﻿ 燃气-蒸汽发射系统内两相流动与传热特性研究
 舰船科学技术  2023, Vol. 45 Issue (24): 212-217    DOI: 10.3404/j.issn.1672-7649.2023.24.041 PDF

Research on two-phase flow and heat transfer characteristics in gas-steam launch system
SONG Yong, ZHAI Yan
The 713 Research Institute of CSSC, Zhengzhou 450015, China
Abstract: Underwater launch technology is the key to the development of submarine missile weapons and equipment. In this paper, the flow and heat transfer characteristics of the gas-steam underwater launching system are studied, and the mathematical models of the high-temperature and high-pressure gas flow in the launching system, the lateral injection of cooling water in the supersonic air flow, and the atomization and evaporation of droplets are established, and calculated The total pressure, static temperature and droplet evaporation rate of the gas-steam mixed working fluid in the channel of the launching system are calculated. The simulation results show that the sudden expansion and gradual expansion structure in the launch power system has a great effect on the total pressure loss of the airflow, and the elbow does not produce too much pressure loss; when the water-to-air flow ratio of the system is 1∶1, the droplet evaporation rate can reach 98%, and injection will increase the total pressure loss and reduce the static temperature at the outlet of the system.
Key words: gas-steam underwater launch system     two-phase flow characteristics     numerical simulation     droplet evaporation
0 引　言

1 数学模型 1.1 物理模型及网格划分

 图 1 发射动力系统结构图 Fig. 1 Launch power system structure diagram

 图 2 发射动力系统计算几何模型图 Fig. 2 Computational geometric model of launch power system
1.2 控制方程

1）燃气为冻结流，即不考虑高温燃气各组分之间的化学反应；

2）燃气视为理想气体；

3）不考虑流场中除液滴外少量的其他固体粒子。

1）质量守恒方程

 $\frac{{\partial \rho }}{{\partial t}} + \frac{\partial }{{\partial {x_j}}}(\rho {u_j}) = {S_m}。$ (1)

2）动量守恒方程

 $\frac{{\partial (\rho {u_i})}}{{\partial t}} + \frac{\partial }{{\partial {x_j}}}(\rho {u_i}{u_j}) = - \frac{{\partial P}}{{\partial {x_i}}} + \frac{{\partial {\tau _{ij}}}}{{\partial {x_j}}} + {F_i} 。$ (2)

3）能量守恒方程

 $\frac{\partial }{{\partial t}}(\rho H) + \frac{\partial }{{\partial {x_j}}} (\rho {u_j}H) =- \frac{{\partial ({u_k}{\tau _{kj}})}}{{\partial {x_j}}} + \frac{{\partial {q_j}}}{{\partial {x_j}}} + {S_H}。$ (3)

 $r = {B_0}{\Lambda _{{{KH}}}} 。$ (4)

 $\frac{{{\Lambda _{{{KH}}}}}}{a} = 9.02\frac{{\left( {1 + 0.45{Z^{0.5}}} \right)\left( {1 + 0.4{T^{0.7}}} \right)}}{{{{\left( {1 + 0.87We_g^{1.67}} \right)}^{0.6}}}}。$ (5)

 $\frac{{{\rm{d}}a}}{{{\rm{d}}t}} = - \left( {a - r} \right)/{\tau _{{\text{KH}}}}，$ (6)

 ${\varOmega _{KH}}\left[ {\frac{{{\rho _l}{a^3}}}{\sigma }} \right] = \frac{{0.34 + 0.38We_g^{1.5}}}{{\left( {1 + Z} \right)\left( {1 + 1.4{T^{0.6}}} \right)}} ，$ (7)

 ${\Lambda _{RT}} = 2 {\text{π}} {C_1}\sqrt {\frac{{3\sigma }}{{{a_p}\left( {{\rho _l} - {\rho _g}} \right)}}}。$ (8)

 ${\tau _{RT}} = \sqrt {\frac{{{\sigma ^{0.5}}\left( {{\rho _l} + {\rho _g}} \right)}}{2}{{\left( {\frac{3}{{{a_p}\left( {{\rho _l} - {\rho _g}} \right)}}} \right)}^{1.5}}} 。$ (9)

 $r = 0.5{\Lambda _{RT}}。$ (10)

 ${\dot m_k} = {\text{π}} {d_k}{D_g}{\rho _g}Sh\ln (1 + B) ，$ (11)
 ${\dot m_k} = {\text{π}} {d_k}\frac{\lambda }{{{c_p}}}Nu\ln (1 + B) 。$ (12)

 ${p_{ls}} = 133.322\exp \left( {18.3036 - \frac{{3816.44}}{{{T_k} - 46.13}}} \right) 。$ (20)

L为液滴汽化潜热，有

 $L = 2257.1 \times {10^3}{\left( {\frac{{647.3 - {T_k}}}{{647.3 - 373.15}}} \right)^{0.31}} 。$ (21)

 $\frac{{d{T_k}}}{{dt}} = \frac{{\left[ {{Q_k} - {Q_h} - {{\dot m}_k}({c_p}T - {c_k}{T_k})} \right]}}{{({m_k}{c_k})}} 。$ (22)

 ${Q_k} = {\text{π}} {d_k}Nu\lambda ({T_k} - T)\frac{{\ln (1 + B)}}{B} 。$ (23)

${Q_h}$为液滴表面蒸发热效应，有

 ${Q_h} = {\dot m_k}L 。$ (24)

