﻿ 基于OpenFOAM的楔形体入水问题研究
 舰船科学技术  2022, Vol. 44 Issue (19): 12-17    DOI: 10.3404/j.issn.1672-7649.2022.19.003 PDF

Research on water entry of wedge bodies based on OpenFOAM
WEI Shan-shan, SUN Shi-yan
School of Naval Architecture and Ocean Engineering, Jiangsu University of Science and Technology, Zhenjiang 212100, China
Abstract: The water entry problem of a two dimensional wedge and double-wedge at different deadrise angles with gravity effect is investigated in the present paper. The CFD numerical model is established based on viscous flow theory through OpenFOAM software. The finite volume method (FVM) is used to discretize the governing equations set consisting of the average Reynolds equation and the continuity equation. The volume of fluid method (VOF) is used to capture the gas-liquid two-phase intersection. Comparisons of the pressure distribution on the body surface and the free surface profile with those through boundary element method in potential flow theory are undertaken. The conclusions includes: The gravity and deadrise angle will both exert noticeable effects on the results, it takes time for the gravity to become prominent, and the pressure of double-wedge is larger than that of single wedge at the same deadrise angle.
Key words: OpenFOAM     double wedges     viscous flow theory     gavity effect     water entry
0 引　言

Zhao和Ma等[1-2]研究了无重力影响时二维楔形体压力分布的峰值位置，表明底升角大约大于40°时峰值位置由射流根部转移到楔形体尖端。Chen[3]建立的二维直升机V形浮标的数值模拟结果也验证了Zhao和Ma等[2]的结论。陈震[4]表明二维楔形体入水压力峰值的传播速度随着入水角度的增大而减小。张健[5]、王玲等[6]、Chen[7]和陈光茂等[8]分别对二维楔形体的入水砰击问题进行仿真分析，研究压力峰值与底升角、入水角度和入水速度的关系。Ma[9]模拟了二维楔体垂直和斜入的入水和水动力冲击过程。Wu等[10]表明有限高度非对称二维楔形体斜入水速度增大时，一段较长时间内的重力效应可以忽略。Sun等[11]首次分析了二维楔形体在波浪中的入水过程，并研究了重力对楔形体入水过程和物面压力分布的影响。陈翔等[12]表明了楔形体入水底升角越小流体沿物面爬升速度越快，射流越明显。Zhang等[13]表明对称楔形体入水过程中两侧受到的压力也是对称的。

1 数值过程

 $\nabla \cdot u = 0 \text{，}$ (1)

 $\dfrac{{\partial {\boldsymbol{u}}}}{{\partial t}} + \left( {{\boldsymbol{u}} \cdot \nabla } \right){\boldsymbol{u}} = - \frac{{\nabla p}}{\rho } + \nu {\nabla ^2}{\boldsymbol{u}} + {\boldsymbol{F}} \text{。}$ (2)

 $\rho = \alpha {\rho _{{\text{water}}}} + \left( {1 - \alpha } \right){\rho _{{\text{air}}}} \text{，}$ (3)
 $\left\{\begin{array}{l}\alpha =\text{0}\text{，}空气 \text{，} \\ \text{0} \lt \alpha \lt 1\text{，}自由表面 \text{，} \\ \alpha =\text{1}\text{，}水 \text{。} \end{array} \right.$ (4)

 $\frac{\partial }{{\partial t}}\left( {\rho k} \right) + \frac{\partial }{{\partial {x_i}}}\left( {\rho k\overline {{u_i}} } \right) = \frac{\partial }{{\partial {x_j}}}\left( {{\Gamma _k}\frac{{\partial k}}{{\partial {x_j}}}} \right) + {G_k} - {Y_k} + {S_k} \text{，}$ (5)
 $\frac{\partial }{{\partial t}}\left( {\rho \omega } \right) + \frac{\partial }{{\partial {x_j}}}\left( {\rho \omega \overline {{u_j}} } \right) = \frac{\partial }{{\partial {x_j}}}\left( {{\Gamma _\omega }\frac{{\partial \omega }}{{\partial {x_j}}}} \right) + {G_\omega } - {Y_\omega } + {D_\omega } + {S_\omega } \text{。}$ (6)

2 数值结果分析 2.1 物理模型和网格划分

 图 1 坐标原点和边界条件示意图 Fig. 1 Sketch of the origin of coordinates and boundary conditions

