﻿ 结构物入水砰击过程求解方法对比研究
 舰船科学技术  2022, Vol. 44 Issue (20): 7-14    DOI: 10.3404/j.issn.1672-7649.2022.20.002 PDF

Comparative study on solution method of water-entry slamming process of the structure
DONG Chuan-rui, MA Ao-jia, YU He, ZHU Hong-min, DING Guo-yuan
China Academy of Launch Vehicle Technology, Beijing 100076, China
Abstract: The water entry process of structure is involved in the process of spacecraft water recovery, amphibious aircraft water landing and ship navigation in high sea conditions. The slamming phenomenon in water entry process has always been one of key and hot basic studies in the development process of the above engineering projects. In this paper, three typical methods (numerical method, simulation method and test method) for solving the water entry slamming problem of structures are studied. The basic principles and engineering implementation methods of the three methods are introduced and their applicability is proved. Free-drop water entry slamming problem of wedge structures is solved and compared. The distribution characteristics of surface pressure on wedges, the time history characteristics of slamming pressure at typical measuring points, the structural acceleration characteristics and free surface changes during water entry are given. It has certain reference significance for the design of water entry structures, the formulation of load conditions and the selection of water entry parameters.
Key words: water-entry     slamming load     numerical simulation     free-drop model test
0 引　言

1 基于边界元算法的数值计算方法 1.1 数学模型

 图 1 典型结构入水问题示意图 Fig. 1 Schematic diagram of water entry problem

 ${\nabla ^{\text{2}}}\phi {\text{ = 0}}。$ (1)

 $\frac{{\partial \phi }}{{\partial n}} = - W{n_z} 。$ (2)

 $\frac{{\partial \zeta }}{{\partial t}} = {\phi _z} - {\phi _x}{\zeta _x} ，$ (3)
 $\frac{{\partial \phi }}{{\partial t}} = - \frac{1}{2}\left( {\phi _x^2 + \phi _z^2} \right) - gz 。$ (4)

 $\frac{{\partial \phi }}{{\partial n}} \to 0，\;\;\;\;\;\;\;\sqrt {{x^2} + {z^2}} \to \infty。$ (5)
1.2 拓展坐标系

 $\varphi = \phi /sW \text{，} \alpha = x/s , \beta = z/s , s = \int_{}^{} {W{\rm{d}}t}。$ (6)

 $\frac{{\partial \varphi }}{{\partial n}} = - W{n_\beta } 。$ (7)

 $\frac{{\partial s\overline \zeta }}{{\partial s}} = {\varphi _\beta } - {\varphi _\alpha }{\overline \zeta _\alpha } ，$ (8)
 $\frac{{\partial sW\varphi }}{{W\partial s}} = - \frac{1}{2}\left( {\varphi _\alpha ^2 + \varphi _\beta ^2} \right) - \frac{{gs\beta }}{{{W^2}}}。$ (9)

 $\frac{{\partial \varphi }}{{\partial n}} \to 0，\;\;\;\;\;\;\;\sqrt {{\alpha ^2} + {\beta ^2}} \to \infty。$ (10)
1.3 控制方程离散

 $A(p)\varphi (p) = \int {\left[ {G(p,q)\frac{{\partial \varphi (q)}}{{\partial {n_q}}} - \varphi (q)\frac{{\partial G(p,q)}}{{\partial {n_q}}}} \right]} {\rm{d}}{s_q}。$ (11)

 $G(p,q) = \frac{1}{2}\ln \left[ {{{\left( {{x_p} - {x_q}} \right)}^2} + {{\left( {{z_p} - {z_q}} \right)}^2}} \right]。$ (12)

 $\left[ {{{\boldsymbol{H}}}} \right]{}_{n' \times n'} \cdot {[\varphi ]_{n' \times {\text{1}}}}{\text{ = }}\left[ {{{\boldsymbol{G}}}} \right]{}_{n' \times n'} \cdot {[{\varphi _n}]_{n' \times {\text{1}}}} 。$ (13)

2 基于ALE算法的数值仿真方法 2.1 算法简介及基本控制方程

ALE算法是计算流固耦合问题时比较适用的算法之一，其综合吸收了2种算法的优势又规避了单一算法的劣势[26]

