﻿ 导流格栅对发射箱内流场环境影响研究
 舰船科学技术  2022, Vol. 44 Issue (20): 71-77    DOI: 10.3404/j.issn.1672-7649.2022.20.014 PDF

Reasearch on influence of diversion grille structure on flow field environment in a launch canister
PAN Shu-guo, TAI Jing-hua, LI Xiang-yu, WU Li-min
The 713 Research Institute of CSSC, Zhengzhou 450015, China
Abstract: In order to study the influence of the diversion grille structure on the gas flow field inside the launch canister, taking the flow field in a certain type of missile launcher as the reasearch object, the opening process of lobes of fragile back cover and bursting process of fragile front cover under gas effect and the flow field simulation under different diversion grille structures were researched and analyzed this paper. The results show that the diversion grille structure can increase the propagation speed of the pressure wave in the direction of the front cover, and effectively shorten the opening time of the fragile front cover. The addition of a diversion plate to change guide grid structures can affect opening of front and back cover to a certain extent, compared with no deflector, the advance of the opening time of the front cover is 14%. The study results have certain guiding significance and engineering application value for the optimization of opening the launcher cover with fragmentation.
Key words: launch canister     gas flow field     diversion grille     fragile front cover
0 引　言

1 理论基础 1.1 基本假设

1）燃气流是性质单一、均匀混合的气体，视为理想气体，满足理想气体状态方程，各成分间无化学反应；

2）忽略其粒子流自身影响以及粒子流与燃气间的动量和能量交换；

3）导弹简化为旋转体；

4）前盖、后盖未破碎/裂时为密闭状态，且不随燃气流载荷变形，前盖破碎后假设为完全打开，前后盖打开过程中弹体保持静止状态。

1.2 控制方程

1）质量守恒方程

 $\frac{\partial \rho}{\partial t}+\frac{\partial \rho u}{\partial x}+\frac{\partial \rho v}{\partial y}+\frac{\partial \rho \omega}{\partial \textit{z}}=0。$ (1)

2）动量守恒方程

 $\begin{split} &\frac{\partial(\rho u)}{\partial t}+\frac{\partial(\rho u u)}{\partial x}+\frac{\partial(\rho u v)}{\partial y}+\frac{\partial(\rho u \omega)}{\partial \textit{z}}= \\ &\mu_{\text {off }}\left(\frac{\partial^{2} u}{\partial x^{2}}+\frac{\partial^{2} u}{\partial y^{2}}+\frac{\partial^{2} u}{\partial \textit{z}^{2}}\right)-\frac{\partial p}{\partial x}，\end{split}$ (2)
 $\begin{split} &\frac{\partial(\rho v)}{\partial t}+\frac{\partial(\rho v u)}{\partial x}+\frac{\partial(\rho v v)}{\partial y}+\frac{\partial(\rho v \omega)}{\partial \textit{z}}= \\ &\mu_{\mathrm{eff}}\left(\frac{\partial^{2} v}{\partial x^{2}}+\frac{\partial^{2} v}{\partial y^{2}}+\frac{\partial^{2} v}{\partial \textit{z}^{2}}\right)-\frac{\partial p}{\partial y}，\end{split}$ (3)
 $\begin{split} &\frac{\partial(\rho w)}{\partial t}+\frac{\partial(\rho w u)}{\partial x}+\frac{\partial(\rho w v)}{\partial y}+\frac{\partial(\rho w w)}{\partial \textit{z}}= \\ &\mu_{\mathrm{eff}}\left(\frac{\partial^{2} w}{\partial x^{2}}+\frac{\partial^{2} w}{\partial y^{2}}+\frac{\partial^{2} w}{\partial \textit{z}^{2}}\right)-\frac{\partial p}{\partial \textit{z}}-\rho g \beta\left(T-T_{\mathrm{ef}}\right)。\end{split}$ (4)

