火炮后效期火药气体流空过程的近似计算方法

火炮后效期内炮膛合力的变化规律对火炮运动计算有着十分重要意义。针对经典后效期理论假设的火药燃气状态参数空间分布与数值解不能严格符合的问题，基于相似性假设从膛内气体的控制方程中分离出描述气体参数分布的微分积分方程组，并提出求解的数值计算方法。根据求得的气体参数分布，导出气体状态参数和炮膛合力在后效期内随时间变化规律的计算公式，计算后效作用系数。以37 mm高射炮和122 mm榴弹炮两种火炮为例进行计算，将导出公式及经典理论的计算结果与数值仿真结果进行对比。结果表明：气体参数分布与数值仿真结果吻合；炮膛合力的变化规律与数值仿真结果很好地符合；后效作用系数与数值仿真结果的相对误差为0.38%～1.80%.

An Approximate Calculation Method for Ejection of Propellant Gas during After-effect Period of Artillery

The resultant force in the bore during after-effect period of artillery becomes significant in analyzing the motion of artillery. As the spatial distribution of propellant gas flow properties in the conventional theoretical assumption of after-effect period does not strictly conform to the numerical solutions, a set of differential-integral equations describing the gas flow distribution are derived from the governing equations of in-bore gas. A numerical method is then proposed for solving the equations. Formulas for evaluating the gas flow properties, the resultant force in the bore, and the after-effect coefficient are obtained based on the gas flow distribution. The calculated results of the formulas in this paper and the conventional theories were compared with the numerically simulated results.The results suggest that the gas flow distribution and the resultant force in the bore calculated by the proposed formulas are in fantastic agreement with the numerically simulated ones. The error between the analytical and computational after-effect coefficients ranges from 0.38% to 1.80%.