 $\frac{{\partial \rho }}{{\partial t}} = - \rho \frac{{\partial {v_i}}}{{\partial {x_i}}} - {w_i}\frac{{\partial \rho }}{{\partial {x_i}}}，$ (14)

 $\rho \frac{{\partial {v_i}}}{{\partial t}} = \frac{{\partial {\sigma _{ij}}}}{{\partial {x_j}}} + \rho {b_i} - \rho {w_i}\frac{{\partial {v_i}}}{{\partial {x_j}}}，$ (15)

 $\rho \frac{{\partial E}}{{\partial t}} = {\sigma _{ij}}\frac{{\partial {v_i}}}{{\partial {x_j}}} + \rho {b_i}{v_i} - \rho {w_j}\frac{{\partial E}}{{\partial {x_j}}}。$ (16)

2.2 软件计算流程

Ls-dyna提供了ALE算法平台，本文仿真使用MSC.PATRAN进行建模，使用LS-Prepost进行关键字修改、耦合定义及后处理，提交Ls-dyna求解器进行计算。

Ls-dyna中通过空材料加状态方程来描述水和空气2种流体材料的物理及力学特性[27]

 $P = [{C_0} + {C_1}\mu + {C_2}{\mu ^2} + {C_3}{\mu ^3}] + [{C_4} + {C_5}\mu + {C_6}{\mu ^2}] \cdot {\rho _0}e。$ (17)

 $\begin{split}\left\{\begin{array}{l}P=\dfrac{{\rho }_{0}{C}^{2}\mu [1+(1-\dfrac{{\gamma }_{0}}{2})\mu -\dfrac{a}{2}{\mu }^{2}]}{[1-({S}_{1}-1)\mu -{S}_{2}\dfrac{{\mu }^{2}}{\mu +1}-{S}_{3}\dfrac{{\mu }^{3}}{{(\mu +1)}^{2}}}+\\ \qquad({\gamma }_{0}+a\mu ){\rho }_{0}e，\quad\quad\quad\quad\quad\,\,\,压缩状态，\\ P={\rho }_{0}{C}^{2}\mu +({\gamma }_{0}+a\mu ){\rho }_{0}e，\quad\quad \,膨胀状态。\end{array} \right. \end{split}$ (18)

 图 2 典型结构物入水问题仿真模型 Fig. 2 Simulation model of water entry problem

3 落体砰击试验方法

 图 3 试验模型 Fig. 3 Test model
4 结果对比与分析

 图 4 砰击压力时历对比 Fig. 4 Comparison of slamming pressure history

 图 5 入水过程中速度及加速度对比 Fig. 5 Comparison of model velocity and acceleration history during water entry

 图 6 自由液面及物面压力分布 Fig. 6 Free surface and surface pressure distribution

 图 7 物面压力分布对比 Fig. 7 Comparison of surface pressure distribution

 图 8 Ls-dyna仿真与边界元法自由液面对比 Fig. 8 Free surface comparison between Ls-dyna simulation and BEM

 图 9 落体试验过程中射流发展情况 Fig. 9 Development of jet flow during free falling test

 图 10 典型时刻压力场及速度场仿真结果 Fig. 10 Simulation results of pressure field and velocity field at typical time
5 结　语

1） Ls-dyna仿真方法和边界元数值模拟方法均可对楔形结构入水砰击问题进行有效求解，通过与试验结果对比，验证了2种方法求解入水载荷及运动特性的精度。

2） Ls-dyna仿真方法和边界元数值方法均可有效模拟出楔形体结构入水后的自由液面变化情况，Ls-dyna可对流动分离、复杂形状结构入水等数值方法较难处理的问题给出满意的求解。

3） 底升角为45°的楔形结构入水过程中砰击载荷作用范围为楔形半宽<1.7倍入水深度的区域。

4） 随着入水深度的增加，射流根部逐渐“健壮”，表现在压力上是从下至上各测点取得峰值时处于静水平面之上的高度逐渐增大，但各测点压力峰值由于结构入水速度的降低会逐渐降低。

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