﻿ 基于CLSVOF-IB方法海洋管道流固耦合特性研究
 舰船科学技术  2022, Vol. 44 Issue (23): 80-86    DOI: 10.3404/j.issn.1672-7649.2022.23.016 PDF

1. 贵州理工学院 航空航天工程学院，贵州 贵阳 550003;
2. 国防科技大学 空天工程学院，湖南 长沙 410073;
3. 中国空气动力研究与发展中心，四川 绵阳 621000

Study of the characteristics of fluid-structure interactions for marine pipeline based on the CLSVOF-IB method
CUI Zuo1, WU Chao2, ZHOU Hou-cun3
1. School of Aerospace Engineering, Guizhou Institute of Technology, Guiyang 550003, China;
2. College of Aerospace Science and Engineering, National University of Defense Technology, Changsha 410073, China;
3. China Aerodynamics Research and Development Center, Mianyang 621000, China
Abstract: In this paper, the CLSVOF-IB method is used to study the interactive forces and the VIV (vortex-induced vibration) characteristics of marine pipeline. The CLSVOF (Coupled Level-Set and VOF) method is used to simulate the ocean free surface, and the immersed boundary (IB) method is adopted to calculate the interactive force between the marine pipeline and the surrounding fluid flow. The numerical results show that the CLSVOF-IB method can be used to simulate the fluid-structure interactions of marine pipeline accurately, and the flow-induced vibration of marine pipeline can be avoided by choosing the proper pipe diameter and inflow velocity. In addition, the numerical results show that by changing the Froude (Fr) number of fluid flow, the effects of marine pipeline on the free surface of ocean wave can be also accurately captured by this method.
Key words: marine pipe     fluid-structure coupling     CLSVOF method     immersed boundary method     vortex-induced vibration
0 引　言

1 数值方法 1.1 Navier-Stokes方程流体求解器

 $\frac{{\partial {u_{\text{i}}}}}{{\partial t}} + \frac{{\partial \left( {{u_{\text{i}}}{u_{\text{j}}}} \right)}}{{\partial {x_{\text{j}}}}} = - \frac{{\partial p}}{{\partial {x_{\text{j}}}}} + \frac{1}{{Re}}\frac{{{\partial ^2}{u_{\text{i}}}}}{{\partial {x_{\text{j}}}{x_{\text{j}}}}} + {f_{\text{i}}} ，$ (1)
 $\frac{{\partial {u_{\text{i}}}}}{{\partial {x_{\text{i}}}}} = 0 。$ (2)

 $\frac{{\partial {{\bar u}_{{i}}}}}{{\partial t}} + \frac{{\partial \left( {{{\bar u}_{{i}}}{{\bar u}_{{j}}}} \right)}}{{\partial {x_{{j}}}}} = - \frac{1}{\rho }\frac{{\partial \bar p}}{{\partial {x_{{i}}}}} + {v_{{t}}}\frac{{{\partial ^2}{{\bar u}_{{i}}}}}{{\partial {x_{{j}}}\partial {x_{{j}}}}} - \frac{{\partial \tau _{{{ij}}}^d}}{{\partial {x_{{j}}}}} + {f_{{i}}} ，$ (3)
 $\frac{{\partial {{\bar u}_{\text{i}}}}}{{\partial {x_{\text{i}}}}} = 0。$ (4)

N-S方程各变量分布在三维正交网格上，控制方程采用中心差分格式离散，由Runge-Kutta格式实现时间推进，其中压力泊松方程通过调用PETS库函数进行求解。本文所使用的N-S求解器在Linux系统下使用Fortran语言编写，采用MPI命令实现程序并行运算，具体算法详见文献[12]。本文计算所需硬件设备为国家超级计算长沙中心“天河”计算机，二维和三维算例分别采用64个和256个CPU进行并行计算。

1.2 CLSVOF方法

 $\frac{{\partial {\boldsymbol{u}}}}{{\partial {\text{t}}}} + {\boldsymbol{u}} \cdot \nabla {\boldsymbol{u}} = \frac{1}{\rho }\left( { - \nabla p + \nabla \cdot \left( {\mu {\mathbf{S}}} \right) + \rho g + \sigma {\mathbf{\kappa }}\delta \left( {{x_s}} \right) - \nabla \cdot {{\mathbf{\tau }}_{sgs}}} \right) ，$ (5)
 $\nabla \cdot {\mathbf{u}} = 0。$ (6)

 $\rho = {\rho _{\text{a}}}\left( {1 - F} \right) + {\rho _{\rm{w}}}F ，$ (7)
 $\mu = {\mu _{\text{a}}}\left( {1 - F} \right) + {\mu _{\rm{w}}}F 。$ (8)

 图 2 Level-set函数 ${\phi _{\text{n}}}$ 和体积分数 ${F_{\text{n}}}$ 的更新过程 Fig. 2 The updating process of Level-set function ${\phi _{\text{n}}}$ and the volume fraction ${F_{\text{n}}}$
 $\frac{{\partial \phi }}{{\partial {{t}}}} + \nabla \cdot \left( {u\phi } \right) = 0 ，$ (9)
 $\frac{{\partial F}}{{\partial {{t}}}} + \nabla \cdot \left( {uF} \right) = 0 。$ (10)

