SIMULATION OF THE MOTION OF AN ELASTIC HULL IN REGULAR WAVES BASED ON MPS-FEM METHOD
-
摘要: 船舶在海洋中航行时经常会受波浪的作用, 在波浪的作用下, 船体可能会发生六自由度的运动. 在船体运动幅度较小时, 可以简单地将船体运动视为刚体运动. 但当波浪环境较为剧烈、船体运动幅度较大时, 船体可能会发生变形, 此时船舶弹性的影响无法忽略. 因此, 研究弹性船体在波浪中的运动对船舶运动性能和航行安全具有重要的意义. 移动粒子半隐式方法MPS方法是一种基于拉格朗日方法表示的无网格粒子类方法, 该方法在模拟具有自由面大变形特征的问题时具有其独特的优势. 有限元方法FEM作为一种传统的并且已被广泛应用的结构求解方法, 具有很好的稳定性、准确性和鲁棒性. 本文将MPS方法与FEM方法二者的优势结合, 基于MPS-FEM耦合方法, 使用自主开发的MPSFEM-SJTU流固耦合求解器, 模拟刚性船体和弹性船体在规则波中的运动, 并分析船体的弹性对船体运动响应的影响. 首先模拟刚性船体在不同波长的规则波中的运动, 研究规则波波长对船体运动响应的影响. 接着分别模拟了刚性和弹性船体在规则波中的运动, 结果表明, 刚性船体的运动幅值大于弹性船体的运动幅值, 而弹性船体船舯附近的压力大于刚性船体.Abstract: A ship always encounters waves and may move with six degrees of freedom in the naval architecture and ocean engineering. The ship can be regarded as a rigid body simply when the motion amplitude is small. However, when the wave gets severe, the ship's motion amplitude get large and the ship hull may deforms a lot. In this situation, ship's elasticity may effects the pressure on the hull and the ship response motion, which cannot be ignored. Therefore, it is of great significance to simulate the motion of an elastic ship in waves and to study the influence of the hull elasticity, which can improve the ship performance and the navigation safety. Moving particle semi-implicit (MPS) method is a mesh free particle method based on Lagrangian representation. This method has its unique advantages in simulating problems with large deformation characteristics of free surfaces. As a traditional structural solution method, finite element method (FEM) has been widely used and has been proved with good stability, accuracy and robustness. In this paper, the advantages of MPS method and FEM method are combined and the in-house fluid-structure interaction solver MPSFEM-SJTU is used to simulate the motions of rigid and elastic hulls in regular waves. The impact of hull elasticity on the hull motion response and the pressure on the hull is analyzed. Firstly, the effect of regular wave length on the motion response of hull is studied by simulating the motion of a rigid hull in regular waves with different wavelengths. Then the motions of rigid and elastic hull in regular waves are simulated respectively. The results show that the motion amplitude of rigid hull, both pitch and heave, are greater than those of the elastic hull. and the pressure near the midship of elastic hull is greater than that of rigid hull. For the pressure distribution on elastic and hull surface, the pressure at the bottom near the midship is greater than that on the rigid hull due to the bending of the elastic ship.
