﻿ 弹库导弹注水保护技术关键参数计算方法
 舰船科学技术  2021, Vol. 43 Issue (3): 175-178    DOI: 10.3404/j.issn.1672-7649.2021.03.034 PDF

Research on calculation method of key parameters of water injection protection technology in missile depot
LI Shi-jun, YANG Wei, PAN Shu-guo, WANG Chang-bo
The 713 Research Institute of CSSC, Zhengzhou 450015, China
Abstract: In this paper, the problem of accidental ignition of a Packless missile in missile depot of warship and injection of high pressure water into jet area of tail nozzle of the missile engine to cool it down is studied. By simplifying the inlet and outlet of the control body and using the parameter comparison method, the calculation method of water injection flow and gas temperature considering the water jet breaking is established, and the calculation and analysis are carried out with the example. This method can provide theoretical basis and calculation method for the design of ammunition depot water injection system.
Key words: without packing missile     ammunition depot safety     water injecting protection     suddenness blast-off of the missle engine     calculation method
0 前　言

 图 1 弹库注水示意图 Fig. 1 Diagram of water injection in ammunition depot

1 注水问题假设条件

1）发动机尾喷管出口处的压力为常量；

2）射流和射流混合物气体符合理想气体定量，采用理想气体状态方程，气体常数近似一致，且液滴均匀分布在控制体内的气体混合物中；

3）液滴在控制体内的分布均匀；

4）射流中的液滴直径相同；

5）液滴中的温度相同，不存在温度梯度，处于饱和状态即 ${T_{sat}} = 393{\rm{K}}$

6）气体和水的热力学特性与温度无关；

7）水滴的拖拽力和传热相关，通过公式表示；

8）控制体的轴向长度取值为发动机尾喷管直径的2倍，即 $n = L /{d_j} = 2$ ，确保控制体取在发动机射流中的核心区，发动机射流核心区的长度采用经验公式 $x_t / d_j = 3.45{\left( {1 + 0.38{M_{je}}} \right)^2}$ 表示，式中 ${M_{je}}$ 为发动机尾喷管气流的Ma数；

9）液滴为刚性球体，不会受气流作用发生变形；

10）忽略辐射热传导作用和由于水的冲击碰撞、破碎消耗的能量。

2 控制方程

 ${\rho _{j1}}{u_{j1}}{A_{j1}} = {\rho _{j2}}{u_{j2}}{A_{j2}} - \eta {\dot m_W}\text{，}$ (1)
 ${\rho _{j2}}u_{j2}^2{A_{j2}} - {\rho _{j1}}u_{j1}^2{A_{j1}} = - {F_d} + \eta {\dot m_W}{u_p}\text{，}$ (2)
 $\begin{split}&{\dot m_{j2}}\left( {{c_{pj}}{T_{j2}}+\frac{{u_{j2}^2}}{2}} \right) =\\ &{\dot m_{j1}}\left( {{c_{pj}}{T_{j1}}+\frac{{u_{j1}^2}}{2}} \right) - {F_d}{u_p}+\eta {\dot m_W}{T_p}{c_{pl}}\text{，}\end{split}$ (3)
 ${\rho _{j1}}{R_{j1}}{T_{j1}} = {\rho _{j2}}{R_{j2}}{T_{j2}}\text{。}$ (4)

 图 2 注水控制体示意图 Fig. 2 Diagram of control body

3 控制体两侧的参数比

 $\frac{{{u_{j2}}}}{{{u_{j1}}}} = \frac{1}{{1 + \eta \dfrac{{{{\dot m}_W}}}{{{{\dot m}_{j1}}}}}} \cdot \left( {1 - \frac{{{F_d}}}{{{\rho _{j1}}u_{j1}^2{A_{j1}}}} + \frac{{\eta {{\dot m}_W}{u_p}}}{{{\rho _{j1}}u_{j1}^2{A_{j1}}}}} \right)\text{，}$ (5)

 $\varphi = \frac{{{F_d}}}{{{\rho _{j1}}u_{j1}^2{A_{j1}}}} = \frac{1}{2}{N_p}{C_D}\frac{{{A_P}}}{{{A_{j1}}}}{\left( {1 - \frac{{{u_p}}}{{{u_{j1}}}}} \right)^2}\text{，}$ (6)

 ${F_d} = \frac{1}{2}{\rho _{j1}}{\left( {{u_{j1}} - {u_p}} \right)^2}{C_D}{A_{PT}}\text{，}$ (7)
 ${N_p} = \frac{3}{2}\left( {\frac{{\dot m}}{{{{\dot m}_{j1}}}}} \right) \cdot \left( {\frac{{{\rho _{j1}}}}{{{\rho _p}}}} \right) \cdot {\left( {\frac{{{{\rm d}_{j1}}}}{{{{\rm d}_p}}}} \right)^3} \cdot n\left( {1 - \eta } \right)\text{，}$ (8)

 $\varphi = \psi \cdot \left( {\frac{{{{\dot m}_W}}}{{{{\dot m}_{j1}}}}} \right)\left( {1 - \eta } \right)\text{，}$ (9)

