﻿ 一体化弹丸弹体和弹托分离特性研究
 舰船科学技术  2020, Vol. 42 Issue (8): 32-37    DOI: 10.3404/j.issn.1672-7649.2020.08.006 PDF

1. 海军工程大学，湖北 武汉 430033;
2. 中国船舶集团公司第七一三研究所，河南 郑州 450015

Research on separation characteristic of intergration launch projectile′s body
GU Gang1,2, LI Xuan2
1. Naval University of Engineering, Wuhan 430033, China;
2. The 713 Research Institute of CSSC, Zhengzhou 450015, China
Abstract: The intergration launch projectile (ILP)is mainly consist of armature, projectilebody and sabot, the sabot plays the role of supporting and protecting the projectile body in a electromagnetic launcher. After the ILP has left of the chamber, the projectile body will be separated from the sabot. To study the behavior of the instantaneous separation between the projectile and the sabot after the ILP has left the chamber, we establish an ILP two-dimension separation model based on the Navier-Stokes govering equation, the 6DOF external ballistics govering equation and the standard turbulence model, and adopted the grid technology(fairing method and local redrawing method)for numerical simulation of the projectile body-sabot separation flow field after the ILP has left the chamber, so as to obtain the sabot and projectile body motion parameters during the separation process.And analyze the ballistic characteristic of body and sabot during separation period. It has provided reference for future optional structure design of intergration launch projectile.
Key words: hydromechanics     intergration launch projectile     sabot separation     dynamic mesh     shock wave     six degrees of freedom
0 引　言

1 计算方法与数值模型 1.1 仿真思路与控制方程

 图 1 仿真流程示意图 Fig. 1 The process of simulation

 $\frac{{\partial U}}{{\partial t}} + \frac{{\partial F}}{{\partial x}} + \frac{{\partial U}}{{\partial y}} = 0{\text{。}}$ (1)

 $E = \frac{p}{{(\gamma - 1)\rho }} + \frac{{{u^2} + {\upsilon ^2}}}{2}{\text{，}}$ (2)

 $p = \rho RT{\text{。}}$ (3)

 $\rho \frac{{{\rm{D}}k}}{{{\rm{D}}t}} = \frac{\partial }{{\partial {x_i}}}[(\mu + \frac{{{\mu _t}}}{{{\sigma _k}}})\frac{{\partial k}}{{\partial {x_i}}}] + {G_k} + {G_b} - \rho \varepsilon - {Y_M}{\text{，}}$ (4)
 $\rho \frac{{{\rm{D}}\varepsilon }}{{{\rm{D}}t}} = \frac{\partial }{{\partial {x_i}}}[(\mu + \frac{{{\mu _t}}}{{{\sigma _k}}})\frac{{\partial \varepsilon }}{{\partial {x_i}}}] + {C_{1\varepsilon }}\frac{\varepsilon }{k}({G_k} + {C_{3\varepsilon }}{G_b}) - {C_{2\varepsilon }}\rho \frac{{{\varepsilon ^2}}}{k}{\text{。}}$ (5)

 $\mu = \rho {C_\mu }\frac{{{k^2}}}{\varepsilon }{\text{。}}$ (6)

 \begin{aligned} & {m\frac{{{\rm{d}}V}}{{{\rm{d}}t}} = P\cos \alpha \cos \beta - X - mg\sin \theta }{\text{，}} \\ & mV\frac{{{\rm{d}}\theta }}{{{\rm{d}}t}} = P(\sin \alpha \cos {\gamma _V} + \cos \alpha \sin \beta \sin {\gamma _V}){\text{ + }} \hfill \\ & \quad \quad \quad Y\cos {\gamma _V} - Z\sin {\gamma _V} - mg\cos \theta \hfill {\text{，}}\\ \\ & - mV\cos \frac{{{\rm{d}}{\psi _V}}}{{{\rm{d}}t}} = P(\sin \alpha \sin {\gamma _V} - \cos \alpha \sin \beta \cos {\gamma _V}) + \hfill\\ & \quad \quad \quad Y\sin {\gamma _V} + Z\cos {\gamma _V} {\text{；}} \end{aligned} (7)

 \begin{aligned} & {J_{{x_1}}}\frac{{{\rm{d}}{\omega _{{x_1}}}}}{{{\rm{d}}t}} + ({J_{{z_1}}} - {J_{{y_1}}}){\omega _{{z_1}}}{\omega _{{y_1}}} = {M_{{x_1}}}{\text{，}} \\ & {J_{{y_1}}}\frac{{{\rm{d}}{\omega _{{y_1}}}}}{{{\rm{d}}t}} + ({J_{{x_1}}} - {J_{{y_1}}}){\omega _{{x_1}}}{\omega _{{z_1}}} = {M_{{y_1}}} {\text{，}} \\ & {J_{{z_1}}}\frac{{{\rm{d}}{\omega _{{z_1}}}}}{{{\rm{d}}t}} + ({J_{{y_1}}} - {J_{{x_1}}}){\omega _{{y_1}}}{\omega _{{x_1}}} = {M_{{z_1}}} {\text{；}} \\ \end{aligned} (8)