-
Key words:
- MPS method /
- regular wave /
- fluid-structure interaction /
- elastic ship hull /
- ship motion
-
表 1 kvlcc2船实船和模型船参数
Table 1. Characteristic parameters of the kvlcc2 ship
Characteristic parameter Real scale Model scale ship length Lpp/m 320.0 3.2 ship breadth B/m 58.0 0.58 ship depth D/m 30.0 0.3 draft d/m 20.8 0.208 displacement $\nabla /m^3$ 312622 0.312 scale ratio 100 − 表 2 船舶运动响应参数
Table 2. Ship motion response parameters
Particle spacing Average peak value Average valley value Average amplitude Attenuation heave/m $\Delta {x} = 0.03\mathrm{m}$ −0.010 −0.0962 0.0265 − $\Delta {x} = 0.035\mathrm{m}$ −0.073 −0.0925 0.0197 −25.26% $\Delta {x} = 0.04\mathrm{m}$ −0.078 −0.101 0.0235 −11.12% pitch/(°) $\Delta {x} = 0.03\mathrm{m}$ 0.055 −0.0425 0.0979 − $\Delta {x} = 0.035\mathrm{m}$ 0.050 −0.0389 0.0887 −9.471% $\Delta {x} = 0.04\mathrm{m}$ 0.049 −0.0305 0.0797 −18.59% 表 3 弹性刚性船体运动响应参数对比
Table 3. Comparison of motion response parameters of elastic and rigid hulls
Average peak value Average valley value Average
amplitudepitch/(°) rigid ship 2.775 −2.9012 5.676 elastic ship 2.091 −2.1619 4.253
(−25.1%)heave/m Rigid ship 0.00764 −0.00714 0.0148 elastic ship 0.00569 −0.00738 0.0131
(−11.5%) -
[1] 王加夏, 周天九, 刘昆等. 规则波迎浪砰击下三维船体耦合响应研究. 江苏科技大学学报(自然科学版), 2020, 34(4): 13-24 (Wang Jiaxia, Zhou Tianjiu, Liu Kun, et al. Fluid-structure coupling response of a three dimensional ship under regular head wave slamming loads. Journal of Jiangsu University of Science and Technology (Natural Science Edition) , 2020, 34(4): 13-24 (in Chinese) [2] Oberhagemann J, Holtmann M, Moctar O, et al. Stern slamming of a LNG carrier. Journal of Offshore Mechanics & Arctic Engineering, 2009, 131(3): 1672-1682 [3] Lakshmynarayanana P, Temarel P, Chen Z. Coupled fluid structure interaction to model three-dimensionaldynamic behaviour of ship in waves//7th International Conference on Hydroelasticity in Marine Technology, Split, Croatia, 2015 [4] Kim Y, Kim K, Kim Y. Analysis of hydroelasticity of floating shiplike structure in time domain using a fully coupled hybrid BEM-FEM. Journal of Ship Research, 2009, 53(1): 31-47 doi: 10.5957/jsr.2009.53.1.31 [5] Malenica S, Tuitman J, Bigot F, et al. Some Aspects of 3D Linear Hydroelastic Models of Springing. International Conference on Hydrodynamics, France, 2008. [6] Gao R, Ren B, Wang G, et al. Numerical modelling of regular wave slamming on surface of open-piled structures with the corrected SPH method. Applied Ocean Research, 149 2012, 34: 173-186 [7] Omidvar P, Stansby P, Rogers B. Wave body interaction in 2D using smoothed particle hydrodynamics (SPH) with variable particle mass. International Journal for Numerical Methods in Fluids, 2012, 68(6): 686-705 doi: 10.1002/fld.2528 [8] Sueyoshi M, Kashiwagi M, Naito S. Numerical simulation of wave-induced nonlinear motions of a two-dimensional floating body by the moving particle semi-implicit method. Journal of Marine Science and Technology, 2008, 13(2): 85-94 doi: 10.1007/s00773-007-0260-y [9] Sueyoshi M. Numerical simulation of extreme motions of a floating body by MPS method. Bridges Across the Oceans, Kobe, Japan, 2004, 1: 566-572 [10] 饶成平. 基于MPS-FEM耦合方法研究孤立波对弹性结构物的砰击. [硕士论文]. 上海: 上海交通大学, 2018Rao Chengping. Numerical investigation of solitary wave-induced slamming on flexible structure by MPS-FEM coupled method. [Master Thesis]. Shanghai: Shanghai Jiao Tong University, 2018 (in Chinese) [11] Zhang G, Rao C, Wan D. Numerical study of solitary wave slamming on a 3-D flexible plate by MPS-FEM Coupled Method//The Twenty-eighth International Ocean and Polar Engineering Conference (ISOPE2018), Sapporo, Japan, June 10-15, 2018: 46-53 [12] Lind S, Xu R, Stansby P, et al. Incompressible smoothed particle hydrodynamics for free-surface flows: A generalised diffusion-based algorithm for stability and validations for impulsive flows and propagating waves. Journal of Computational