 图 1 多相流耦合系统 Fig. 1 Coupling system of multiphase flow
1.3 浸入边界方法

 $\varphi \left( x \right) = \sqrt {{{\left( {{{x - }}{{{x}}_0}} \right)}^2} + {{\left( {{{y - }}{{{y}}_0}} \right)}^2}} - {R_0} 。$ (11)

 $\frac{{\partial u}}{{\partial t}} + \nabla \cdot \left( {uu} \right) = - \nabla p + v{\nabla ^2}u + f ，$ (12)

 $\frac{{{u^{{{n + 1}}}} - {u^{{n}}}}}{{\Delta t}} = \nabla \cdot \left( {uu} \right) - \nabla p + v{\nabla ^2}u + {f^{{{n + 1}}}} ，$ (13)

 ${f^{{{n + 1}}}} = \frac{{{V^{{{n + 1}}}} - {u^{{n}}}}}{{\Delta t}} - \left( {\nabla \cdot \left( {uu} \right) - \nabla p + v{\nabla ^2}u} \right)。$ (14)

 图 3 基于Level-set函数和IB法的线性插值图 Fig. 3 The interpolation stencil for the Level-set function and IB method
 $\left( {{x_1},{y_1}} \right) = \left( {{x_0} - {n_{\text{x}}}{\varphi _0},{y_0} - {n_{\text{y}}}{\varphi _0}} \right)。$ (15)

 $\left\{ {\begin{array}{*{20}{c}} {\left[ {{x_2},{y_2}} \right] = \left[ {{x_0},{y_0} + {\text{sign}}\left( {{n_{\text{y}}}} \right) \cdot \Delta y} \right]}，\\ {\left[ {{x_3},{y_3}} \right] = \left[ {{x_0} + {\text{sign}}\left( {{n_{\text{x}}}} \right) \cdot \Delta x,{y_0}} \right]} 。\end{array}} \right.$ (16)

 ${u_{{\text{0i}}}} = {b_{\text{1}}} + {b_{\text{2}}}{x_{\text{0}}} + {b_{\text{3}}}{y_{\text{0}}} 。$ (17)

 $\left[ {\begin{array}{*{20}{c}} {{b_{\text{1}}}} \\ {{b_{\text{2}}}} \\ {{b_{\text{3}}}} \end{array}} \right] = {{\mathbf{A}}^{{{ - 1}}}}\left[ {\begin{array}{*{20}{c}} {{u_{{\text{1i}}}}} \\ {{u_{{\text{2i}}}}} \\ {{u_{{\text{3i}}}}} \end{array}} \right] = {\left[ {\begin{array}{*{20}{c}} {\text{1}}&{{x_{\text{1}}}}&{{y_{\text{1}}}} \\ {\text{1}}&{{x_{\text{2}}}}&{{y_{\text{2}}}} \\ {\text{1}}&{{x_{\text{3}}}}&{{y_{\text{3}}}} \end{array}} \right]^{{{ - 1}}}}\left[ {\begin{array}{*{20}{c}} {{u_{{\text{1i}}}}} \\ {{u_{{\text{2i}}}}} \\ {{u_{{\text{3i}}}}} \end{array}} \right]\left( {i = 1,2,3} \right)。$ (18)

2 海洋管道绕流研究

 图 4 不同雷诺数下海洋管道绕流的流场特征 Fig. 4 The flow field characteristics of marine pipe at different Reynolds numbers

3 海洋管道涡激振动研究

 图 5 海洋管道涡激振动算例 Fig. 5 The vortex vibration case of an ocean pipeline
 $\ddot y + 2\zeta \left( {\frac{2}{{{U_{red}}}}} \right)\dot y + {\left( {\frac{{2{\text{π}} }}{{{U_{red}}}}} \right)^2}y = \frac{1}{{2n}}{C_L}。$ (19)

 图 6 海洋管道最大位移和振动频率随雷诺数的变化情况 Fig. 6 The maximum displacement and vibration frequency of marine pipeline varied with Re numbers

 图 7 海洋管道的稳态位移 Fig. 7 Steady displacement of marine pipeline
4 海洋管道对波面影响分析

 图 8 海洋管道与自由波面算例示意图 Fig. 8 Schematic diagram of marine pipeline interacted with free surface

Fr数为1.2时，管道绕流对应自由波面变化的俯视图如图9所示，当Fr数分别为0.8，1.2和1.6时，管道对海洋波面影响的俯视图如图10所示。结果表明CLSVOF-IB数值算法能够较好捕捉海洋管道与流体自由界面的相互作用，计算多相流界面时有较高精度。

 图 9 海洋管道对波面影响波面变化图 Fig. 9 Effect of marine pipeline on wave surface

 图 10 不同Fr数海洋管道波面变化的俯视图 Fig. 10 Top view of wave surface of marine pipeline varied with Fr numbers
5 结　语

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