﻿ 高密度垂直发射系统燃气排导性能仿真
 舰船科学技术  2023, Vol. 45 Issue (23): 212-216    DOI: 10.3404/j.issn.1672-7649.2023.23.041 PDF

Numerical simulation on the gas drainage performance of high-density vertical launch system
TAI Jing-hua, LI Yong-kang, WANG Yong
The 713 Research Institute of CSSC, Zhengzhou 450015, China
Abstract: In order to improve the loading density of small-caliber ammunition on ships,base on the structure of a high-density vertical launch system, the gas flow field in the system was taken as the research object. Moreover, three-dimensional N-S equation was used to study the gas drainage performance during the initial launch process of the missile, and the simulation results of the flow field under difference flow structures were compared and analyzed. The results show that the design of this type of launcher can meet the performance requirements of smooth gas discharge from the launcher box. In addition, when the angle between the diversion surface and the horizontal plane is 45°, the drainage efficiency reaches 79.98%, and the internal pressure state is the better. The research results can provide some theoretical support and data reference for the optimal design of gas drainage system and the engineering application of high-density vertical launch system.
Key words: vertical launch     gas drainage     diversion surface
0 引　言

1 数值模拟方法 1.1 基本假设

1）假设燃气流为理想气体，是性质单一稳定，满足理想气体状态方程；

2）忽略燃气凝相带来的影响以及凝相与燃气两相间的动量和能量交换；

3）忽略导弹运动带来的发射初始流场变化，认为发射初始阶段导弹静止不动。

1.2 控制方程

1）质量守恒方程

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

2）动量守恒方程：

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

3）能量守恒方程：

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

1.3 湍流模型

1）湍流动能方程：

 $\begin{split} \frac{{\partial (\rho k)}}{{\partial t}} + &\frac{{\partial (\rho k{u_i})}}{{\partial {x_i}}} = \frac{\partial }{{\partial {x_j}}}\left[\left(\mu + \frac{{{\mu _t}}}{{{\sigma _k}}}\right)\frac{{\partial k}}{{\partial {x_j}}}\right] +\\ & {G_k} + {G_b} - \rho \varepsilon - {Y_M} + {S_k} 。\end{split}$ (6)

2）湍流动能耗散率方程：

 $\begin{split} \frac{{\partial (\rho \varepsilon )}}{{\partial t}} + &\frac{{\partial (\rho \varepsilon {u_i})}}{{\partial {x_i}}} = \frac{\partial }{{\partial {x_j}}}[(\mu + \frac{{{\mu _t}}}{{{\sigma _\varepsilon }}})\frac{{\partial \varepsilon }}{{\partial {x_j}}}] + \\ & {G_{1\varepsilon }}\frac{\varepsilon }{k}({G_k} + {G_{3\varepsilon }}{G_b}) - {G_{2\varepsilon }}\rho \frac{{{\varepsilon ^2}}}{k} + {S_\varepsilon } 。\end{split}$ (7)

2 计算模型 2.1 几何模型和网格划分

 图 1 高密度垂直热发射装置基本组成和结构示意图 Fig. 1 The composition and structure diagram of high density vertical launch emitter

 图 2 计算域网格模型 Fig. 2 The grid model of computing domain
2.2 边界条件设置

1）入口边界条件

 图 3 发动机推力和压强随时间变化曲线 Fig. 3 Curve of engine thrust and pressure over time

2）出口边界条件

2.3 工况设置

3 仿真结果及分析 3.1 流场分析

 图 4 发射筒燃气流场区域示意图 Fig. 4 The diagram of gas flow field in the launcher

 图 5 发射初始燃气流场温度云图 Fig. 5 Temperature nephogram of gas flow field at the initial launch
3.2 导流面夹角影响分析

 图 6 燃气撞击导流面示意图 Fig. 6 The diagram of gas impacting diversion surface

 图 7 不同时刻下XY平面速度流线示意图 Fig. 7 The diagram of XY plane velocity streamline at different times

 图 8 t=20 ms时不同工况下XY平面速度流线示意图 Fig. 8 The diagram of XY plane velocity streamline under different working conditions when t=20 ms

 图 9 导流面无量纲压力对比 Fig. 9 Comparison of dimensionless pressure at the diversion surface
 ${W_P} = \frac{{{p_m}}}{{{p_{in}}}}。$ (8)

3.3 排导性能影响
 $\eta = \displaystyle\frac{{{{\dot m}_0}}}{{{{\dot m}_i}}} = \frac{{\displaystyle\sum\limits_{k = 1}^n {{\rho _k}{A_k}{{\overline v }_k}} }}{{\displaystyle\sum\limits_{i = 1}^m {{\rho _i}{A_i}{{\overline v }_i}} }} 。$ (9)

4 结　语

1）为满足小口径弹药装载密度的需求，基于某型高密度垂直发射系统建立内部三维流场模型，通过数值仿真揭示了导弹发射初始过程燃气流场流动规律，验证了其合理性；

2）通过改变不同导流型面的夹角，对比分析后得到性能更优的燃气排导结构，燃气排导效率达到79.98%，承受压力降低至1.07 MPa，减弱了燃气流冲击带来的影响。

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