﻿ 燃气蒸汽式弹射内弹道研究
 舰船科学技术  2017, Vol. 39 Issue (3): 118-122 PDF

1. 武汉第二船舶设计研究所，湖北 武汉 430064;
2. 北京理工大学，北京 100081

Research on interior ballistic of gas-steam ejection
YAN Feng1, SHI Shao-yan2, JIANG Yi2
1. Wuhan Second Ship Design and Research Institute, Wuhan 430064, China;
2. Beijing Institute of Technology, Beijing 100081, China
Abstract: Gas-steam ejection with its simple structure, the advantages of moderate temperature and steady pressure output, is widely applied to underwater vehicle emission systems. Study of gas-steam ejection device flow field is of great significance in device design and improvement. By using three different simulation models of gas-steam catapult interior ballistics calculation shows: flow field simulation should be carried out at the same time introducing vaporization model and component transport model, which is more consistent with the actual situation. The influence of temperature on the vaporization model for flow field is more obvious than that of pressure and velocity. The simulation results can be used for gas-steam-catapult design and provide theoretical support for device improvement.
Key words: ejection     two-phase flow     vaporization model     component transport model
0 引　言

1 数学建模 1.1 物理模型

 图 1 物理模型 Fig. 1 Physical model
1.2 汽化模型 1.2.1 水的汽化过程

 图 2 水汽化过程示意图 Fig. 2 Diagram of water vaporization process

1）定压加热阶段

 ${q_l} = h' - {h_l} = \left( {u' - {u_l}} \right) + p\left( {v' - {v_l}} \right)\text{，}$ (1)

 ${q_l} = u' - {u_l}\text{。}$ (2)

2）水的定压汽化阶段

b 点饱和水继续加热，水开始沸腾汽化。汽化过程中，水蒸气与水的温度、压力均保持不变，但饱和水和饱和蒸汽二者所组成的混合物（称为湿蒸汽）的比容迅速增加。当水完全变为水蒸气时，汽化过程结束。此时蒸汽不再含有饱和水，称此时的蒸汽为干饱和蒸汽。由饱和水b 变为干饱和蒸汽c 的过程由图中的b–c 线所示。显然b–c 线既是等压线又是等温线，但含饱和蒸汽的质量不同。为了确定湿蒸汽的状态，除了要知道饱和温度ts （或饱和压力ps ）外，还需知道另一个参数——干度x，即在饱和状态下，饱和汽占饱和水和饱和汽总和的百分数。

 $\Delta H = h'' - h' = \left( {u'' - u'} \right) + p\left( {v'' - v'} \right)\text{。}$ (3)

3）定压过热阶段

 $q = h - h'' = \int_{{t_s}}^t {{C_p}{\rm d}t} = {C_p}(t - {t_s})\text{，}$ (4)

 $Q = {q_l} + \Delta H + q = {C_l}({t_s} - {t_l}) + \Delta H + {C_p}(t - {t_s})\text{。}$ (5)
1.2.2 计算模型

 {\dot m_l} = \left\{ \begin{aligned}& {\lambda _l}{\alpha _l}{\rho _l}\left| {{T_l} - {T_{sat}}} \right|/{T_{sat}}, {T_l} \geqslant {T_{sat}}\text{，}\\& 0, {T_l} < {T_{sat}}\text{；}\end{aligned} \right. (6)

 {\dot m_v} = \left\{ \begin{aligned}0, {T_v} \geqslant {T_{sat}}\text{，} \quad \quad \quad \quad \quad \quad \quad \quad \\{\lambda _v}{\alpha _v}{\rho _v}\left| {{T_v} - {T_{sat}}} \right|/{T_{sat}}, {T_v} < {T_{sat}}\text{。}\end{aligned} \right. (7)

 $\dot m = {\dot m_l} - {\dot m_v}\text{，}$ (8)

 ${S_k} = - \Delta H\dot m \text{。}$ (9)

1.2.3 水蒸气的状态方程

 $P = \frac{{RT}}{{V - b}} - \frac{{a(T)}}{{{V^2} + bV}}\text{，}$ (10)

 \left\{ \begin{aligned}& a(T) = {a_0}{\{ 1 + n[1 - {(T/{T_c})^{0.5}}]\} ^2}\text{，}\\& n = 0.48 + 1.574\omega - 0.17{\omega ^2}\text{。}\end{aligned} \right. (11)
1.3 组分输运模型

 $\frac{\partial }{{\partial t}}\left( {\rho {Y_i}} \right) + \nabla \cdot \left( {\rho \overrightarrow \upsilon {Y_i}} \right) = - \nabla \cdot \overrightarrow {{J_i}} + {S_i}\text{，}$ (12)

 $\sum\limits_{i = 1}^N {{Y_i}} = 1\text{。}$ (13)

 \begin{aligned}\frac{\partial }{{\partial t}} & \left( {{\rho ^q}{\alpha ^q}{Y_i}^q} \right) + \nabla \cdot \left( {{\rho ^q}{\alpha ^q}{{\vec \upsilon }^q}{Y_i}^q} \right) = \\& - \nabla \cdot {\alpha ^q}{\overrightarrow {{J_i}} ^q} + {\alpha ^q}{S_i} + \sum\limits_{p = 1}^n {\left( {{{\dot m}_{{p^i}{q^j}}} - {{\dot m}_{{q^j}{p^i}}}} \right)} \text{。}\end{aligned} (14)

2 仿真方法 2.1 仿真工况

2.2 初始条件

 图 3 初始时刻气液两相分布图 Fig. 3 Gas-liquid two-phase distribution at the initial time
3 仿真结果与分析

 图 4 运载器位移曲线 Fig. 4 The displacement curve of vehicle

 图 5 液态冷却水质量变化曲线 Fig. 5 The mass curve of liquid water

 图 6 t’时刻工况 2 与工况 3 冷却水体积分数云图 Fig. 6 Volume fraction of cooling water in condition 2 and condition 3 att' moment

 图 7 t' 时刻工况 2 与工况 3 流场温度云图 Fig. 7 Temperature contour in condition 2 and 3 att' moment

 图 8 t" 时刻工况 3 燃气体积分数云图 Fig. 8 Volume fraction of gas in condition 3 att" moment

 图 9 t" 时刻工况 3 水蒸气体积分数云图 Fig. 9 Volume fraction of steam in condition 3 att" moment

4 结　语

1）对燃气-蒸汽式弹射装置进行流场仿真计算时应考虑汽化效应的影响，汽化效应对流场的温度较压力、速度的影响更明显。

2）由于水蒸气与燃气、空气的物理性质差异较大，在两相流模型中耦合汽化模型时，需同时引入组分输运模型，否则仿真结果误差较大。

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