 $\frac{{\eta {{\dot m}_W}{u_p}}}{{{\rho _{j1}}u_{j1}^2{A_{j1}}}} = \eta \left( {\frac{{{{\dot m}_W}}}{{{{\dot m}_{j1}}}}} \right)\left[ {1 - \frac{{{{\operatorname{Re} }_p}}}{{{{\operatorname{Re} }_{j1}}}} \cdot \frac{{{{\rm d}_{j1}}}}{{{{\rm d}_p}}}} \right]\text{，}$ (10)

 $\begin{split}\frac{{{u_{j2}}}}{{{u_{j1}}}} = &\frac{1}{{1 + \eta \dfrac{{{{\dot m}_W}}}{{{{\dot m}_{j1}}}}}}\left[ {1 - \psi \cdot \left( {\frac{{{{\dot m}_W}}}{{{{\dot m}_{j1}}}}} \right)\left( {1 - \eta } \right)} \right.+ \\ &\left. { \eta \left( {\frac{{{{\dot m}_W}}}{{{{\dot m}_{j1}}}}} \right)\left( {1 - \frac{{{{\operatorname{Re} }_p}}}{{{{\operatorname{Re} }_{j1}}}} \cdot \frac{{{{\rm d}_{j1}}}}{{{{\rm d}_p}}}} \right)} \right]\text{，}\end{split}$ (11)

 $\begin{split}\frac{{{T_{j2}}}}{{{T_{j1}}}} =& \frac{1}{{\left( {1 + \eta \dfrac{{{{\dot m}_W}}}{{{{\dot m}_{j1}}}}} \right)}}\left[ {1 + \frac{{u_{j1}^2}}{{2{c_{pj}}{T_{j1}}}} - \frac{{{F_d}{u_p}}}{{{{\dot m}_{j1}}{c_{pj}}{T_{j1}}}}} \right. +\\ &\left. { \frac{{\eta {{\dot m}_W}{T_p}{c_{pl}}}}{{{{\dot m}_{j1}}{c_{pj}}{T_{j1}}}}} \right] - \frac{{u_{j2}^2}}{{2{c_{pj}}{T_{j1}}}}\text{，}\end{split}$ (12)

 $\frac{{u_{j1}^2}}{{2{c_{pj}}{T_{j1}}}} = \frac{{\gamma - 1}}{2}M_{j1}^2\text{，}$ (13)
 $\frac{{u_{j2}^2}}{{2{c_{pj}}{T_{j1}}}} = {\left( {\frac{{{u_{j2}}}}{{{u_{j1}}}}} \right)^2}\left( {\frac{{\gamma - 1}}{2}} \right)M_{j1}^2\text{，}$ (14)

 $\begin{split}\frac{{{T_{j2}}}}{{{T_{j1}}}} =& \frac{1}{{\left( {1 + \eta \dfrac{{{{\dot m}_W}}}{{{{\dot m}_{j1}}}}} \right)}}\left[ {1 + \frac{{\gamma - 1}}{2}M_{j1}^2 - \psi \cdot \left( {\frac{{{{\dot m}_W}}}{{{{\dot m}_{j1}}}}} \right)\left( {1-\eta } \right)\frac{{{u_{j1}}{u_p}}}{{{c_{pj}}{T_{j1}}}}} \right. +\\ &\left. { \frac{{\eta {{\dot m}_W}{T_p}{c_{pl}}}}{{{{\dot m}_{j1}}{c_{pj}}{T_{j1}}}}} \right] - {\left( {\frac{{{u_{j2}}}}{{{u_{j1}}}}} \right)^2}\left( {\frac{{\gamma - 1}}{2}} \right)M_{j1}^2\text{，}\\[-18pt]\end{split}$ (15)

 $\frac{{M{a_{j2}}}}{{M{a_{j1}}}} = \frac{{\dfrac{{{u_{j2}}}}{{{c_{j2}}}}}}{{\dfrac{{{u_{j1}}}}{{{c_{j1}}}}}} = \frac{{{u_{j2}}}}{{{u_{j1}}}} \cdot \sqrt {\frac{{\gamma R{T_{j1}}}}{{\gamma R{T_{j2}}}}} = \frac{{{u_{j2}}}}{{{u_{j1}}}} \cdot \sqrt {\frac{{{T_{j1}}}}{{{T_{j2}}}}} \text{。}$ (16)
4 方程中的参数计算

 $\frac{d_{j 1}}{d_{p}}=\sqrt{\frac{1}{C_{1}} \cdot \frac{\operatorname{Re}_{j 1}}{\rho_{j 1} / \rho_{p}}}\text{，}$ (19)
 $\operatorname{Re}_{p}=C_{2} \frac{\operatorname{Re}_{j 1}}{{\rm d}_{j 1} / {\rm d}_{p}}\text{。}$ (20)
6 算例分析

 图 3 注水量对温度的影响曲线 Fig. 3 Influence curve of water injection on temperature
7 结　语

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