 图 2 计算域示意图图 Fig. 2 Sketch of the computational domain

 图 3 楔形体周边网格示意图 Fig. 3 Sketch of the grid surrounding the wedge
2.2 数值结果分析

2.2.1 45°底升角单楔形体入水

$\gamma = {\text{4}}5^\circ$ 单楔形体不同工况下的结果如图4图6所示。其中图4（d）和图5（d）给出了无量纲自由液面形状，图6的相似解引自Sun等[11]的基于势流理论的45°底升角无限高度楔形体匀速入水时的压力分布曲线。

 图 4 45°楔形体3 m/s入水自由液面形状 Fig. 4 The free surface profile of 45° wedge with 3 m/s

 图 5 45°楔形体6 m/s入水自由液面形状 Fig. 5 The free surface profile of 45° wedge with 6 m/s

 图 6 重力影响下45°楔形体表面压力分布 Fig. 6 The pressure on the 45° wedge surface with the gravity effect

2.2.2 30°底升角单楔形体入水

$\gamma = {\text{30}}^\circ$ 单楔形体不同工况下的结构如图7图9所示。其中图7（d）和图8（d）给出了无量纲自由液面形状，图9的相似解引自许国冬[14]的基于势流理论的30°底升角无限高度楔形体匀速入水时的压力分布曲线。

 图 7 30°楔形体3 m/s入水自由液面形状 Fig. 7 The free surface profile of 30° wedge with 3 m/s

 图 8 30°楔形体6 m/s入水自由液面形状 Fig. 8 The free surface profile of 30° wedge with 6 m/s

 图 9 重力影响下30°楔形体表面压力分布 Fig. 9 The pressure on the 30° wedge surface with the gravity effect

2.2.3 双楔形体以给定速度入水的数值结果分析

 图 10 双楔形体模型坐标原点和边界条件示意图 Fig. 10 Sketch of the origin of coordinates and boundary conditions of the double wedges

$\gamma = {\text{4}}5^\circ$ 双楔形体不同工况下的结果如图11图14所示。其中图13图14分别引入图6与之对应的单楔形体数值结果。

 图 11 45°双楔形体3 m/s入水自由液面形状 Fig. 11 The free surface profile of 45° double wedges with 3 m/s

 图 13 3 m/s匀速入水45°双楔形体表面压力分布 Fig. 13 The pressure on the 45° double wedges surface of entry with constant velocity 3 m/s

 图 14 6 m/s匀速入水45°双楔形体表面压力分布 Fig. 14 The pressure on the 45° double wedges surface of entry with constant velocity 6 m/s

 图 12 45°双楔形体6 m/s入水自由液面形状 Fig. 12 The free surface profile of 45° double wedges with 6 m/s

$\gamma = 30^\circ$ 双楔形体不同工况下的结果如图15图18所示。其中图17图18分别引入图9与之对应的单楔形体数值结果进行对比。

 图 15 30°双楔形体3 m/s入水自由液面形状 Fig. 15 The free surface profile of 30° double wedges with 3 m/s

 图 17 3 m/s匀速入水30°双楔形体表面压力分布 Fig. 17 The pressure on the 30° double wedges surface of entry with constant velocity 3 m/s

 图 18 6 m/s匀速入水30°双楔形体表面压力分布 Fig. 18 The pressure on the 30° double wedges surface of entry with constant velocity 6 m/s

 图 16 30°双楔形体6 m/s入水自由液面形状 Fig. 16 The free surface profile of 30° double wedges with 6 m/s
3 结　语

1）当入水时间较短时，不同时刻的无量纲自由液面曲线基本重合，随着时间的增加，射流从物体顶部分离，自由射流在重力作用下发生弯曲向下的现象。

2）当入水时间较短时，排除初始阶段的不准确压力，不同时刻的物面无量纲压力曲线是基本重合的，并且与基于势流理论的自相似解非常接近，随着时间的增加，重力的作用变得显著，压力在重力作用下降低。

3）在相同入水速度和相同底升角条件下，双楔形体物面压力大于单楔形体物面压力，并且在砰击发生的短暂时间范围内，刚开始影响不大，从某一时刻开始，受一个楔形体扰动的流体到达相邻楔形体以后，相邻楔形体压力差值瞬间变得显著。此外，若提升速度，被楔形体扰动的流体速度加快，相邻楔形体受到的压力影响更大。

4）当降低楔形体底升角时，相当于增加楔形体周围被扰动的流体速度，因此相邻楔形体受到的压力也提升的更快。

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