﻿ 浅水区域船舶航行下沉量的数值计算
 舰船科学技术  2022, Vol. 44 Issue (20): 42-45    DOI: 10.3404/j.issn.1672-7649.2022.20.008 PDF

1. 江苏海事职业技术学院，江苏 南京 211170;
2. 上海海事大学 商船学院，上海 200135

Numerical calculation of ship sinking in shallow water
XIE Bao-feng1, ZHANG Shu-kui1, HU Shen-ping2
1. Jiangsu Maritime Institute, Nanjing 211170, China;
2. Merchant Marine College, Shanghai Maritime University, Shanghai 200135, China
Abstract: During the navigation in the shallow water area, due to the influence of the current and pressure, the sinking of the ship has a great change compared with the deep water area. The appearance of the shallow water effect has a negative impact on the ship, which will increase the risk of the ship hitting the bottom, especially with the increasing tonnage of the ship, the shallow water effect is more obvious. In order to solve this problem, this paper establishes a ship's sinking model, and studies the characteristics of ship's sinking in shallow water based on CFD computational fluid theory.
Key words: subsidence     CFD computational fluid theory     simulation     shallow water effect
0 引　言

1）船底相对海水的流动速度

2）纵倾运动

1）海水流动方向不同

2）下沉量不同

1 船舶浅水区域航行的下沉量数学模型搭建

 图 1 船舶下沉量数学模型 Fig. 1 Mathematical model of ship sinking

 $\begin{gathered} \frac{{\partial u}}{{\partial x}} + \frac{{\partial v}}{{\partial y}} + \frac{{\partial w}}{{\partial z}} = 0, \\ \rho \frac{{{\rm{D}}u}}{{{\rm{D}}t}} = \rho {f_x} - \frac{{\partial p}}{{\partial x}} + \mu {\nabla ^2}u, \\ \rho \frac{{{\rm{D}}v}}{{{\rm{D}}t}} = \rho {f_y} - \frac{{\partial p}}{{\partial y}} + \mu {\nabla ^2}v, \\ \rho \frac{{{\rm{D}}w}}{{{\rm{D}}t}} = \rho {f_z} - \frac{{\partial p}}{{\partial z}} + \mu {\nabla ^2}wn 。\\ \end{gathered}$

 $\begin{gathered} \rho \overline {u_i^\prime u_j^\prime } = {\mu _t}\left( {\frac{{\partial {u_i}}}{{\partial {x_j}}} + \frac{{\partial {u_j}}}{{\partial {x_i}}}} \right) - \frac{2}{3}\left( {\rho k + {\mu _t}\frac{{\partial {u_k}}}{{\partial {x_k}}}} \right){\delta _{ij}}，\\ k = \frac{1}{2}\overline {u_i^\prime u_j^\prime }。\\ \end{gathered}$

 $- \rho \left( {{{u'}_i}} \right) = {\mu _1}\left( {\frac{{\partial {u_i}}}{{\partial {x_i}}} + \frac{{\partial {u_j}}}{{\partial {x_j}}}} \right) - \frac{1}{3}\left( {{\rho _{}}k + {\mu _1}\frac{{\partial {u_i}}}{{\partial {x_i}}}} \right){\sigma _0} 。$

 ${\mu _1} = {H_0}\frac{k}{\varepsilon }。$

2 基于CFD的浅水区船舶航行下沉量数值计算 2.1 船舶航行下沉量数值计算流程

 图 2 基于CFD的船舶航行下沉量计算流程图 Fig. 2 Flow chart of ship navigation subsidence calculation based on CFD

 $\begin{gathered} F = \frac{1}{2}P{V^2}{\left( {\frac{L}{2}} \right)^2}{C_p}，\\ M = \frac{1}{2}P{V^2}{\left( {\frac{1}{2}} \right)^3}{{\text{C}}_q}。\\ \end{gathered}$