Physics, 2012, 231(4): 1499-1523 doi: 10.1016/j.jcp.2011.10.027 [13] Sun P, Luo M, Touzé DL, et al. The suction effect during freak wave slamming on a fixed platform deck: Smoothed particle hydrodynamics simulation and experimental study. Physics of Fluids, 2019, 31(11): 117108 doi: 10.1063/1.5124613 [14] Zhang G, Zhao W, Wan D. Moving particle semi-implicit method coupled with finite element method for hydroelastic responses of floating structures in waves. European Journal of Mechanics-B Fluids, 2022, 95: 63-82 doi: 10.1016/j.euromechflu.2022.04.005 [15] Zhang Y, Wan, D. Numerical study of interactions between waves and free rolling body by IMPS method. Computers and Fluids, 2017, 155: 124133 [16] Xie F, Zhao W, Wan D. MPS-DEM coupling method for interaction between fluid and thin elastic structures. Ocean Engineering, 2021, 236: 109449 doi: 10.1016/j.oceaneng.2021.109449 [17] Zhang G, Zha R, Wan D. MPS–FEM coupled method for 3D dam-break flows with elastic gate structures. European Journal of Mechanics-B Fluids, 2022, 94: 171-189 doi: 10.1016/j.euromechflu.2022.02.014 [18] Sun Y, Xi G, Sun Z. A fully Lagrangian method for fluid–structure interaction problems with deformable floating structure. Journal of Fluids and Structures, 2019, 90: 379-395 doi: 10.1016/j.jfluidstructs.2019.07.005 [19] Sun Z, Djidjeli K, Xing J, et al. Coupled MPS-modal superposition method for 2 D nonlinear fluid-structure interaction problems with free surface. Journal of Fluids and Structures, 2016, 61: 295-323 [20] Sun Z, Zhang G, Zong Z, et al. Numerical analysis of violent hydroelastic problems based on a mixed MPS-mode superposition method. Ocean Engineering, 2019, 179: 285-297 [21] Koshizuka S, Nobe A, Oka Y. Numerical analysis of breaking waves using the moving particle semi-implicit method. International Journal for Numerical Methods in Fluids, 1998, 26(7): 751-769 doi: 10.1002/(SICI)1097-0363(19980415)26:7<751::AID-FLD671>3.0.CO;2-C [22] Khayyer A, Gotoh H. Development of CMPS method for accurate water-surface tracking in breaking waves. Coastal Engineering Journal, 2008, 50(2): 179-207 doi: 10.1142/S0578563408001788 [23] Tanaka M, Masunaga T. Stabilization and smoothing of pressure in MPS method by quasi-compressibility. Journal of Computational Physics, 2010, 229(11): 4279-4290 doi: 10.1016/j.jcp.2010.02.011 [24] 张雨新. 改进的MPS方法及其三维并行计算研究. [博士论文]. 上海: 上海交通大学, 2014Zhang Yuxin. Development and application of 3D parallel improved meshless MPS method. [PhD Thesis]. Shanghai: Shanghai Jiao Tong University, 2014 (in Chinese)) [25] Khayyer A, Gotoh H. Modified moving particle semi-implicit methods for the prediction of 2D wave impact pressure. Coastal Engineering, 2009, 56(4): 419-440 doi: 10.1016/j.coastaleng.2008.10.004 [26] Khayyer A, Gotoh H. A higher order Laplacian model for enhancement and stabilization of pressure calculation by the MPS method. Applied Ocean Research, 2010, 32(1): 124-131 doi: 10.1016/j.apor.2010.01.001 [27] Lee B, Park J, Kim M, et al. Step-by-step improvement of MPS method in simulating violent free-surface motions and impact-loads. Computer Methods in Applied Mechanics and Engineering, 2011, 200: 1113-1125 doi: 10.1016/j.cma.2010.12.001 [28] Zhang, Y, Wan D, Hino T. Comparative study of MPS method and level-set method for sloshing flows. Journal of Hydrodynamics, 2014, 26(4): 577-585 doi: 10.1016/S1001-6058(14)60065-2 [29] Newmark N. A Method of computation for structural dynamics. Journal of the Engineering Mechanics Division. 1959, 85(3): 67-94 [30] Turek S, Hron J. Proposal for numerical benchmarking of fluid-structure interaction between an elastic object and laminar incompressible flow//Fluid structure Interaction, Springer, 2006: 371–385 [31] Sun PN, Touze DL, Oger G, et al. An accurate FSI-SPH modeling of challenging fluid-structure interaction problems in two and three dimensions. Ocean Engineering, 2021, 211: 109552 -