﻿ 水平圆柱体上波流力特征的数值模拟
 舰船科学技术  2021, Vol. 43 Issue (11): 27-32    DOI: 10.3404/j.issn.1672-7649.2021.11.005 PDF

Numerical simulation of the characteristics of wave-current forces on a horizontal cylinder
WANG Yan, WANG Shu-qi, WANG Kun-peng
School of Naval Architecture and Ocean Engineering, Jiangsu University of Science and Technology, Zhenjiang 212003, China
Abstract: In order to study the influence of wave -current on a horizontal cylinder, the wave-current force on the horizontal cylinder is studied in this paper. Firstly, the numerical model is verified and analyzed, and then the wave-current forces and the free surface deformation under different conditions are simulated.The results show that: For partially submerged horizontal cylinder, the wave reflection and blocking effects increase with the increase of wave amplitude, the wave-current forces increase with the increase of wave amplitude and vertical position, and the positive vertical force tends to a certain value with the increase of frequency. For the submerged horizontal cylinder, with the increase of depth, the wave reflection decreases and the wave reflection increases and is greater than the wave reflection.
Key words: horizontal cylinder     different amplitude     wave-current force
0 引　言

1 数值模型 1.1 控制方程

 $\frac{{\partial \rho {\mu _i}}}{{\partial {x_i}}} = 0{\text{，}}$ (1)
 $\frac{{\partial \rho {\mu _i}}}{{\partial t}} + \frac{{\partial p{\mu _i}{\mu _j}}}{{\partial {x_j}}} = - \frac{{\partial p}}{{\partial {x_i}}} + \mu \frac{\partial }{{\partial xj}}\left( {\frac{{\partial {\mu _i}}}{{\partial {x_j}}} + \frac{{\partial {\mu _j}}}{{\partial {x_i}}}} \right) + \rho g {\text{。}}$ (2)

1.2 自由液面处理方法

 $\alpha =\left\{\begin{array}{*{20}{c}}0{\text{，}}&\text{气相}{\text{，}}\\ 0\sim 1{\text{，}}&\text{自由表面}{\text{，}}\\ 1{\text{，}}&\text{液相}{\text{。}}\end{array} \right.$ (3)

 $\rho {\text{ = }}\alpha {\rho _w} + \left( {1 - \alpha } \right){\rho _a} {\text{，}}$ (4)
 $\mu {\text{ = }}\alpha {\mu _w} + \left( {1 - \alpha } \right){\mu _a}{\text{。}}$ (5)

1.3 边界条件

 图 1 数值波浪水槽的示意图 Fig. 1 Sketch of numerical wave flume
1.4 流体作用力

 $F = {F_p} + {F_\nu } = - \int {pn{\rm{d}}s + \int {\tau S{\rm{d}}s} } {\text{。}}$ (6)

2 数值验证

 图 2 数值水槽模拟的示意图 Fig. 2 The computation domain of water channel

 图 3 水平圆柱上的波流力 Fig. 3 Wave-current forces on a horizontal cylinder
 ${F_x}' = \frac{{{F_x}}}{\rho g\text{π} {D^2}l {\vphantom {{\rho g\text{π} {D^2}l} }}/4} {\text{，}}$ (7)
 ${F_z}' = \frac{{{F_z}}}{{{\rho g\text{π} {D^2}l {\vphantom {{\rho g\text{π} {D^2}l} }}}/4}}{\text{。}}$ (8)

3 数值计算与结果分析 3.1 算例设置和计算参数

3.2 网格收敛性验证

 图 4 不同网格下的圆柱水平波流力时间历程 Fig. 4 Time-series of horizontal wave-current forces on a cylinder with different mesh
3.3 数值结果与分析

3.3.1 波流与水平圆柱体相互作用时的自由表面变形

 图 5 不同波幅下圆柱上游2D与下游2D的时间历时曲线 Fig. 5 Time-series curves of 2D upstream and 2D downstream of cylinder under different wave amplitudes

 图 6 不同深度下圆柱上游2D与下游2D的时间历时曲线 Fig. 6 Time-series curves of 2D upstream and 2D downstream of cylinder under different wave amplitudes

 图 7 不同波幅下圆柱上游2D与下游2D处自由液面的傅里叶谱对比 Fig. 7 Comparison of Fourier spectra of free surface at 2D upstream and 2D downstream of cylinder under different wave amplitudes

 图 8 不同垂向位置下圆柱上游2D与下游2D处自由液面的傅里叶谱对比 Fig. 8 Comparison of Fourier spectrum of free surface at 2D upstream and 2D downstream of cylinder at different vertical positions
3.3.2 波流对水平圆柱的作用力分析

 图 9 波流力时间历程 Fig. 9 Time-series of wave-current force

 图 10 波流下的涡量场分布图 Fig. 10 Distribution of vorticity field under wave-current

 图 11 不同S/D下正向波流力随A/r的变化对比 Fig. 11 Comparison of forward wave-current force with A/r under different S/D

 图 12 不同S/D下负波流力随A/r的变化对比 Fig. 12 Comparison of negative wave-current force with A /r under different S/D

 图 13 不同A/r下正向波流力随频率的变化对比 Fig. 13 Comparison of forward wave-current force with frequencies at different A/r
4 结　语

1）在水平圆柱体部分淹没时，随着波幅的增加，波浪的反射与阻塞作用都在增加，但波浪反射大于阻塞作用；圆柱在完全淹没时，随着淹没深度的增加，波浪反射作用减小，阻塞作用增大且大于反射作用，所以波幅与垂向位置对于圆柱所受波流力的研究有着极大的影响。

2）水平圆柱所受的波流力随波幅的增大而增大，在部分浸没时，波流力随着波幅的增大，正负方向的力开始变得不对称起来，水平力正方向的大小逐渐大于负方向，负垂向力的大小逐渐大于正垂向力的数值，这主要受波浪反射和阻塞的影响。

3）随着波幅与垂向位置的改变，圆柱所受的波流力也呈现了一些规律。在部分淹没的情况下，随着波幅的增加和垂向位置的增加，水平波流力的大小在增加，垂向波流力的大小在减小；在完全淹没的情况下，水平波流力的大小在减小，正垂向波流力在增加，负垂向波流力的大小在减小，这是波浪的反射与阻塞共同作用下的结果。

4）在部分浸没下，随着频率的增加，水平圆柱所受的波流正向垂向力趋于平缓接近一个特定值。

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