﻿ 水下容器开启过程流场特性仿真研究
 舰船科学技术  2017, Vol. 39 Issue (8): 124-127 PDF

Flow characteristics simulation of the opening process of underwater container
YAN Feng, LI Gang, PENG Ze-ming
Wuhan Second Ship Design and Research Institute, Wuhan 430064, China
Abstract: During the opening of the underwater container, seawater injects into the container expeditiously, which exerts an influence on the stability of the carrier. The Mixture multiphase method was used to calculate the gas-liquid flow field, the zone moving and dynamic laying was used to update the meshes. The different opening angle conditions were simulated, the result of the simulation shows that the fluctuate of the pressure at the bottom of the container and the mass of water injecting into the container are acuter, when the openning angle is smaller, as well as the peak valve. With the increase of the opening angle, the fluctuate becomes gentle. The research can provide theoretical support for the design of underwater container and the optimization of the process.
Key words: underwater container     Mixture model     multiphase flow     pressure field
0 引　言

1 数学建模 1.1 物理模型

 图 1 物理模型 Fig. 1 Physical model
1.2 控制方程

1）连续方程
 $\frac{\partial }{{\partial t}}\left( {{\rho _m}} \right) + \nabla \cdot \left( {{\rho _m}{{\overrightarrow \upsilon }_m}} \right) = 0{\text{。}}$

2）动量方程

 \begin{aligned} \frac{\partial }{{\partial t}}\left( {{\rho _m}{{\overrightarrow \upsilon }_m}} \right) + & \nabla \cdot \left( {{\rho _m}{{\overrightarrow \upsilon }_m}{{\overrightarrow \upsilon }_m}} \right) = - \nabla p + \nabla \cdot \left[ {{\mu _m}\left( {\nabla {{\overrightarrow \upsilon }_m} + \overrightarrow \upsilon _m^T} \right)} \right] +\\ & {\rho _m}\overrightarrow g +\overrightarrow F + \nabla \cdot \left( {\sum\limits_{k = 1}^n {{\alpha _k}{\rho _k}{{\overrightarrow \upsilon }_{dr,k}}{{\overrightarrow \upsilon }_{dr,k}}} } \right){\text{。}}\end{aligned}

3）能量方程
 $\frac{\partial }{{\partial t}}\sum\limits_{k = 1}^n {{\alpha _k}{\rho _k}{E_k}} \!+\! \nabla \cdot \left( {\sum\limits_{k = 1}^n {{\alpha _k}{{\overrightarrow \upsilon }_k}\left( {{\rho _k}{E_k} + p} \right)} } \right) \!=\! \nabla \cdot \left( {k{}_{eff}\nabla T} \right) \!+\! {S_E}{\text{。}}$

4）相对速度与漂移速度

 ${\overrightarrow \upsilon _{pq}} = {\overrightarrow \upsilon _p} - {\overrightarrow \upsilon _q},$

${\overrightarrow \upsilon _{dr,p}} = {\overrightarrow \upsilon _{pq}} - \sum\limits_{k = 1}^n {{c_k}{{\overrightarrow \upsilon }_{qk}}}$

5）次要相的体积分数方程

 $\frac{\partial }{{\partial t}}\left( {{\alpha _p}{\rho _p}} \right) \!+\! \nabla \cdot \left( {{\alpha _p}{\rho _p}{{\overrightarrow \upsilon }_m}} \right) \!=\! - \nabla \cdot \left( {{\alpha _p}{\rho _p}{{\overrightarrow \upsilon }_{dr,p}}} \right) \!+\!\! \sum\limits_{q = 1}^n {\left( {{{\dot m}_{qp}} \!-\!\! {{\dot m}_{pq}}} \right)} {\text{。}}$
6）RNG k-ε湍流模型方程

