﻿ 光滑深海立管涡激振动DES模拟
 舰船科学技术  2016, Vol. 38 Issue (3): 128-133 PDF

1. 北京信息科技大学计算机学院, 北京 100101;
2. 北京信息科技大学网络文化与数字传播北京市重点实验室, 北京 100101

Numerical Simulation of Vortex Induced Vibration on Smooth Marine Riser Using DES Model
ZHU Min-ling1, 2, LV Xue-qiang2
1. School of Computer Science, Beijing Information Science and Technology University, Beijing 100101, China;
2. Beijing Key Laboratory of Internet Culture and Digital Dissemination Research, Beijing Information Science and Technology University, Beijing 100101, China
Abstract: DES (Detached Eddy Simulation) method was used to simulate vortex induced vibration of smooth marine riser. The height of first layer of the grid and Grid-independent solution and time step-independence solution is obtained. The lift coefficient, the drag coefficient, Strouhal number (St) and other results agree well with experimental data and other numerical results. The results show that, DES method based on SST k-ω turbulence model is credible and valid to simulate vortex induced vibration of smooth marine riser; the requirement of the first layer of the grid can be satisfied by 0.5Δy1.
Key words: DES    Marine riser    Vortex induced vibration    Grid    Time step
0 引言

1 数值模型建立 1.1 N-S 方程

 $\frac{{\partial {u_i}}}{{\partial {x_i}}} = 0,$ (1)
 $\frac{{\partial {u_i}}}{{\partial t}} + \frac{{\partial \left( {{u_i}{u_j}} \right)}}{{\partial {x_j}}} = - \frac{1}{\rho }\frac{{\partial p}}{{\partial {x_i}}} + \nu \frac{{{\partial ^2}{u_i}}}{{\partial {x_i}\partial {x_j}}},$ (2)

1.2 Menter k-ω SST 两方程湍流模式
 $\begin{array}{*{20}{l}} {\frac{{\partial \left( {\rho k} \right)}}{{\partial t}} + {u_i}\frac{{\partial \left( {\rho k} \right)}}{{\partial {x_i}}} = \;{P_k} - \frac{{\rho {k^{3/2}}}}{{{l_{k - \omega }}}} + \frac{\partial }{{\partial {x_i}}}\left[ {\left[ {{\mu _l} + \frac{{{\mu _l}}}{{{\sigma _k}}}} \right]\frac{{\partial k}}{{\partial {x_i}}}} \right],} \end{array}$ (3)
 $\begin{array}{*{20}{l}} {\frac{{\partial \left( {\rho \omega } \right)}}{{\partial t}} + {u_i}\frac{{\partial \left( {\rho \omega } \right)}}{{\partial {x_i}}} = {C_\omega }{P_\omega } - {\beta _\omega }\rho {\omega ^2} + \;\frac{\partial }{{\partial {x_i}}}\left[ {\left[ {{\mu _l} + \frac{{{\mu _l}}}{{{\sigma _k}}}} \right]\frac{{\partial k}}{{\partial {x_i}}}} \right] + \;2\rho \left( {1 - {F_1}} \right)\frac{1}{\omega }{\sigma _{{\omega ^2}}}\frac{{\partial k}}{{\partial {x_i}}}\frac{{\partial \omega }}{{\partial {x_i}}}.} \end{array}$ (4)

 ${\mu _l} = \min \left[{\frac{{\rho k}}{\omega },\frac{{{a_1}\rho k}}{{\Omega {F_2}}}} \right],$ (5)

 ${l_{k - \omega }} = \frac{{{k^{1/2}}}}{{{\beta _k}\omega }},$ (6)
F1F2为混合函数，PkPw为湍流生成项，具体定义根据参考文献[7]给出。

1.3 DES 方法

DES 方法用长度尺度替代 k- SST 中长度尺度，从而使得计算区域在附面层使用 k- SST 模型，在主流分离区域使用大涡模拟模型。

 $l = min\left[{{l_{k - \omega }},{C_{{\text{DES}}}}\Delta } \right],$ (7)

2 研究对象与数值方法 2.1 计算域及其离散

 图 1 计算域示意图 Fig. 1 Fluid computational domain

 图 2 离散网格及放大图 Fig. 2 Mesh and its local magnification
2.2 数值方法与边界条件

3 结果及分析 3.1 网格第一层高度对结果影响

 ${y^ + } = 0.172\frac{{\Delta y}}{D}{\text{ }}R{e^{0.9}},$ (8)

NASA 粘性网格厚度计算器[12]也可估算网格第一层高度。NASA 粘性网格厚度计算器是基于空气介质在平板湍流中按照 Sutherland’s law[13] 来计算空气粘性厚度，估算Δy。本文中，按 NASA 粘性网格厚度计算器估算得到的第一层网格高度称为Δy2。计算得到Δy1 > Δy2

 图 3 Re = 200 计算结果随网格第一层高度变化规律 Fig. 3 Calculated results of different Δy when Re = 200

3.2 网格数量对结果影响

 图 4 阻力系数时均值随网格数变化规律 Fig. 4 Drag coefficient of different meshes
 图 5 升力系数幅值随网格数变化规律 Fig. 5 lift coefficient of different meshes
 图 6 斯特罗哈尔数随网格数变化规律 Fig. 6 Strouhal number of different meshes
3.3 时间步长对结果影响

 图 7 阻力系数时均值随时间步长变化规律 Fig. 7 Drag coefficient of different time steps
 图 8 升力系数幅值随时间步长变化规律 Fig. 8 Lift coefficient of different time steps
 图 9 斯特罗哈尔数随时间步长变化规律 Fig. 9 Strouhal number of different time steps

3.4 Re = 200 结果

 图 10 Re = 200 瞬时流场等值线云图 Fig. 10 Transient contours when Re = 200
 图 11 Re = 200 阻力时程曲线 Fig. 11 Drag coefficient vs time when Re = 200
 图 12 Re = 200 升力时程曲线 Fig. 12 Lift coefficient vs time when Re = 200
4 结语

1）基于 SST k-ω 湍流模型的 DES 方法模拟低雷诺数圆柱绕流涡激振动结果合理；

2）随着网格第一层高度Δy 的减小，y+降低。按 0.5Δy1 确定 DES 方法的第一层网格高度可得到满足要求的；

3）增加网格数量可使计算结果更接近实验结果，但网格数量到一定程度后再增加对结果改善不明显。本文中 80.0 万网格结果最优；

4）减小时间步长可提高计算精度，需针对不同对象进行时间步长无关解研究。

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