 \begin{aligned} & \frac{{{\rm{d}}x}}{{{\rm{d}}t}} = V\cos \theta \cos {\psi _V} {\text{，}} \\ & \frac{{{\rm{d}}y}}{{{\rm{d}}t}} = V\sin \theta {\text{，}} \\ & \frac{{{\rm{d}}z}}{{{\rm{d}}t}} = - V\cos \theta \sin {\psi _V}{\text{；}} \\ \end{aligned} (9)

 \begin{aligned} & \frac{{{\rm{d}}\vartheta }}{{{\rm{d}}t}} = {\omega _{{y_1}}}\sin \gamma + {\omega _{{z_1}}}\cos \gamma {\text{，}} \\ & \frac{{{\rm{d}}\psi }}{{{\rm{d}}t}} = ({\omega _{{y_1}}}\cos \gamma - {\omega _{{z_1}}}\sin \gamma )/\cos \vartheta {\text{，}} \\ & \frac{{{\rm{d}}\gamma }}{{{\rm{d}}t}} = {\omega _{{x_1}}} - \tan \vartheta ({\omega _{{y_1}}}\cos \gamma - {\omega _{{z_1}}}\sin \gamma ){\text{。}} \\ \end{aligned} (10)

 $\begin{split}\frac{{\rm{d}}}{{{\rm{d}}t}}&\int_V {\rho \phi {\rm{d}}V} + \int_{\partial V} {\rho \phi (u - {u_g}){\rm{d}}A = }\\ & \int_{\partial V} {\varGamma \nabla \phi {\rm{d}}A} + \int_V {{S_\phi }{\rm{d}}V}{\text{。}} \end{split}$ (11)

1.2 数值模型立与离散设置

 图 2 简化后一体化弹丸模型 Fig. 2 Simplified model of ILP

 图 3 二维流场模型示意图 Fig. 3 Two-dimensional flow field model

 图 4 一体化弹丸附近网格分布图 Fig. 4 Grid distribution of ILP nearby

2 结果分析对比与讨论 2.1 不同时刻分离流场分析

 图 5 一体化弹丸脱壳时不同时刻x-y压力云图 Fig. 5 x-y stress nephogram ofILP, separation at different time

T=0.24 ms时刻弹体弹托远离加剧，内部泄压完成，对称的低压涡流区脱离弹托尾部后移，并蔓延至两弹托另一侧同尾部流场耦合形成一个拓展的低压流场区。弹托沿着轴线方向形成一定的倾角，其内表面开始逐渐成为迎风面。弹托内外表面分别出现高低压区，在分界处形成了脱体激波。弹托的压差形成了很强的翻转力矩，但相对于上下弹托的耦合流场相对于弹体而言是对称的，弹体可以沿着原先的弹道飞行。

T=0.48 ms时刻弹体弹托的耦合流场继续加强，弹体被整个流场完全包裹。对比整个过程发现，在此时间段，弹体受到弹托不对称性的干扰最大，最容易失稳。上下弹托前沿处收到的气动压力达到28个标准大气压值（见图6），之后该处值迅速下降。在T=0.72 ms弹体表面压力值由于激波区耦合作用的减弱而降低，同时弹托后沿区域低压区压力值达到最大，之后耦合流场逐渐分离，在T=0.96 ms时刻耦合基本结束。

 图 6 压力随时间的变化 Fig. 6 Changes of pressure with time

T=1.22 ms一体化弹丸脱壳基本结束，弹托和弹托各自流场完全分离。但弹托流场形成的弱余波反射在弹体的头部的上方和尾翼的下方，该弱余波对弹体而言形成了偏转力矩，对弹体飞行稳定性可能造成一定的影响。图6显示在分离结束后期，弹托前沿低压区达到了最大值。

2.2 弹托6DOF运动结果与分析

 图 7 试验同模拟仿真弹托不同时刻分离状态对比 Fig. 7 Comparisom between test and simulation of ILP,separation state at different time

 图 8 弹体、弹托质心轴向距离随时间变化 Fig. 8 Changes of projectile body and sabot,barycenter at axial direction with time

 图 9 阻力系数随时间的变化 Fig. 9 Changes of drag coefficient with time

 图 10 升力系数随时间的变化 Fig. 10 Changes of lift coefficient with time

 图 11 俯仰力矩系数随时间的变化 Fig. 11 Changes of pitching moment coefficient with time
3 结　语

1）研究结果表明，一体化弹的分离过程属于风阻型脱壳，在分离过程中弹体、弹托分离流场呈现激波生成、耦合和分离的复杂过程。耦合流场的波阻对弹托分离起到最主要的作用，弹体由于流场的对称性受耦合流场的影响较小。

2）分离终了时期，弹托分离流场的反射余波使得弹体前后方分别产生了高低压区，该区域产生的不平衡力（矩）有可能使弹体出现失稳的情况，需要进一步研究。

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