基于CIP类方法的液舱晃荡数值模拟研究与应用
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摘要
作为复杂的流体运动现象,液体发生晃荡时会伴随产生波面破碎、波对舱壁的高速砰击、液滴形成及气泡卷入等强非线性现象,并表现出很强随机性。本文对晃荡现象数值研究现状,特别是CIP法在晃荡现象研究的发展进行了较全面的回顾,在此基础上,采用基于CIP(Constrained Interpolation Profile)法的自编程序,对晃荡现象机理进行研究。主要分为以下几个内容:
1)系统介绍了CIP方法的基本原理以及应用于晃荡现象的处理。
详细说明了CIP方法与压力修正(SIMPLE类)方法的区别与联系,所采用的数学模型,利用CIP法对流场进行分步求解的步骤。
2)选定适当的数值模型对晃荡现象进行描述并进行程序的实现。
在原理介绍的基础上实现程序编写。结合CIP方法应用于晃荡现象的特点,采用交错网格描述流场信息,在边界处采用虚网格保证边界条件的处理。应用带有预处理矩阵K的Bi-CGSTAB方法求解压力泊松方程,提高计算精度和效率。
3)将所编制的程序用于溃坝问题的模拟,以作为大变形自由液面的验算。
对溃坝过程中的液面变化进行了监测,与Fluent计算结果相比较,验证所编写程序可以对自由液面进行很好的捕捉;对溃流下游固定壁面处压力测点的载荷变化进行监测,与实验结果的比较表明,所编写程序可以反映流场中压力的变化。
4)在溃坝模拟验算的基础上,利用自编程序进行晃荡问题的研究。
针对不同液深及晃荡幅值的工况进行相应计算,在非谐振激励下,各种液深下的晃荡强度均小于谐振激励,但高液深时的差异较小。对壁面压力进行监测发现,当舱内形成驻波,舱壁所受冲击压力显著变小。
Violent sloshing is a strongly nonlinear problem, which may involve phenomena such as breaking waves, high-speed impacts on tank walls, liquid droplet formation and air bubble entrainment, and is of high randomness. In this paper, the state of the art of the study on sloshing with numerical method, especially the application of the CIP method in sloshing simulation is reviewed. Some research about the mechanism of sloshing has been taken based on the foundation, with the self-programming code of Fortran language. The main work and important conclusions of this paper are listed as follows:
1) Give an overall review of the principle of CIP method and the application is sloshing
Specify the difference between fractional step method and pressure correction method, choose proper mathematic model to describe the sloshing phenomenon, and describe the fractional solving steps with CIP method.
2) The choice of proper numerical model and programming
Program with Fortran language based on the introduction. Combining the characteristics of the CIP method applied to sloshing phenomenon, staggered grid is adopted to store the information of the fluid field, and an exterior fictitious one-cell layer adjacent to each side of the physical domain is added to allow imposition of discrete boundary condition. Use the Bi-CGSTAB method with preconditioning matrix K to calculate the Poisson equation of pressure precisely and efficiently.
3) Simulate the dam-breaking problem to validate the code in the use of large deformation of free surface
Monitor the deformation of the free surface, and compare the result with computation by Fluent, which certify the capture of the free surface; the comparison between the monitored pressure and experimental data at the solid wall downstream showed that the code is feasible to monitor the variant of the pressure.
4) Simulate the sloshing phenomenon with the code based on the validation of the dam-breaking problem
Cases of different liquid level and sloshing amplitude are simulated. The results show that the intensity of sloshing in the bestir of the non-resonance frequency is smaller than the resonance frequency liquid with both depths, while in high level cases the difference is not obvious; the monitored pressure show that the slamming pressure is much smaller when stationary waves are formed in the tank.
1)系统介绍了CIP方法的基本原理以及应用于晃荡现象的处理。
详细说明了CIP方法与压力修正(SIMPLE类)方法的区别与联系,所采用的数学模型,利用CIP法对流场进行分步求解的步骤。
2)选定适当的数值模型对晃荡现象进行描述并进行程序的实现。
在原理介绍的基础上实现程序编写。结合CIP方法应用于晃荡现象的特点,采用交错网格描述流场信息,在边界处采用虚网格保证边界条件的处理。应用带有预处理矩阵K的Bi-CGSTAB方法求解压力泊松方程,提高计算精度和效率。
3)将所编制的程序用于溃坝问题的模拟,以作为大变形自由液面的验算。
对溃坝过程中的液面变化进行了监测,与Fluent计算结果相比较,验证所编写程序可以对自由液面进行很好的捕捉;对溃流下游固定壁面处压力测点的载荷变化进行监测,与实验结果的比较表明,所编写程序可以反映流场中压力的变化。
4)在溃坝模拟验算的基础上,利用自编程序进行晃荡问题的研究。
针对不同液深及晃荡幅值的工况进行相应计算,在非谐振激励下,各种液深下的晃荡强度均小于谐振激励,但高液深时的差异较小。对壁面压力进行监测发现,当舱内形成驻波,舱壁所受冲击压力显著变小。
Violent sloshing is a strongly nonlinear problem, which may involve phenomena such as breaking waves, high-speed impacts on tank walls, liquid droplet formation and air bubble entrainment, and is of high randomness. In this paper, the state of the art of the study on sloshing with numerical method, especially the application of the CIP method in sloshing simulation is reviewed. Some research about the mechanism of sloshing has been taken based on the foundation, with the self-programming code of Fortran language. The main work and important conclusions of this paper are listed as follows:
1) Give an overall review of the principle of CIP method and the application is sloshing
Specify the difference between fractional step method and pressure correction method, choose proper mathematic model to describe the sloshing phenomenon, and describe the fractional solving steps with CIP method.
