﻿ 连续分层环境中Suboff激发的自由面尾迹数值仿真
 舰船科学技术  2021, Vol. 43 Issue (11): 20-26    DOI: 10.3404/j.issn.1672-7649.2021.11.004 PDF

1. 武汉第二船舶设计研究所，湖北 武汉 430064;
2. 华中科技大学 航空航天学院，湖北 武汉 430074

Numerical investigation of free surface wake excited by Suboff in continuously stratified fluid
WU Jian-wei1, YU Hao-cheng2, WANG Yun1, MENG Qing-jie1, PENG Liang1, ZHENG Jian-guo2
2. School of Aerospace Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
Abstract: The interaction between underwater-vehicle and fluid will generate specific hydrodynamic wakes on the freesurface. In order to study the mechanism and characteristics of the hydrodynamic wake, unsteady Reynolds-Averaged Naiver-Stokes (URANS) model together with VOF (Volume of Fluid) method is adopted to simulate the free surface wake excited by the full-scale Suboff model in the continuously stratified fluid. Firstly, the effect of continuously stratified fluid on the characteristics of free surface wake is investigated. The flow structure and free surface wake in the continuously stratified and homogeneous fluid are compared in detail. Secondly, the wake characteristics under different depths in continuously stratified fluid are studied. When the diving depth is 20 m, the maximum wave height is up to 3.35 m. With the increase of the depth, the perturbation of the free surface caused by the Suboff becomes smaller. Consequently, the free surface wake becomes weaker.
Key words: continuously stratified fluid     Suboff     wake     RANS
0 引　言

1 数值方法 1.1 控制方程

 $\frac{{\partial \overline {{u_i}} }}{{\partial {x_i}}} = 0,$ (1)
 $\rho \frac{{\partial \overline {{u_i}} }}{{\partial t}} + \rho \overline {{u_j}} \frac{{\partial \overline {{u_i}} }}{{\partial {x_j}}} = \rho \overline {{F_i}} - \frac{{\partial \overline p }}{{\partial {x_i}}} + \frac{\partial }{{\partial {x_j}}}\left(\mu \frac{{\partial \overline {{u_i}} }}{{\partial {x_j}}} - \rho \overline {u'_iu'_j} \right){\text{。}}$ (2)

1.2 湍流模型

RANS方程组中有关湍流脉动值的雷诺应力项 $\rho \overline {u'_i u'_j}$ 是未知的。为了使方程封闭，选用Realizable k-ε湍流模型对雷诺应力项进行建模，湍动能k及耗散率ε输运方程分别为：

 $\begin{split} \frac{\partial }{\partial t}(\rho k)+\frac{\partial }{\partial {x}_{j}}(\rho k{u}_{j})=&\frac{\partial }{\partial {x}_{j}}\left[\left(\mu +\frac{{\mu }_{t}}{{\sigma }_{k}}\right)\frac{\partial k}{\partial {x}_{j}}\right]+\\ &{P}_{k}+{P}_{b}-\rho ϵ-{Y}_{M}+{S}_{k} {\text{，}} \end{split}$ (3)
 $\begin{split}\frac{\partial }{{\partial t}}(\rho \varepsilon ) + \frac{\partial }{{\partial {x_j}}}(\rho \varepsilon {u_j}) =& \frac{\partial }{{\partial {x_j}}}\left[ {\left( {\mu + \frac{{{\mu _t}}}{{{\sigma _\varepsilon }}}} \right)\frac{{\partial \varepsilon }}{{\partial {x_j}}}} \right] +\rho {\mkern 1mu} {C_1}S\varepsilon - \\ &\rho {\mkern 1mu} {C_2}\frac{{{\varepsilon ^2}}}{{k + \sqrt {\nu \varepsilon } }} + {C_{1\varepsilon }}\frac{\varepsilon }{k}{C_{3\varepsilon }}{P_b} + {S_\varepsilon }{\text{，}} \end{split}$ (4)

