留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

基于线性化Navier-Stokes方程二维水槽内单涡到双涡的数值模拟

韩红阳 罗志强

韩红阳, 罗志强. 基于线性化Navier-Stokes方程二维水槽内单涡到双涡的数值模拟[J]. 应用数学和力学, 2016, 37(9): 953-968. doi: 10.21656/1000-0887.370118
引用本文: 韩红阳, 罗志强. 基于线性化Navier-Stokes方程二维水槽内单涡到双涡的数值模拟[J]. 应用数学和力学, 2016, 37(9): 953-968. doi: 10.21656/1000-0887.370118
HAN Hong-yang, LUO Zhi-qiang. Single- to Double-Vortex Numerical Simulation in 2D Water Tanks Based on the Linearized Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 2016, 37(9): 953-968. doi: 10.21656/1000-0887.370118
Citation: HAN Hong-yang, LUO Zhi-qiang. Single- to Double-Vortex Numerical Simulation in 2D Water Tanks Based on the Linearized Navier-Stokes Equations[J]. Applied Mathematics and Mechanics, 2016, 37(9): 953-968. doi: 10.21656/1000-0887.370118

基于线性化Navier-Stokes方程二维水槽内单涡到双涡的数值模拟

doi: 10.21656/1000-0887.370118
基金项目: 国家自然科学基金(11561037);云南省教育厅科学研究基金重点项目(2015z035)
详细信息
    作者简介:

    韩红阳(1991—),女,硕士生(E-mail: 1559751143@qq.com);罗志强(1973—),男,博士(通讯作者. E-mail: zql1009@126.com).

  • 中图分类号: O357.41

Single- to Double-Vortex Numerical Simulation in 2D Water Tanks Based on the Linearized Navier-Stokes Equations