2) The choice of proper numerical model and programming
Program with Fortran language based on the introduction. Combining the characteristics of the CIP method applied to sloshing phenomenon, staggered grid is adopted to store the information of the fluid field, and an exterior fictitious one-cell layer adjacent to each side of the physical domain is added to allow imposition of discrete boundary condition. Use the Bi-CGSTAB method with preconditioning matrix K to calculate the Poisson equation of pressure precisely and efficiently.
3) Simulate the dam-breaking problem to validate the code in the use of large deformation of free surface
Monitor the deformation of the free surface, and compare the result with computation by Fluent, which certify the capture of the free surface; the comparison between the monitored pressure and experimental data at the solid wall downstream showed that the code is feasible to monitor the variant of the pressure.
4) Simulate the sloshing phenomenon with the code based on the validation of the dam-breaking problem
Cases of different liquid level and sloshing amplitude are simulated. The results show that the intensity of sloshing in the bestir of the non-resonance frequency is smaller than the resonance frequency liquid with both depths, while in high level cases the difference is not obvious; the monitored pressure show that the slamming pressure is much smaller when stationary waves are formed in the tank.
引文
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[2] Verhagen JHG, van Wijngaarden L. Nonlinear oscillations of fluid in a container[J]. J Fluid Mech, 1965,22: 737-751.
[3] Faltinsen O M. A nonlinear theory of sloshing in rectangular tanks[J]. J ship Res, 1974, 18(4): 224-241.
[4] Faltinsen O M. A numerical nonlinear method of sloshing in tank with two dimensional flow [J]. JSR, 1978,22.
[5] Milkelis N.E., Miller J.K., et al. Sloshing in Partially Filled Liquid Tanks and Its Effect on Ship Motions: Numerical Simulations and Experimental Verification [J]. Transactions of the Rova1 Institute of Naval Architect, 1984,126: 267-281.
[6] Arai. M. Experimental and numerical studies of sloshing pressure in liquid cargo tanks [J]. Journal of the Society of Naval Architects of Japan, 1984,155: 114-121.
[7] Nagahama, M. Nagahama, S., Nekado, Y., Yama: nori, T. and Hori, T.A 3-Dimensional analysis of sloshing by means of tank wall fitted coordinate system [J]. Journal of the Society of Naval Architects of Japan, 1992,172: 487-489.
[8] Arai. M., Cheng L Y. 1noue Y. 3D Numerical simulation of impact load due to liquid cargo sloshing [J]. Journal of The Society of Naval Architects of Japan, 1992,171.
[9] Arai. M... Cheng L Y. 1noue Y. Numerical simulation of sloshing in a cubic and a cylindrical tank [J]. J. Kansai Soc. N.A. Japan, 1993,219: 177-184.
[10] Armenio. V. An improved MAC method (SIMAC) for unsteady high-Reynolds free surface flows [J]. Int. J. Num. Methods Fluids, 1997,24: 185-214.
[11] Armenio. V. Dynamic loads on submerged bodies in a viscous numerical wave tank at small KC numbers [J]. Ocean Eng. 1998, 25(10): 881-905.
[12] Hirt, C. W, Nichols B.D. Volume of fluid (VOF) method for the dynamics of free surface fluid flow [J]. J Compute Physics, 1981,39: 201-225。
[13]朱仁庆.液体晃荡及其与结构的相互作用[D].无锡:中国船舶科学研究中心, 2001,博士学位论文.
[14]朱仁庆,王志东,方智勇.液舱内大幅晃荡引起的压强预报[J].船舶力学, 2004,8(6):71-78.
[15]端木玉,朱仁庆.不同液舱结构形式对晃荡的影响分析[J].水动力学研究与进展, 2006,A辑,21(6).
[16]祁江涛,顾民. LNG船液舱晃荡的数值模拟[J].中国造船, 2007,48卷增刊.
[17]沈猛.基于改进VOF法的棱形液舱液体晃荡分析及应用[D].上海:上海交通大学, 2008,硕士学位论文.
[18]朱仁庆,方志勇. Leve1-set法预报液舱内剧烈晃荡引起的冲击压强[J].船舶力学, 2008,12(3):344-351.
[19]黄广茂,方智勇.基于Leve1-set法的液体晃荡与弹性液舱耦合作用研究[J].船舶工程, 2007,29(6).
[20]方智勇,朱仁庆,杨松林.基于Leve1-set法和通度概念液体晃荡特性研究[J].海洋工程, 2007,25(2).
[21]毛益明,汤文辉.自由表面流动问题的SPH方法数值模拟[J].解放军理工大学学报(自然科学版), 2001, 2(5):92-94.
[22]陈正云,朱仁庆,祁江涛.基于SPH法的二维液体大幅晃荡数值模拟[J].船海工程, 2008,37(2):44-47.
[23]崔岩,吴卫,龚凯等.二维矩形水槽晃荡过程的SPH方法模拟[J].水动力学研究与进展, 2008,A辑,23(6): 618-624.
[24] F. Xiao, T.Yabe. A method to trace sharp interface of two fluids in calculations involving shocks[J]. Shock Waves, 1994,4:101-108.
[25]汤寒松.双曲方程CIP方法分析与改进[D].北航流体所博士后出站报告,第二部分,1995.
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