional flow is employed to describe the flow pattern in light-gas chamber and the movement of projectile. These two groups of equations are coupled together by the movement of piston to simulate the whole launch process of two-stage light-gas gun. The former equations are solved numerically with the classical Runge-Kutta method, and the latter equations are solved numerically with the second-order MacCormack scheme and the Harten＇ s second-order TVD scheme, respectively. The computation for the whole launch process of the two-stage light-gas gun is accomplished by ahemation between these two computations. The effects of different schemes on the simulation results are also analyzed. The results show the higher precision can be gained using MacCormack scheme while shock can be captured more exactly using TVD scheme.