3）能量守恒方程

 $\begin{split} &\frac{\partial\left(\rho T^{\prime}\right)}{\partial t}+\frac{\partial\left(\rho u T^{\prime}\right)}{\partial x}+\frac{\partial\left(\rho v T^{\prime}\right)}{\partial y}+\frac{\partial\left(\rho w T^{\prime}\right)}{\partial \textit{z}}= \\ &\frac{\lambda_{\text {eff }}}{C_{p}}\left(\frac{\partial^{2} T}{\partial x^{2}}+\frac{\partial^{2} T}{\partial y^{2}}+\frac{\partial T^{2}}{\partial \textit{z}^{2}}\right)+S_{T}。\end{split}$ (5)

1.3 湍流模型

1）湍流动能方程

 $\begin{split} &\frac{\partial(\rho k)}{\partial t}+\frac{\partial\left(\rho k u_{i}\right)}{\partial x_{i}}=\frac{\partial}{\partial x_{j}}\left[\left(\mu+\frac{\mu_{t}}{\sigma_{{k}}}\right) \frac{\partial k}{\partial x_{j}}\right] +\\ &G_{k}+G_{b}-\rho \varepsilon-Y_{M}+S_{k}。\end{split}$ (6)

2）湍流动能耗散率方程

 $\begin{split} &\frac{\partial(\rho \varepsilon)}{\partial t}+\frac{\partial\left(\rho \varepsilon u_{i}\right)}{\partial x_{i}}=\frac{\partial}{\partial x_{j}}\left[\left(\mu+\frac{\mu_{t}}{\sigma_{\textit{z}}}\right) \frac{\partial \varepsilon}{\partial x_{j}}\right]+ \\ &G_{1 \textit{z}} \frac{\varepsilon}{k}\left(G_{k}+G_{3 \textit{z}} G_{i b}\right)-G_{2 \textit{z}} \rho \frac{\varepsilon^{2}}{k}+S_{\textit{z}}。\end{split}$ (7)

2 计算模型及边界条件 2.1 计算模型及工况

 图 1 发射箱模型 Fig. 1 The launch canister model

 图 2 导流格栅模型 Fig. 2 The diversion grille model
2.2 燃气计算参数

 图 3 燃烧室压力曲线 Fig. 3 The pressure curve of combustor

2.3 后盖计算参数

 图 4 后盖受力分析 Fig. 4 Stress analysis of fragile back cover
 $M(\theta)=F_{x} \times L_{0} \sin \left(\theta-\theta_{0}\right)+F_{y} \times l_{0} \cos \left(\theta-\theta_{0}\right)。$ (8)

 $F_{x}=F(\theta) \operatorname{tg}(a), F_{Y}=F(\theta)。$ (9)

 $M(\theta)=F(\theta) t_{t}\left(\operatorname{tg}(a) \sin \left(\theta-\theta_{t}\right)+\cos \left(\theta-\theta_{t}\right)\right)。$ (10)

 $\sin a=\left(L-l_{0} \cos \left(\theta-\theta_{0}\right)\right) / l 。$ (11)

 $f(\theta)=F(\theta) \times \frac{l_{0}\left(\operatorname{tg}(a) \sin \left(\theta-\theta_{0}\right)+\cos \left(\theta-\theta_{0}\right)\right)}{L}。$ (12)

 图 5 后盖裂片张开状态受力 Fig. 5 Forced in the open state of back cover lobes
 $t \omega=\iint_{t}^{t} r \times P {\rm{d}} r {\rm{d}} y+M_{3}-M(\phi)。$ (13)

 图 6 裂片转动部分形状 Fig. 6 Partial shape of rotating lobes
 $M_{g}=m g \times \frac{1}{3} L \cos \theta。$ (14)

 $I \dot{\omega}=\iint_{x} r \times P {{\rm{d}}x{\rm{d}}y}+m_{\dot{\theta}} \times \frac{1}{3} L \cos \theta-f(\theta) \times L。$ (15)
2.4 裂片运动方程验证

 图 7 后盖胀破过程流场计算模型 Fig. 7 Calculation model of flow field in the process of bursting and cracking of fragile back cover

