﻿ 流体可压缩性对高速入水载荷的影响研究
 舰船科学技术  2022, Vol. 44 Issue (19): 6-11    DOI: 10.3404/j.issn.1672-7649.2022.19.002 PDF

1. 西安精密机械研究所 总体部，陕西 西安 710077;
2. 西北工业大学 航海学院，陕西 西安 710072

Effect of fluid compressibility on high-speed water entry loads
FENG Peng-hui1,2, QIN Xiao-hui1, LIU Gang-qi1, ZHOU Jing-jun1, WANG Zhong1
1. Xi'an Precision Machinery Research Institute, Xi′an 710077, China;
2. School of Marine Science and Technology, Northwestern Polytechnical University, Xi′an 710072, China
Abstract: Rocket-assisted torpedoes suffer from the severe trans-medium mechanical environment caused by water entry. This article establishes a mathematical model of gas-liquid-vapor three-phase coupled flow based on the homogeneous equilibrium flow and the VOF multiphase flow. The overset grid technology is adopted to realize the coupling analysis of water entry between the multiphase flow and the 6-DOF body dynamics. The effects of gas compressibility and liquid compressibility on the high-speed water entry loads of body are investigated. Further, the corresponding effects of different water entry speeds (100～300 m/s) and deadrise angles (10° and 40°) are analyzed comprehensively. The results can help readers clearly understand the mechanism of fluid compressibility action during the high-speed water entry, which provides a helpful guidance for the relevant designs of load-reduced nose and scaling test.
Key words: high-speed water entry     fluid compressibility     multiphase flow     load reduction
0 引　言

1 模型描述 1.1 几何模型

 图 1 几何模型及网格划分 Fig. 1 Geometrical model and meshing
1.2 数学模型

1）控制方程

 $\frac{{\partial \rho }}{{\partial t}} + \nabla \left( {\rho \overrightarrow U } \right) = 0 ，$ (1)
 $\rho \frac{{\partial \overrightarrow U }}{{\partial t}} + \rho \overrightarrow U \cdot \nabla \overrightarrow U = \nabla \left\{ {\mu \left[ {\nabla \overrightarrow U + {{\left( {\nabla \overrightarrow U } \right)}^{\text{T}}}} \right]} \right\} - \nabla p。$ (2)

 ${\rho _{{m}}} = {\rho _{{g}}}{\alpha _{{g}}} + {\rho _{{v}}}{\alpha _{{v}}} + {\rho _l}\left( {1 - {\alpha _{\text{g}}} - {\alpha _{\text{v}}}} \right)。$ (3)

2）状态方程

 $\rho = {\rho _0}{\left( {1 + \dfrac{{n\left( {p - {p_0}} \right)}}{{{E_0}}}} \right)^{\frac{1}{n}}}。$ (4)

3）空化模型

 $\begin{split} & \frac{{\partial {\alpha _{\text{v}}}{\rho _{\text{v}}}}}{{\partial t}} + \nabla \left( {{\alpha _{\text{v}}}{\rho _{\text{v}}}{{\overrightarrow U }_{\text{v}}}} \right) = \\ &\frac{{3\left( {{\alpha _{\text{v}}} + {\alpha _{{\text{nuc}}}}} \right)\left( {1 - {\alpha _{\text{v}}}} \right)}}{{{R_{{B}}}}}\frac{{{\rho _{\text{l}}}{\rho _{\text{v}}}}}{{{\rho _{{m}}}}}\sqrt {\frac{2}{3}\frac{{{p_{{\text{sat}}}} - p}}{{{\rho _{\text{l}}}}}} \left( {p < {p_{{\text{sat}}}}} \right) - \\ & \frac{{3{\alpha _{\text{v}}}\left( {1 - {\alpha _{\text{v}}}} \right)}}{{{R_{{B}}}}}\frac{{{\rho _{\text{l}}}{\rho _{{v}}}}}{{{\rho _{{m}}}}}\sqrt {\frac{2}{3}\frac{{p - {p_{{\text{sat}}}}}}{{{\rho _{\text{l}}}}}} \left( {p \geqslant {p_{{\text{sat}}}}} \right) 。\\[-10pt] \end{split}$ (5)

1.3 模型验证

 图 2 数值结果与试验结果的对比 Fig. 2 Comparison between the simulated and experimental results
2 结果与讨论

 ${C_{{d}}} = \dfrac{{{F_{{d}}}}}{{\dfrac{1}{2}\rho {u^2}S}}。$ (6)

2.1 流体可压缩性对入水载荷的影响

 图 3 流体可压缩性对入水载荷的影响 Fig. 3 Effects of fluid compressibility on water-entry loads

 图 4 楔形头入水过程示意图[17] Fig. 4 Schematic diagram of fluid-solid interaction during conical nose water entry

 图 5 300 m/s入水时液相可压缩性对压力场的影响 Fig. 5 Effect of liquid compressibility on the pressure distribution at the speed of 300 m/s
2.2 不同速度下流体可压缩性的影响规律

 图 6 入水时液相可压缩性对载荷的影响 Fig. 6 Effect of liquid compressibility on the water entry loads

 图 7 入水时液相可压缩性对压力场的影响 Fig. 7 Effect of liquid compressibility on the pressure distribution
2.3 不同头型下流体可压缩性的影响规律

 图 8 横升角40°的锥形头入水时液相可压缩性对载荷的影响 Fig. 8 Effect of liquid compressibility on the water entry loads of conical nose with the deadrise angle of 40°

 图 9 不同头型、入水速度和马赫数对液相可压缩性作用的影响 Fig. 9 Effects of different noses and speeds on the liquid compressibility role and the water entry impact
3 结　语

1）气-液两相流体可压缩性主要对冲击载荷有影响，其中液相可压缩性影响占主导作用；

2）液相可压缩性的作用机理主要是，可压缩性会使沾湿面附近压力扰动传递受阻，局部高压区表现出更强的聚集性，导致作用在沾湿面全局的流体阻力减小。

3）基于结构体挤压流体局部形成合速度对应的液相马赫数，可以作为液相可压缩性对冲击载荷的影响判别特征数。液相马赫数越大，液相可压缩性的影响将逐渐明显，液相马赫数大于0.4时，液相不可压缩会使冲击载荷被高估10%以上。

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