 ${A_0} = 4.04,\;\;{A_s} = \sqrt 6 \cos \phi\text{，}$ (5)
 $\phi =\frac{1}{3}{\mathrm{cos}}^{-1}(\sqrt{6}W),W=\frac{{S}_{ij}{S}_{jk}{S}_{ki}}{{\tilde{S}}^{3}}\text{，}$ (6)
 $\tilde{S}=\sqrt{{S}_{ij}{S}_{ij}},{S}_{ij}=\frac{1}{2}\left(\frac{\partial {u}_{j}}{\partial {x}_{i}}+\frac{\partial {u}_{i}}{\partial {x}_{j}}\right)\text{。}$ (7)
1.3 VOF方法

 $\frac{{\partial {\alpha _{\text{q}}}}}{{\partial t}} + {u_i}\frac{{\partial {\alpha _{\text{q}}}}}{{\partial {x_i}}} = 0 {\text{，}}$ (8)

 $\sum\limits_{q = 1}^n {{\alpha _q}} = 1{\text{，}}$ (9)

 $\rho = \sum\limits_{q = 1}^n {{\alpha _q}} {\rho _q} {\text{。}}$ (10)

1.4 计算设置 1.4.1 研究对象

 图 1 Suboff标模外形示意图 Fig. 1 Geometry of the Suboff model

 图 2 实际工况下海水的密度随深度变化的曲线图 Fig. 2 Density profile of stratified fluid
1.4.2 计算域与边界条件

 图 3 计算域及对应的边界条件示意图 Fig. 3 The computational domain and boundary conditions
1.4.3 计算网格

 图 4 当前计算所使用的网格 Fig. 4 Grid of current simulation
2 结果分析 2.1 数值模型验证

 图 5 数值模型验证 Fig. 5 Numerical model validation
2.2 流体分层的影响

 图 6 两种工况下液体密度在深度方向上的变化 Fig. 6 Variation of fluid density in depth direction at two conditions

 图 7 单层液体与连续分层环境中Suboff周围流场对比（潜深50 m，航速30 kn）。 Fig. 7 Comparison of flow field around Suboff in pure and stratified fluid, where the depth is 50 m and the velocity is 30 kn.

 图 8 潜深为50 m，航速为30 kn时对称平面上x速度云图的比较 Fig. 8 Comparison of x velocity contour on the symmetry plane, where the depth is 50 m and the velocity is 30 kn

 图 9 单层液体和连续分层环境中的水下航行体产生的自由面尾迹的对比 Fig. 9 Comparison of free surface wake generated by underwater-vehicle in pure and stratified fluid

 图 10 连续分层与单层液体环境中的表面波波形图 Fig. 10 The shape of free surface wave in pure and stratified fluid
2.3 潜深对尾迹的影响

 图 11 潜深20 m，航速30 kn的图形 Fig. 11 The figure of depth is 20 m and the velocity is 30 kn.

 图 12 潜深50 m，航速30 kn的图形 Fig. 12 The figure of depth is 50 m and the velocity is 30 kn.

 图 13 潜深80 m，航速30 kn图形 Fig. 13 The figure of depth is 80 m and the velocity is 30 kn.

 图 14 不同潜深下自由面尾迹的波形图 Fig. 14 The shape of free surface wake at different depths
3 结　语

1）考察了密度连续分层环境对自由面尾迹的影响。通过对连续分层和单层液体2种工况下流场结构以及尾迹特征进行详细的对比研究发现，密度的变化不会对Suboff周围的流场产生较大的影响。在2种工况下，自由面尾迹均呈现出明显的开尔文波系结构，且波形、最大波高以及最大波速基本保持相同。通过对流场的深入分析发现，潜体的运动会对周围的流场产生扰动，这种扰动会一直传播至自由面。由于自由面附近流体密度的差异较大，受到扰动后会导致原来的平衡位置出现两种不同密度的流体。为了恢复平衡，自由面附近流体重力和浮力会互相作用，使得液面出现波动。在这2种工况下，扰动源完全相同，所以自由面尾迹的特征基本相同。

2）对不同潜深下Suboff产生的自由面尾迹进行了研究。研究表明，随着潜航深度的增加，自由面尾迹的最大波高和波速急剧减小，尾迹特征减弱。通过对Suboff周围流场进行详细的解析发现，由于粘性作用的存在，随着潜深的增加，潜体对自由面附近流体的加速作用减小，自由面附近受到的扰动逐渐变小，所以激发的尾迹变得更加微弱。

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