International Journal of Fluid Dynamics
Vol. 06  No. 04 ( 2018 ), Article ID: 28090 , 11 pages
10.12677/IJFD.2018.64020

Numerical Simulation of Internal Solitary Waves Based on Fluent and Dynamic Response Analysis of Top Tension Risers

Hui Han1, Xiaomin Li1*, Fei Wang2, Haiyan Guo1

1College of Engineering, Ocean University of China, Qingdao Shandong

2College of Civil Engineering and Architecture, Shandong University of Science and Technology, Qingdao Shandong

Received: Nov. 27th, 2018; accepted: Dec. 12th, 2018; published: Dec. 19th, 2018

ABSTRACT

In this paper, a numerical flume of internal solitary wave with various design amplitudes is established based on the Fluent software. The internal solitary wave is simulated by mass source wave-generating method and the simulation results are compared with the physical experiment and theoretical results. The data of wave-induced flow field are obtained by monitoring function of the software. Combined with the modified Morison equation, the effect of internal solitary wave on the top tension riser is calculated, and its dynamic response is analyzed by finite element method. The results indicate that the mass source wave-generating method adopted in this paper is in good agreement with the experimental and theoretical results. Under the large amplitude internal solitary wave, the horizontal force of internal solitary wave on the riser in the upper fluid is obviously greater than that on the riser in the lower fluid. The riser under the action of internal solitary wave will undergo large deformation and produce large stress. When the valley reaches the riser, the stress and deformation reach the maximum.

Keywords:Internal Solitary Wave, Numerical Simulation, Top Tensioned Riser, Dynamic Response

1中国海洋大学工程学院，山东 青岛

2山东科技大学土木工程与建筑学院，山东 青岛

1. 引言

2. 造波理论与方法

2.1. 理论模型

Figure 1. Sketch of theoretical models for internal solitary waves

$\eta \left(x,t\right)={\eta }_{0}\mathrm{sec}{h}^{2}\left(\frac{x-ct}{l}\right)$

$\begin{array}{l}c={c}_{0}+\frac{{c}_{1}}{3}{\eta }_{0}\\ l=\sqrt{\frac{12{c}_{2}}{{c}_{1}{\eta }_{0}}}\\ {c}_{0}=\sqrt{\frac{g{h}_{1}{h}_{2}\left({\rho }_{2}-{\rho }_{1}\right)}{{\rho }_{1}{h}_{2}+{\rho }_{2}{h}_{1}}}\\ {c}_{1}=-\frac{3{c}_{0}}{2}\frac{{\rho }_{1}{h}_{2}^{2}-{\rho }_{2}{h}_{1}^{2}}{{\rho }_{1}{h}_{1}{h}_{2}^{2}+{\rho }_{2}{h}_{2}{h}_{1}^{2}}\\ {c}_{2}=\frac{{c}_{0}}{6}\frac{{\rho }_{1}{h}_{2}{h}_{1}^{2}+{\rho }_{2}{h}_{1}{h}_{2}^{2}}{{\rho }_{1}{h}_{2}+{\rho }_{2}{h}_{1}}\end{array}$

$\eta \left(x,t\right)=\frac{{\eta }_{0}}{B+\left(1-B\right){\mathrm{cosh}}^{2}\left(\frac{x-{c}_{e}t}{{l}_{e}}\right)}$

$\begin{array}{l}{c}_{e}={c}_{0}+\frac{{\eta }_{0}}{3}\left({c}_{1}+\frac{1}{2}{c}_{3}{\eta }_{0}\right)\\ {l}_{e}=\sqrt{\frac{12{c}_{2}}{\left({c}_{1}+\frac{1}{2}{c}_{3}{\eta }_{0}\right){\eta }_{0}}}\\ B=\frac{-{c}_{3}{\eta }_{0}}{2{c}_{1}+{c}_{3}{\eta }_{0}}\end{array}$

2.2. 造波方法

Figure 2. Sketch of the mass source wave-generating method

$\begin{array}{l}\frac{\partial \rho }{\partial t}+\frac{\partial \left(\rho {u}_{i}\right)}{\partial {x}_{i}}=S\left(x,z,t\right)\\ \frac{\partial \left(\rho {u}_{i}\right)}{\partial t}+\frac{\partial \left(\rho {u}_{i}{u}_{j}\right)}{\partial {x}_{j}}=\frac{\partial }{\partial {x}_{j}}\left[\mu \frac{\partial {u}_{i}}{\partial {x}_{j}}\right]-\frac{\partial {p}_{i}}{\partial x}+\rho {g}_{i}\end{array}$

$\underset{0}{\overset{t}{\int }}{\int }_{S1}{S}_{1}\left(x,z,t\right)\text{d}{S}_{1}\text{d}t=-{\rho }_{1}\underset{0}{\overset{t}{\int }}c\eta \left(t\right)\text{d}t$

$\underset{0}{\overset{t}{\int }}{\int }_{S2}{S}_{2}\left(x,z,t\right)\text{d}{S}_{2}\text{d}t={\rho }_{2}\underset{0}{\overset{t}{\int }}c\eta \left(t\right)\text{d}t$

${S}_{1}\left(t\right)=-\frac{{\rho }_{1}c\eta \left(t\right)}{{A}_{1}}$

${S}_{2}\left(t\right)=\frac{{\rho }_{2}c\eta \left(t\right)}{{A}_{2}}$

3. 模型建立与验证

3.1. 数值水槽的建立

3.2. Fluent设置

UDF设置：利用Fluent中的DEFINE_SOURCE宏编写理论UDF，将源项添加到造波源区域，嵌入到造波区控制方程中。

3.3. 数值造波模拟结果及分析

Table 1. Setting of numerical simulation condition

Figure 3. Comparison of numerical waveform with experimental and theoretical results

4. 大振幅内波下立管的动力响应

4.1. 模型验证

Table 2. Parameters of internal solitary wave

Figure 4. Comparison of numerical waveform with theoretical results

4.2. 结果与分析

Table 3. Parameters of top tension riser

${f}_{x}=\frac{1}{2}{C}_{D}\rho D\left(U-\stackrel{˙}{x}\right)|U-\stackrel{˙}{x}|+{C}_{M}\rho \frac{\text{π}{D}^{2}}{4}\left(\stackrel{˙}{U}-\stackrel{¨}{x}\right)$

Figure 5. Displacements of riser at different moments

Figure 6. Stresses of the riser at different moments

Figure 7. Time-histories of displacement for nodes in different depth

Figure 8. Displacement of riser with trough arrives

Figure 9. Stresses of riser with trough arrives

5. 结论

Numerical Simulation of Internal Solitary Waves Based on Fluent and Dynamic Response Analysis of Top Tension Risers[J]. 流体动力学, 2018, 06(04): 158-168. https://doi.org/10.12677/IJFD.2018.64020

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14. NOTES

*通讯作者。