 图 8 后盖裂开时间8 ms时试验和仿真对比 Fig. 8 Comparison of test and simulation when the cracking time of fragile back cover is 8 ms

2.5 边界条件

1）入口边界条件

2）出口边界条件

3）壁面边界条件

4）前盖打开条件

5）后盖破裂条件

3 计算结果及分析 3.1 燃气运动分析

 图 9 后盖破裂前压力波在箱内运动情况 Fig. 9 The movement of pressure wave in the box before the crack of fragile back cover

3.2 导流格栅对后盖打开时间影响

 图 10 后盖裂片打开时间对比 Fig. 10 Comparison of opening time of back cover lobes
3.3 导流格栅对前盖打开时间影响

 图 11 后盖打开过程中压力波在箱内运动 Fig. 11 The movement of pressure wave in the canister during the opening of fragile back cover

 图 12 发射箱前盖附近压强曲线变化 Fig. 12 Change of pressure curve near the front cover of launch canister

4 试验验证

 图 13 发射箱内测点布置 Fig. 13 The location of monitoring point in the launcher

 图 15 发射箱测点压强曲线变化 Fig. 15 Change of pressure curve at monitoring point of launch canister
5 结　语

1）发射箱内增加导流格栅结构，有助于压力波向前盖传播，缩短前盖开启时间。同时，其对发射箱前部压力峰值影响较小，压力波动范围在0.51%～0.97%左右，避免弹体元件等因压力波动而出现受损的情况。

2）导流格栅结构对后盖开启过程的影响程度不显著，不同仿真工况下的后盖开启时刻基本相近，裂片完全打开时刻的变化范围在1.3 ms以内。

3）通过增设导流盘来改变导流格栅结构，从结果看，会对发射箱的前盖开启时间等性能参数具有一定的影响。带导流盘的格栅结构相对于无导流盘工况，前盖打开时刻缩短的幅度为15.9%。

 [1] 陈愚, 孙凤云. 贮运发射箱的结构与设计[J]. 包装工程, 2012, 33(15): 132-135. [2] 杨雨潼, 吴石, 陈愚, 等. 自然环境对贮运发射箱的影响[J]. 装备环境工程, 2009, 6(6): 82-83,87. DOI:10.3969/j.issn.1672-9242.2009.06.021 [3] 张艳, 李仙会, 庄辛. 导弹贮运发射箱易碎端盖研究进展[J]. 理化检验(物理分册), 2019, 55(3): 145-150,164. [4] 段苏宸, 姜毅, 牛钰森, 等. 发射箱易碎后盖开启过程的数值计算[J]. 兵工学报, 2018, 39(6): 1117-1124. DOI:10.3969/j.issn.1000-1093.2018.06.011 [5] 牛钰森, 姜毅, 史少岩, 等. 与燃气射流耦合的易碎后盖开启过程数值分析[J]. 兵工学报, 2015, 36(1): 87-93. DOI:10.3969/j.issn.1000-1093.2015.01.013 [6] 夏胜禹. 基于动网格技术燃气开盖研究[D]. 北京: 北京理工大学, 2015. [7] 金建峰, 徐刚, 申明辉, 等. 发射箱压力波传播的数值分析及试验验证[J]. 强度与环境, 2014, 41(5): 24-27. DOI:10.3969/j.issn.1006-3919.2014.05.005 [8] 邵庆, 张保刚, 惠卫华, 等. 贮运发射箱易碎易裂自动开盖研究[J]. 弹箭与制导学报, 2017, 37(1): 27-31. [9] 刘琦, 傅德彬, 姜毅. 贮运发射箱内燃气射流的非定常冲击波流场数值模拟[J]. 弹箭与制导学报, 2005, 25(2): 382-384. DOI:10.3969/j.issn.1673-9728.2005.02.125 [10] 吴利民, 陈劲草. 垂直发射装置排导系统内燃气流运动研究[J]. 舰船科学技术, 2007, 29(z1): 69-70,94. [11] 张兆顺. 湍流[M]. 北京: 国防工业出版社, 2002: 264–266.