﻿ 层化环境下自由表面散度场的数值与实验研究
 舰船科学技术  2022, Vol. 44 Issue (15): 60-65    DOI: 10.3404/j.issn.1672-7649.2022.15.013 PDF

Numerical and experimental analysis of divergence of free surface in a stratified fluid
HOU Jian-jun, LI Da-wei, GAO Yuan-bo, YU Kai-bo
Dalian Naval Academy, Dalian 214082, China
Abstract: The surface divergence field excited by submarine is an important hydrodynamic characteristic of wake and is an important source of non-acoustic detection. In this paper, CFD was used to numerically simulate the free surface divergence field excited by Suboff model in a stratified fluid environment, and PIV technology was used to verify the numerical simulation results in a stratified pool. The results show that the Kelvin angle and the maximum intensity of the divergence wake calculated by simulation are in good agreement with the experimental values. With the increase of the internal Froude number, the Kelvin angle of divergence field on the submarine wake surface gradually decreases from double e exponent function to decrease linear function.
Key words: Suboff     simulation     PIV     divergence
0 引　言

 图 1 合成孔径雷达检测的尾迹 Fig. 1 Wake detected by SAR

1 数值模拟方法 1.1 计算模型

 图 2 潜艇与跃层的网格划分 Fig. 2 Meshing of submarine and thermocline
1.2 湍流模型

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

1.3 计算方法验证

 图 3 潜艇对称截面处的压力分布(Cp ) Fig. 3 Pressure distribution at symmetric section (Cp) of submarine
2 水池实验设置

 图 4 PIV测量系统采集示意图 Fig. 4 schematic diagram of PIV experiment
3 数值与实验结果分析

 图 5 表面散度场(下层，ρ3=1040 kg/m3，U=33 cm/s) Fig. 5 Divergence field(bottom, ρ3=1040 kg/m3，U=33 cm/s)

 图 6 散度取样位置及表面散度角 Fig. 6 Divergence sampling position and surface divergence Angle

 图 7 不同速度表面散度场水池实验结果（ρ3=1 040 kg/m3） Fig. 7 Pool experiment results of surface divergence field at different velocities (ρ3=1 040 kg/m3)

 图 8 不同速度表面散度场水池实验结果（ρ3=1 020 kg/m3） Fig. 8 Pool experiment results of surface divergence field at different velocities (ρ3=1 020 kg/m3)

ρ3=1040 kg/m3，拖曳速度分别为33 cm/s和55 cm/s时，表面散度场极值及尾迹开角的水池实验结果与数值模拟结果的比较如表1所示。

 图 9 表面散度拟合曲线 Fig. 9 Fitting curve of surface divergence

 图 10 拖曳速度与最大散度关系 Fig. 10 Relationship between drag velocity and maximum divergence
4 实际尺度模型

 图 11 表面散度随时间的变化情况(实际目标) Fig. 11 Variation of surface divergence with time (actual target)

 图 12 表面流场特性随航速的变化(实际目标) Fig. 12 Variation of surface flow field characteristics with speed (actual target)

5 结　语

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