# 基于HUST-Ship的方波数值造波方法研究 Numerical Studies of Square Wave Generation Using HUST-Ship

DOI: 10.12677/AMS.2020.74016, PDF, HTML, XML, 下载: 113  浏览: 484

Abstract: When two waves in different directions meet due to different weather patterns, a cross wave pattern will be generated, which will finally result in the spread of square waves on the sea surface. The emergence of square waves will threaten the navigation performance of the ship and may lead to ship capsized in severe case. In this paper, the numerical square wave flume is developed by using the in-house CFD software HUST-Ship. In the process of data simulation, by means of solving the RANS equation of incompressible fluid, the analytical solution of the corresponding regular wave is imposed at the inlet boundary, and the free surface is captured by level-set method. Two regular waves with a cross angle of 90 degrees and the same wavelength and phase are superimposed. The probe is used to deal with the simulation results and trace the selected points to obtain the relative errors between the simulation results and the analytical solutions. Moreover, error analysis is used to ensure the accuracy of the numerical tank.

1. 引言

2. 流体控制方程和数值方法

2.1. 控制方程

HUST-Ship采用有限差分法对URANS方程进行离散，采用水平集法对自由液面进行捕获。不可压缩连续方程和RANS方程如下：

$\frac{\partial {u}_{i}}{\partial {x}_{i}}=0$ (1)

$\frac{\partial \stackrel{¯}{{u}_{i}{u}_{j}}}{\partial {x}_{j}}=-\frac{1}{\rho }\frac{\partial p}{\partial {x}_{i}}+\frac{\partial }{\partial {x}_{j}}\left[\gamma \left(\frac{\partial \stackrel{¯}{{u}_{i}}}{\partial {x}_{j}}+\frac{\partial \stackrel{¯}{{u}_{j}}}{\partial {x}_{i}}\right)\right]-\frac{\partial \left(-\stackrel{¯}{{{u}^{\prime }}_{i}{{u}^{\prime }}_{j}}\right)}{\partial {x}_{j}}+{f}_{i}$ (2)

$\frac{\partial \phi }{\partial t}+v\nabla \phi =0$ (3)

$\nabla v\cdot {n}_{j}=0,\text{\hspace{0.17em}}\text{\hspace{0.17em}}{n}_{j}=\frac{\partial \phi /\partial {x}_{i}}{|\partial \phi /\partial {x}_{i}|}$ (4)

2.2. 造波与消波的方法

$\eta \left(t\right)=A\mathrm{cos}\left(kx-\omega t+\phi \right)$ (5)

$u=A\omega \frac{\mathrm{cosh}k\left(z+d\right)}{\mathrm{sinh}kd}\mathrm{sin}\left(kx-\omega t+\phi \right)$ (6)

$w=A\omega \frac{\mathrm{sinh}k\left(z+d\right)}{\mathrm{sinh}kd}\mathrm{sin}\left(kx-\omega t+\phi \right)$ (7)

$\frac{\partial u}{\partial t}+u\frac{\partial u}{\partial x}+v\frac{\partial u}{\partial y}={g}_{x}-\frac{1}{\rho }\frac{\partial p}{\partial x}+v\left[\frac{{\partial }^{2}u}{\partial {x}^{2}}+\frac{{\partial }^{2}u}{\partial {y}^{2}}\right]-\mu \left(x\right)u$ (8)

$\frac{\partial v}{\partial t}+u\frac{\partial v}{\partial x}+v\frac{\partial v}{\partial y}={g}_{y}-\frac{1}{\rho }\frac{\partial p}{\partial y}+v\left[\frac{{\partial }^{2}v}{\partial {x}^{2}}+\frac{{\partial }^{2}v}{\partial {y}^{2}}\right]-\mu \left(x\right)v$ (9)

$\mu \left(x\right)=\left\{\begin{array}{l}{a}_{s}\left(x-{x}_{0}\right)/{L}_{s}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}x>{x}_{0}\\ 0\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}\text{\hspace{0.17em}}x\le {x}_{0}\end{array}$ (10)

${x}_{0}$ 为消波开始起作用的位置； ${L}_{s}$ 为阻尼层总长度； ${a}_{s}$ 为消波的强度。消波强度是一个经验值。值越大，消波强度越大。但是，如果这个值太大，可能会产生负面影响，导致更严重的反射波。因此，有必要选择一个合理的消波强度值，以获得更好的模拟结果。

3. 数值波浪水池

4. 方波数值造波和误差分析

Figure 1. Dimension of the computation domain

Figure 2. Boundary condition

Figure 3. Grid distribution

Figure 4. Numerical results of square wave

Figure 5. Analytical results of square wave

$x=0.02\mathrm{cos}\left(5.461x-13.884t\right)+0.02\left(-5.461y-13.884t\right)$ (11)

Figure 6. Monitor points of wave amplitudes in computational domain

Figure 7. Comparison of wave amplitude between numerical and analytical results at point 1

Figure 8. Comparison of wave amplitude difference between numerical and analytical results at point 1

Figure 9. Comparison of wave amplitude between numerical and analytical results at point 2

Figure 10. Comparison of wave amplitude difference between numerical and analytical results at point 2

Figure 11. Comparison of wave amplitude between numerical and analytical results at point 3

Figure 12. Comparison of wave amplitude difference between numerical and analytical results at point 3

Figure 13. Comparison of wave amplitude between numerical and analytical results at point 4

Figure 14. Comparison of wave amplitude difference between numerical and analytical results at point 4

5. 结论

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