Funds: The National Natural Science Foundation of China(11561037)
  • 摘要: 建立了Navier-Stokes方程的预估校正有限差分方法,在此基础上求得了二维水槽内部单涡到双涡的数值解,所得结果与前人的数值结果和解析解吻合很好.数值模拟结果表明,自由振动运动中自由面波高因粘性作用会发生衰减,且Reynolds数越大衰减越缓慢.在短时间内倾斜加速度激励下对于不同Reynolds数会出现一定周期的单涡.经过长时间的倾斜激励,水槽内涡场由单涡变化成双涡,而且只在较低的Reynolds数条件下出现双涡.
  • [1] Abramson H N.The Dynamic Behavior of Liquids in Moving Containers [M]. Washington D C: National Aeronautics and Space Administration, 1966.
    [2] Ibrahim R A.Liquid Sloshing Dynamics, Theory and Applications [M]. Cambridge University Press, 2005.
    [3] Faltinsen O M, Timokha A N.Sloshing [M]. Cambridge University Press, 2009.
    [4] XIN Zhou-ping, Yanagisawa T. Zero-viscosity limit of the linearized Navier-Stokes equations for a compressible viscous fluid in the half-plane[J].Communications on Puer and Applied Mathematics,1999,52(4): 479-541.
    [5] Harlow F H, Welch J E. Numerical calculation of time-dependent viscous incompressible flow of fluid with free surface[J].Physics of Fluids,1965,8(12): 2182-2189.
    [6] Oden J T. Finite-element analogue of Navier-Stokes equations[J].Journal of the Engineering Mechanics Division,1970,96(4): 529-534.
    [7] Sames P C, Marcouly D, Schellin T E. Sloshing in rectangular and cylindrical tanks[J].Journal of Ship Research,2002,46(3): 186-200.
    [8] YUE Bao-zeng, LIU Yan-zhu. ALE finite element method for free surface Navier-Stokes flow using fractional step methods[J].Journal of Hydrodynamics,2003,18(4): 463-469.
    [9] YANG Wei, LIU Shu-hong, LIN Hong. Viscous liquid sloshing damping in cylindrical container using a volume of fluid method[J].Science in China Series E: Technological Sciences,2009,52(6): 1484-1492.
    [10] Lee H C. Weighted least-squares finite element methods for the linearized Navier-Stokes equations[J].International Journal of Computer Mathematics,2014,91(9): 1964-1985.
    [11] CHEN Bang-fuh, Nokes R. Time-independent finite difference analysis of fully non-linear and viscous fluid sloshing in a rectangular tank[J].Journal of Computational Physics,2005,209(1): 47-81.
    [12] CHEN Bang-fuh, WU Chih-hua. Effects of excitation angle and coupled heave-surge-sway motion on fluid sloshing in a three-dimensional tank[J].Journal of Marine Science and Technology,2011,16(1): 22-50.
    [13] WU Chih-hua, CHEN Bang-fuh. Transient response of sloshing fluid in a three dimensional tank[J].Journal of Marine Science and Technology,2012,20(1): 26-37.
    [14] WU Chih-hua, Faltinsen O M, CHEN Bang-fuh. Dynamics of vortex evolution in a 2D baffled tank[J].Computers and Mathematics With Applications,2016,71(1): 1-28.
    [15] 罗纪生, 周恒. 湍流边界层底层相干结构的一个理论模型[J]. 应用数学和力学, 1993,14(11): 939-947.(LUO Ji-sheng, ZHOU Heng. A theoretical model of the coherent structure in the wall region of a turbulent boundary layer[J].Applied Mathematics and Mechanics,1993,14(11): 939-947.(in Chinese))
    [16] 滕斌, 赵明, 何广华. 三维势流场的比例边界有限元求解方法[J]. 计算力学学报, 2006,23(3): 301-306.(TENG Bin, ZHAO Ming, HE Guang-hua. Computation of potential flow around three-dimensional obstacles by a scaled boundary finite-element method[J].Chinese Journal of Computational Mechanics,2006,23(3): 301-306.(in Chinese))
    [17] 菅永军, 鄂学全, 柏威. 参数激励圆柱形容器中的非线性Faraday波[J]. 应用数学和力学,2003,24(10): 1057-1068.(JIAN Yong-jun, E Xue-quan, BAI Wei. Nonlinear Faraday waves in a parametrcally excited circular cylindrical container[J].Applied Mathematics and Mechanics,2003,24(10): 1057-1068.(in Chinese))
    [18] 何银年. Navier-Stokes方程的有限元边界元耦合方法[J]. 计算物理, 2002,19(3): 217-220.(HE Yin-nian. The coupling method of FE and BE for the Navier-Stokes equation[J].Chinese Journal of Computational Physics,2002,19(3): 217-220.(in Chinese))
    [19] LI Xin-liang, FU De-xun, MA Yan-wen, XIAN Liang. Direct numerical simulation of compressible turbulent flows[J].Acta Mechanica Sinica,2010,26(6): 795-806.
    [20] 陈豫眉, 谢小平. 非定常线性化Navier-Stokes方程的非协调流线扩散有限元法分析[J]. 应用数学和力学, 2010,31(7): 822-834.(CHEN Yu-mei, XIE Xiao-ping. Streamline diffusion nonconforming finite element method for the time-dependent linearized Navier-Stokes equations[J].Applied Mathematics and Mechanics,2010,31(7): 822-834.(in Chinese))
    [21] LUO Zhi-qiang, CHEN Zhi-min. Numerical simulation of standing wave with 3D predictor-corrector finite difference method for potential flow equations[J].Applied Mathematics and Mechanics(English Edition),2013,34(8): 931-944.
    [22] 罗志强, 陈志敏. 基于σ坐标变换下的Navier-Stokes方程数值模拟[J]. 南开大学学报(自然科学版), 2012,45(2): 55-61.(LUO Zhi-qing, CHEN Zhi-min. Numerical simulation of incompressible Navier-Stokes equations with σ coordinate transformations[J].Acta Scientiarum Naturalium Universitatis Nankaiensis,2012,45(2): 55-61.(in Chinese))
    [23] WU Guo-xiong, Taylor R E, Greaves D M. The effect of viscosity on the transient free-surface waves in a two-dimensional tank[J].Journal of Engineering Mathematics,2001,40(1): 77-90.
    [24] Mei C C.The Applied Dynamics of Ocean Surface Waves[M]//Liu L F, ed.Advanced Series on Ocean Engineering.Vol1. World Scientific Publishing Co Pte Ltd, 1989.
  • 加载中
计量
  • 文章访问数:  641
  • HTML全文浏览量:  35
  • PDF下载量:  616
  • 被引次数: 0
出版历程
  • 收稿日期:  2016-04-14
  • 修回日期:  2016-07-16
  • 刊出日期:  2016-09-15

目录

    /

    返回文章
    返回