﻿ 基于体积力方法的船舶波浪回转运动数值仿真
 舰船科学技术  2022, Vol. 44 Issue (1): 39-45    DOI: 10.3404/j.issn.1672-7649.2022.01.008 PDF

1. 海军装备部驻武汉地区军事代表局，湖北 武汉430064;
2. 华中科技大学 船舶与海洋工程学院，湖北 武汉 430074

Numerical simulation of ship turning in wave based on body-force method
CAO Ge1, YU Jia-wei2, FENG Da-kui2, ZHANG Zhi-guo2, YAO Chao-bang2
1. Military Representative Bureau of the Department of Naval Equipment in Wuhan, Wuhan 430064, China;
2. School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
Abstract: It is very important for ship maneuverability to study the maneuvering motion of a free-running ship in waves. This paper presents the simulation studies of the turning motion in the regular wave of the full-appendage ONRT model. Numerical simulations are performed using viscous CFD code HUST-Ship to solve the RANS equation coupled with six degrees of freedom (6DOF) solid body motion equations and dynamic overset grids designed for ship hydrodynamics. RANS equations are discretized by finite difference method and solved by PISO algorithm. The moving domain method is adopted and the propeller is replaced by the iterative body-force method for the turning motion in wave to improve the computation efficiency. The simulated parameters of the turning trajectories in wave are compared with test data to verify the reliability of simulation. Furthermore, the motion characteristic parameters are analyzed to study the influence of waves on the turning motion in this paper.
Key words: maneuverability in wave     iterative body-force     dynamic overset grids     six degrees of freedom
0 引　言

1 数值方法和数学模型

1.1 改进体积力模型

RANS方程是通过对连续性方程和动量方程时均化得到：

 $\frac{{\partial {U_i}}}{{\partial {x_i}}} = 0 ，$
 $\frac{{\partial {U_i}}}{{\partial t}} + {U_j}\frac{{\partial {U_i}}}{{\partial {x_j}}} = - \frac{1}{\rho }\frac{{\partial P}}{{\partial {x_i}}} + \frac{1}{\rho }\frac{\partial }{{\partial {x_j}}}(\mu \frac{{\partial {U_i}}}{{\partial {x_j}}} - \rho \overline {u_i'u_j'} ) + {f_{bi}}。$

1.2 自由液面模拟方法

 $\frac{{\partial \varphi }}{{\partial t}} + v\nabla \varphi = 0 {。}$

1.3 坐标系与六自由度运动

HUST-Ship中船舶运动的求解涉及2个右手的笛卡尔坐标系分别为大地坐标系O-XYZ与船体坐标系OS-XSYSZS，如图1所示。为预报船舶运动姿态的变化，HUST-Ship中集成了六自由度运动模块，六自由度运动方程在船体坐标系下求解，船体的平动和转动在大地坐标系下表示，船体的速度、加速度以及所受力和力矩在船体坐标系中表达。根据刚体动力学与动量矩定理，船舶六自由度运动方程[10]可表示为：

 ${m[\dot u - vr + wq] = X}，$
 ${{m[\dot v - wp + ur] = Y}}，$
 ${{m[\dot w - uq + vp] = Z}}，$
 ${{{I}}_x}{{\dot p + [}}{{{I}}_z}- {{{I}}_y}{{]qr = K}}，$
 ${{{I}}_{{y}}}{{\dot q + [}}{{{I}}_x} - {{{I}}_z}{{]rp = M}}，$
 ${{{I}}_{{z}}}{{\dot r + [}}{{{I}}_y} - {{{I}}_x}{{]pq = N}} 。$

 图 1 六自由度参考系 Fig. 1 6DOF Coordinate system
1.4 数值造波[20]

HUST-Ship中使用速度边界造波方法产生目标波浪。当仿真的目标波浪波长为 $\lambda$ ，波高为 $A$ 时，其入口处的自由液面变化为：

 ${{\eta (t) = A{\rm{cos}}(kx - \omega t + \varphi )}}，$

 ${{u = A\omega }}\frac{{{{{\rm{cos}}hk(z + d)}}}}{{{{{\rm{sin}}hkd}}}}{{{\rm{cos}}(kx - \omega t + \varphi )}} ，$
 ${{w = A\omega }}\frac{{{{{\rm{sin}}hk(z + d)}}}}{{{{{\rm{sin}}hkd}}}}{{{\rm{sin}}(kx - \omega t + \varphi )}} 。$

 图 2 规则波仿真结果 Fig. 2 Regular wave simulation result
2 研究对象与计算域 2.1 研究对象

2.2 网格划分

 图 3 全附体ONRT网格 Fig. 3 Full-appendage ONRT grids
2.3 计算域与边界条件

 图 4 移动计算域 Fig. 4 Moving domains

 图 5 计算域与边界条件 Fig. 5 Computational domain and boundary conditions
3 结果与分析

3.1 静水自航转速匹配

HUST-Ship中，比例积分速度控制器(PI speed controller)[12]用于在静水自航仿真时匹配对应目标航速的螺旋桨转速：

 ${{n = p(}}{{{U}}_{t{\rm{arg}} et}} - {{{U}}_{{\rm{ship}}}}{{) + I}}\int {{{(}}{{{U}}_{t{\rm{arg}} et}}-{{{U}}_{{\rm{ship}}}}{\text{)}}{\rm{dt}}}。$

 图 6 航速和螺旋桨转速匹配过程 Fig. 6 Ship speed and propeller rotational speed variations
3.2 定转速波浪自航仿真

 图 7 迎浪自航航速，垂荡和纵摇对比 Fig. 7 Comparisons of ship speed, heave and pitch in regular wave

3.3 波浪回转仿真结果

 图 8 规则波中ONRT回转轨迹 Fig. 8 ONRT turning trajectory in regular wave

ONRT波浪回转过程中的六自由度运动如图9所示。可以发现，首向角为300°时横摇角幅值最大，达到9.5°，而纵摇运动幅值最小时船模处于横浪状态，当垂荡运动幅值小幅波动时ONRT遭遇随浪。另外，由于规则波具有周期性，导致垂荡、横摇、纵摇运动的时历曲线有显著波频振荡特性，但在XY面的平动如纵荡、横荡、首摇没有展现大的波频特性，该特征与前人研究一致[9]，进一步证明了计算结果的可靠性。如图10所示，ONRT波浪回转过程中航速和首摇角速度变化与试验结果的整体趋势一致，波动频率与试验吻合，波动幅值会稍有不同。

 图 9 ONRT波浪回转六自由度运动变化 Fig. 9 6DOF motions for ONRT turning in regular wave

 图 10 ONRT波浪回转航速与首向角速度变化 Fig. 10 Ship speed and yaw rate variations for ONRT turning in regular wave

 图 11 ONRT波浪回转舵力变化 Fig. 11 Rudder forces for ONRT turning in regular wave
4 结　语

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