1.3 数值方法

1.4 模型验证

 图 3 燃气-蒸汽发射动力系统计算网格无关性检验结果 Fig. 3 Independence test results of calculation grid for gas-steam launch power system

Barata等[14]研究了横向气流中的液滴蒸发特性。其工况中气流速度为10 m/s，气流温度为800 K，液滴初始直径为0.23 mm。本文计算粒径结果如下：0 s时为0.23 mm，0.01 s时0.218 mm，0.02 s时0.199 mm，0.03 s时0.189 mm和0.04 s下0.173 mm。对应时刻的文献中结果分别0.23 mm、0.223 mm、0.206 mm、0.193mm和0.178 8 mm。对比可知本文液滴蒸发计算结果与文献中结果基本一致。

Lin[15]采用水为工质进行了超声速条件下，液体横向射流雾化的试验研究。观测了射流液体的穿透深度和液滴索泰尔平均直径（SMD）情况，获得射流穿透深度与气液动量比之间的经验关系式。试验条件如表2所示。

 图 4 穿透深度计算值与实验值对比 Fig. 4 Comparison of penetration depth calculation value and experimental value
2 结果与讨论

 图 5 发射动力系统纯燃气工况及燃气-蒸汽工况质量加权平均总压分布情况 Fig. 5 The distribution of mass-weighted average total pressure of the launch power system under pure gas conditions and gas-steam conditions

 图 6 发射动力系统纯燃气工况及燃气-蒸汽工况静温分布情况 Fig. 6 The static temperature distribution of the pure gas and gas-steam operating conditions of the launch power system

 图 7 燃气-蒸汽工况下发射动力系统内冷却水蒸发情况 Fig. 7 Evaporation of cooling water in the launch power system under gas-steam conditions

3 结　语

1）纯燃气工况及燃气-蒸汽工况下，发射动力系统内突扩结构及渐扩结构对气流总压损失有着决定性作用；2）弯管结构并没有对发射动力系统总压产生太大损失；3）冷却水的注入对于气流总压有着明显耗散损失作用；4）冷却水注入后发射动力系统出口静温大幅下降；5）在冷却水注入高温燃气后，在毫秒量级内发射动力系统又回归稳定工作状态；6）冷却水注入发射动力系统后，在发射动力系统内几乎全部蒸发。

 [1] PAUL C, GLEN C. Submarine missile launch system[P]. United States Patent, 3857321, December, 31. [2] 赵世平, 李江, 何国强, 等. 固体燃气发生器动力模拟水下发射试验研究[J]. 固体火箭技术, 2006, 29(1): 5-8. DOI:10.3969/j.issn.1006-2793.2006.01.002 [3] 吕翔, 李江, 陈剑, 等. 变深度水下发射系统内弹道实验研究[J]. 固体火箭技术, 2012, 35(1): 24-28. DOI:10.3969/j.issn.1006-2793.2012.01.005 [4] 肖虎斌, 赵世平. 燃气蒸汽式发射动力装置复杂内流场数值模拟[J]. 固体火箭技术, 2009(4): 392-395. DOI:10.3969/j.issn.1006-2793.2009.04.009 [5] 芮守祯, 邢玉明. 导弹弹射装置冷却器中液滴轨迹及特性的数值模拟[J]. 舰船科学技术, 2010, 32(4): 113-116. DOI:10.3404/j.issn.1672-7649.2010.04.028 [6] YANG S, LE JIALING, WEI H E, et al. Fuel atomization and droplet breakup models for numerical simulation of spray combustion in a scramjet combustor[C]//AIAA International Space Planes and Hypersonic Systems and Technologies Conference, 2013. [7] BHANDARKAR A, MANNA P, CHAKRABORTY D. Assessment of droplet breakup models in high-speed cross-flow[J]. Atomization & Sprays, 2017: 61–79. [8] 阎超. 计算流体力学方法及应用[M]. 北京: 北京航空航天大学出版社, 2006. [9] 胡晓磊, 乐贵高, 马大为, 等. 喷水对冷却器流场影响数值研究[J]. 计算机仿真, 2015, 32(1): 117-121. [10] 杨琦, 郭佳肄, 胡晓磊. 喷水对燃气-蒸汽弹射内弹道影响数值研究[J]. 赤峰学院学报(自然科学版), 2016, 32(14): 191-192. DOI:10.13398/j.cnki.issn1673-260x.2016.14.081 [11] 李仁凤, 乐贵高, 马大为, 等. 结构参数对燃气-蒸汽弹射载荷和弹道影响[J]. 上海交通大学学报, 2016(11): 1789-1793. DOI:10.16183/j.cnki.jsjtu.2016.11.022 [12] 李仁凤, 乐贵高, 马大为, 等. 进气角与注水规律对燃气-蒸汽弹射的影响[J]. 航空动力学报, 2017(4): 961-969. DOI:10.13224/j.cnki.jasp.2017.04.023 [13] 胡晓磊, 孙船斌, 李仁凤, 等. 喷水孔数量对燃气-蒸汽弹射内弹道的影响[J]. 弹道学报, 2018(2): 37-41. DOI:10.12115/j.issn.1004-499X(2018)02-07 [14] BARATA J M M, MATOS H M M, SILVA A R R. Numerical simulation of an array of evaporating droplets through a crossflow[C]//43 rd AIAA Aerospace Sciences Meeting and Exhibit. 2005: 2005. [15] LIN K C, KENNEDY P, JACKSON T. Structures of water jets in a mach 1.94 supersonic crossflow[C]// AIAA Aerospace Sciences Meeting and Exhibit, 2004.