 $\begin{array}{l}\displaystyle\frac{{\partial \left( {\rho k} \right)}}{{\partial t}} + \frac{{\partial \left( {\rho k{u_i}} \right)}}{{\partial {x_i}}} = \frac{\partial }{{\partial {x_j}}}\left( {{\alpha _k}{\mu _{eff}}\frac{{\partial k}}{{\partial {x_j}}}} \right) + {G_k} + \rho \varepsilon ,\\[10pt]\displaystyle\frac{{\partial \left( {\rho \varepsilon } \right)}}{{\partial t}} + \frac{{\partial \left( {\rho \varepsilon {u_i}} \right)}}{{\partial {x_i}}} = \frac{\partial }{{\partial {x_j}}}\left( {{\alpha _\varepsilon }{\mu _{eff}}\frac{{\partial \varepsilon }}{{\partial {x_j}}}} \right) + \frac{{C_{1\varepsilon }^*\varepsilon }}{k}{G_k} - {C_{2\varepsilon }}\rho \frac{{{\varepsilon ^2}}}{k}{\text{。}}\end{array}$
 \begin{aligned}{\text{式中：}}\quad\quad\quad & {\mu _{eff}} = \mu + {\mu _i};\\[3pt]& {\mu _i} = \rho {C_\mu }\frac{{{k^2}}}{\varepsilon };\\[3pt]& {C_\mu } = 0.0845,{\alpha _k} = {\alpha _\varepsilon } = 1.39;\\[3pt]& C_{1\varepsilon }^* = {C_{1\varepsilon }} - \frac{{\eta \left( {1 - \eta /{\eta _0}} \right)}}{{1 + \beta {\eta ^3}}};\\[3pt]& {C_{1\varepsilon }} = 1.42,{C_{2\varepsilon }} = .68;\\& \eta = {\left( {2{E_{ij}} \cdot {E_{ij}}} \right)^{1/2}}\frac{k}{\varepsilon };\\[3pt]& {E_{ij}} = \frac{1}{2}\left( {\frac{{\partial {u_i}}}{{\partial {x_j}}} + \frac{{\partial {u_j}}}{{\partial {x_i}}}} \right);\\[3pt]& {\eta _0} = 4.377;\beta = 0.012 {\text{。}}\quad\quad\quad\quad\quad\quad\quad\quad\quad\end{aligned}
2 仿真方法 2.1 控制方程离散

2.2 仿真算法

Simple算法的基本思想如下：对于给定的压力场（可以是假定的值或是上一次迭代计算所得到的结果），求解离散形式的动量方程，得到速度场。因为压力场是假定的或不精确的，这样得到的速度场一般不满足连续方程，因此必须对给定的压力场加以修正。修正的原则是与修正后的压力场相对应的速度场能满足这一迭代层次上的连续方程。据此原则，将由动量方程的离散形式所规定的压力与速度的关系代入连续方程的离散形式，从而得到压力修正方程，由压力修正方程得出压力修正值。接着，根据修正后的压力场，求得新的速度场。然后检查速度场是否收敛，若不收敛，用修正后的压力值作为给定的压力场，开始下一层次的计算，如此反复，直到获得收敛的解，求解步骤如图2所示。

 图 2 Simple算法流程图 Fig. 2 Flow chart of Simple arithmetic
3 仿真结果与分析 3.1 不同开启角度对容器底部压力和容器内进水量的影响

 图 3 不同开启角度（α1＜α2＜α3）容器底部压力变化曲线 Fig. 3 The pressure curve at the bottom of container with different opening angle

 图 4 不同开启角度（α1＜α2＜α3）容器内进水量变化曲线 Fig. 4 The mass of water injecting into the container with different opening angle
3.2 容器底部压力和容器内进水量变化机理分析

 图 5 容器底部压力与进水量对照图 Fig. 5 Comparison of the pressure at the bottom of the container and the mass of water injecting into the container

 图 6 容器底部温度与进水量对照图 Fig. 6 Comparison of the temperature at the bottom of the container and the mass of water injecting into the container
4 结　语

1）容器开启角度越小，底部压力和进水量越大，且震荡越剧烈；底部压力较进水量的波动幅度更大；随着时间的推移，两者逐渐趋于稳定；

2）容器底部压力震荡所产生的水锤现象是由海水压力和残余气体压力两者互相作用所产生的压缩波冲击容器底部而引起的；

3）进水量的变化是由于压缩波、膨胀波所引起的底部压力波动而引起的，在压缩波形成过程中，进水量逐渐增加，压缩波在底部反弹为膨胀波后，将容器内海水排挤出容器外，进水量减少。

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