Numerical Studies on Violent Sloshing and Resonance Frequencies in a Three-Dimensional Prismatic Tank

doi:10.16183/j.cnki.jsjtu.2020.066

Abstract

Abstract:

To predict the resonance frequency of the real liquefied natural gas (LNG) tank, a Cartesian grid based three-dimensional (3D) multiphase flow model is used to simulate violent sloshing in a prismatic tank at different filling levels and excitation frequencies. In this model, a semi-implicit finite difference method is adopted to solve the incompressible two-phase flow Navier-Stokes (N-S) equations on a staggered Cartesian grid. Besides, a radial basis function ghost cell method (RBFGCM) is used to treat the irregular tank walls and a 3D gradient-augmented level set (GALS) method is used to capture highly nonlinear free surfaces. Based on the present model, the violent sloshing induced by rolling excitations in the 3D prismatic tank is simulated. Satisfactory convergences of grid sizes and time steps demonstrate the high accuracy and reliability of the present method. Moreover, the present results of the impulsive pressure and wave elevation agree well with the experimental data for different filling water depths. In addition, violent sloshing phenomena are captured such as wave rolling. Furthermore, the relationship between the pressure amplitude on the tank wall and the excitation frequency at four filling levels are investigated to identify the resonance frequency of the prismatic tank, to provide theorical guides for structrual design of the tanks.

Key words: Cartesian grid, level set method, sloshing, prismatic tank, resonance frequency

CLC Number:

O359

XIN Jianjian, FANG Tian, SHI Fulong. Numerical Studies on Violent Sloshing and Resonance Frequencies in a Three-Dimensional Prismatic Tank[J]. Journal of Shanghai Jiao Tong University, 2021, 55(2): 161-169.

Figures/Tables 10

Fig.1

Fig.2

Fig.3

Fig.4

Fig.5

Fig.6

Fig.7

Fig.8

Fig.9

Tab.1

References 15

[1]	王德禹，金咸定，李龙渊. 液舱流体晃荡的模型试验[J]. 上海交通大学学报，1998, 32(11): 3-5.
	WANG Deyu, JIN Xianding, LI Longyuan. On model experiment of sloshing in tanks[J]. Journal of Shanghai Jiao Tong University, 1998, 32(11): 3-5.
[2]	李裕龙，朱仁传，缪国平，等. 波浪中载液船舶运动的时域模拟[J]. 上海交通大学学报，2012, 46(3): 379-384.
	LI Yulong, ZHU Renchuan, MIAO Guoping, et al. Simulation of ship motions coupled with tank sloshing in time domain[J]. Journal of Shanghai Jiao Tong University, 2012, 46(3): 379-384.
[3]	ELAHI R, PASSANDIDEH-FARD M, JAVANSHIR A. Simulation of liquid sloshing in 2D containers using the volume of fluid method[J]. Ocean Engineering, 2015, 96: 226-244.
[4]	BATTAGLIA L, CRUCHAGA M, STORTI M, et al. Numerical modelling of 3D sloshing experiments in rectangular tanks[J]. Applied Mathematical Modelling, 2018, 59: 357-378.
[5]	SHAMSODDINI R, ABOLPUR B. Investigation of the effects of baffles on the shallow water sloshing in a rectangular tank using a 2D turbulent ISPH method[J]. China Ocean Engineering, 2019, 33(1): 94-102.
[6]	WANG J, ZOU L, WAN D. Numerical simulations of zigzag maneuver of free running ship in waves by RANS-Overset grid method[J]. Ocean Engineering, 2018, 162: 55-79.
[7]	BAI W, LIU X, KOH C G. Numerical study of violent LNG sloshing induced by realistic ship motions using level set method[J]. Ocean Engineering, 2015, 97: 100-113.
[8]	JIANG S C, TENG B, BAI W, et al. Numerical simulation of coupling effect between ship motion and liquid sloshing under wave action[J]. Ocean Engineering, 2015, 108: 140-154.
[9]	ZHAO Y, CHEN H C. Numerical simulation of 3D sloshing flow in partially filled LNG tank using a coupled level-set and volume-of-fluid method[J]. Ocean Engineering, 2015, 104: 10-30.
[10]	KIM Y, SHIN Y S, LEE K H. Numerical study on slosh-induced impact pressures on three-dimensional prismatic tanks[J]. Applied Ocean Research, 2004, 26(5): 213-226.
[11]	LEE S H, LEE Y G, JEONG K L. Numerical simulation of three-dimensional sloshing phenomena using a finite difference method with marker-density scheme[J]. Ocean Engineering, 2011, 38(1): 206-225.
[12]	XIN J, SHI F, JIN Q, et al. A radial basis function based ghost cell method with improved mass conservation for complex moving boundary flows[J]. Computers & Fluids, 2018, 176: 210-225.
[13]	XIN J J, SHI F L, JIN Q, et al. Gradient-augmented level set two-phase flow method with pretreated reinitialization for three-dimensional violent sloshing[J]. Journal of Fluids Engineering, 2020, 142(1): 011402.
[14]	NAVE J C, ROSALES R R, SEIBOLD B. A gradient-augmented level set method with an optimally local, coherent advection scheme[J]. Journal of Computational Physics, 2010, 229(10): 3802-3827.
[15]	MIKELIS N E, MILLER J K, TAYLOR K V. Sloshing in partially filled liquid tanks and its effect on ship motions: Numerical simulations and experimental verification[J]. Royal Institutioin of Naval Architects Transactions, 1984, 126(10): 267-281.

液舱	ω_n/(rad·s^－1)
液舱	h/H=0.46	h/H=0.61	h/H=0.75	h/H=0.90
矩形液舱	5.23	5.69	5.97	6.16
菱形液舱	5.1	5.5	5.6	5.9