﻿ 横摇-垂荡复合激励下液舱晃荡的压力特性研究
 舰船科学技术  2022, Vol. 44 Issue (19): 22-27    DOI: 10.3404/j.issn.1672-7649.2022.19.005 PDF

1. 江苏海洋大学 海洋工程学院，江苏 连云港 222005;
2. 江苏省海洋资源开发研究院，江苏 连云港 222005

Pressure characteristics of liquid sloshing under roll-heave compound excitation
ZHANG Hui-xia1,2, LI Shi1, ZOU Chang-fang1,2
1. School of Ocean Engineering, Jiangsu Ocean University, Lianyungang 222005, China;
2. Jiangsu Institute of Marine Resources Development, Lianyungang 222005, China
Abstract: The multiphase flow model based on VOF method is used to study the two degree of freedom sloshing of two-dimensional rectangular tank under the compound excitation of roll and heave. Contrasting analysis of the sloshing pressure characteristics under roll excitation alone and roll-heave compound excitation. The results show that the sloshing pressure curve under compound excitation has multiple periodic forms, and the addition of heave excitation has an amplifying effect on the sloshing pressure, but this effect is not obvious when the two excitation frequencies are similar. Fourier analysis is made on the pressure curve of compound excitation, count the amplitude changes of four main frequencies: roll frequency, heave frequency and their sum and difference. It is found that with the increase of heave frequency, the influence of roll frequency on sloshing pressure gradually decreases, while the other three frequencies become more influential to the pressure.
Key words: sloshing     compound excitation     pressure time domain characteristics     pressure frequency domain characteristics
0 引　言

1 无关性分析

 图 1 液舱模型尺寸与横摇参数(m) Fig. 1 Tank size and rolling parameters (m)

 图 2 不同网格数量下晃荡压力计算结果 Fig. 2 Calculation results of sloshing pressure under different grid numbers
2 横摇激励下晃荡压力特点

 $f_n=\frac{1}{2{\text{π}}} \sqrt{g\frac{n {\text{π}}}{L}tanh \left(\frac{n {\text{π}}}{L}H\right)}。$ (1)

 $\omega =A_I \cos 2{\text{π}} f_rt。$ (2)

 $A_I=\frac{2{\text{π}}^2 f_r}{15} 。$ (3)

 图 3 25%H横摇激励晃荡压力随频率分布特点 Fig. 3 Distribution characteristics of sloshing pressure with rolling excitation under 25%H

 图 4 fr=0.81 Hz点P处压力时程曲线 Fig. 4 Pressure time history curve at point P with fr = 0.81 Hz
3 复合激励下液舱晃荡压力特点

 $V=A_2\sin 2 {\text{π}} f_ht ，$ (4)

 $A_2=0.1{\text{π}} f_h。$ (5)

3.1 数值模型验证

 图 5 数值模拟垂荡激励下自由液面变化 Fig. 5 Numerical simulation of free surface change under heaving excitation

 图 6 Constantin L垂荡激励实验自由液面变化 Fig. 6 Free surface change in Constantin L heaving excitation experiment
3.2 复合激励下晃荡压力时域特征

 图 7 工况1~工况9晃荡特征 Fig. 7 Sloshing characteristics under conditions 1~9

 图 8 工况19~工况27晃荡特征 Fig. 8 Sloshing characteristics under conditions 19~27

 图 9 工况37~工况45晃荡特征 Fig. 9 Sloshing characteristics under conditions 37~45

3.3 复合激励下晃荡压力频域特征

 图 10 横摇与垂荡复合激励工况下晃荡压力变化 Fig. 10 Variation of sloshing pressure under compound excitation of roll and heave

 图 11 fh不同,晃荡载荷随fr变化情况 Fig. 11 Variation of sloshing load with fr for different fh

 图 12 各主要频率的幅值变化 Fig. 12 Amplitude variation of main frequencies

4 结　语

1）当frfh时，每个运动周期内的压力载荷变化会出现多种类型的压力载荷变化，多个运动周期组合形成的更大周期；当fr=fh时，压力载荷曲线与单纯横摇相同，每个运动周期内的压力载荷变化稳定。

2）横摇与垂荡复合激励中，横摇激励频率起主导作用，当fr=fh时，垂荡激励会减小晃荡压力，fh>fr时垂荡激励放大晃荡压力的作用会更加明显，但效果没有改变横摇激励频率显著。

3）随着fh的不断增大，fr对晃荡压力的影响会逐渐降低但仍为主要影响因素，fhfr+fhfr−fh对压力载荷的影响不断增加，多种频率的影响使压力时程曲线呈现多种周期形式，在这些周期内压力双峰大小交替性变化。

 [1] 蔡忠华. 液货船液舱晃荡问题研究[D]. 上海: 上海交通大学, 2012. [2] 张秋艳. 二维矩形液舱内液体晃荡的数值模拟[D]. 大连: 大连理工大学, 2011. [3] 金鑫, 刘飞飞, 邹寅劼, 等. 纵荡与升沉耦合激励下晃荡波特性及响应规律研究[J]. 水道港口, 2021, 42(3): 309-317. DOI:10.3969/j.issn.1005-8443.2021.03.004 [4] ZHANG Hai-tao , SUN Bei-bei. Numerical simulation of nonlinear sloshing in a 2D vertically moving container[J]. Advanced Materials Research, 2013, 2717(819-819). [5] IDA M S, ODD M. Faltinsen.. Linear sloshing in a 2D rectangular tank with a flexible sidewall[J]. Journal of Fluids and Structures, 2017, 73. [6] NING De-Zhi, SONG Wei-Hua, LIU Yu-Long, et al. A boundary element investigation of liquid sloshing in coupled horizontal and vertical excitation[J]. Journal of Applied Mathematics, 2012, 2012. [7] GREEN M D, ZHOU Yipeng, DOMINGUEZ J M, et al.. Smooth particle hydrodynamics simulations of long-duration violent three-dimensional sloshing in tanks[J]. Ocean Engineering, 2021, 229. [8] CONSTANTIN L, D COURCY J J, TITURUS B, et al.. Sloshing induced damping across Froude numbers in a harmonically vertically excited system[J]. Journal of Sound and Vibration, 2021, 510. [9] CONSTANTIN L, DE COURCY J, TITURUS B, et al. Analysis of damping from vertical sloshing in a SDOF system[J]. Mechanical Systems and Signal Processing, 2020(prepublish). [10] 邹昶方. 液舱晃荡非线性动力学行为研究[D]. 上海: 上海交通大学, 2016.