 ${S_\varphi } = \frac{d}{{\sin \theta }}\left[ {\sin \left( {{\varphi _0} + \Delta \varphi + \theta } \right) - \sin \left( {{\varphi _0} + \theta } \right)} \right] 。$

 ${S_\varphi } = \frac{L}{2}\left[ {\sin \left( {{\varphi _0} + \Delta \varphi } \right) - \sin \left( {{\varphi _0}} \right)} \right] 。$
2.2 定义船舶航行下沉量数值计算的边界条件

Wigley船模表面的型值点方程如下：

 $y = \frac{B}{2}\left[ {1 - {{\left( {\frac{{2X}}{L}} \right)}^2}} \right]\left[ {1 - {{\left( {\frac{Z}{T}} \right)}^2}} \right] 。$

 图 3 船舶在海水中的流固耦合界面划分 Fig. 3 Division of fluid solid coupling interface of ship in seawater

1）入口边界条件

 ${C_0} = \frac{{{R_0}}}{{0.5\rho {v_m}^2{s_m}}} 。$

2）出口边界条件

3）壁面边界条件

4）对称面边界条件

2.3 定义船舶航行下沉量数值计算的计算域

 图 4 船舶航行下沉量数值模拟计算域 Fig. 4 Calculation domain of numerical simulation of ship navigation subsidence

 ${\xi _1} = \frac{{0.07}}{{{{\left( {{{\rm{lg}}Re} - 3} \right)}^2}}} 。$

2.4 船舶航行下沉量数值计算

Wigley船模的吃水平均深度为7.5 m，浅水区域的水深定义为10 m，船底海水的流动速度随船宽方向的分布曲线如图5所示。

 图 5 船底海水的流动速度分布曲线 Fig. 5 Flow velocity distribution curve of sea water at ship bottom

Wigley船模的平均吃水增量如下式：

 $\Delta d = \frac{{D - {\raise0.7ex\hbox{$F$} \mathord{\left/ {\vphantom {F g}}\right.} \lower0.7ex\hbox{$g$}}}}{{100TPC}} \text{，}$

 图 6 浅水区域下沉量与船舶吃水增量的关系 Fig. 6 The relationship between shallow water subsidence and ship draft increment
3 结　语

 [1] 王澄. 基于计算流体力学的船舶风载荷计算方法分析[J]. 天津理工大学学报, 2021, 37(2): 21-26. WANG Cheng. Analysis of ship wind load calculation method based on computational fluid dynamics[J]. Journal of Tianjin University of Technology, 2021, 37(2): 21-26. DOI:10.3969/j.issn.1673-095X.2021.02.005 [2] 杨春蕾, 王金宝. 船舶时域破损稳性问题的计算流体力学方法[J]. 中国造船, 2020, 61(S2): 430-438. YANG Chun-lei, Wang Jin-bao. Computational fluid dynamics method for time domain damage stability of ships[J]. China Shipbuilding, 2020, 61(S2): 430-438. DOI:10.3969/j.issn.1000-4882.2020.z2.046 [3] 杨波, 石爱国, 吴明. 基于计算流体力学理论的船舶横摇阻尼系数计算[J]. 中国航海, 2012, 35(3): 76-80. YANG Bo, SHI Ai-guo, WU Ming. Calculation of ship rolling damping coefficient based on computational fluid dynamics[J]. China Navigation, 2012, 35(3): 76-80. DOI:10.3969/j.issn.1000-4653.2012.03.017 [4] 陈伟民, 陈霞萍. 计算流体力学在船舶线型优化中的应用[J]. 上海船舶运输科学研究所学报, 2007(1): 30-32. CHEN Wei-min, CHEN Xia-ping. Application of computational fluid dynamics in ship linetype optimization[J]. Journal of Shanghai Institute of Ship Transportation Science, 2007(1): 30-32. DOI:10.3969/j.issn.1674-5949.2007.01.005