矩形槽内水体大幅晃动分析中截断误差影响范围判断方法探讨
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摘要
液体大幅晃动是目前CFD研究中一个热点。在CFD中,偏微分方程离散所产生的截断误差是主要的误差来源,且与网格尺度密切相关。本文首先从理论上介绍了截断误差的产生过程,由此过程可知截断误差与物理粘性的作用具有类似性。以此概念为基础,根据液体晃动动力响应的特点提出了在液体大幅晃动分析中,如何通过对物理粘性系数的参数敏感性分析,判断截断误差的作用范围从而判断计算精度是否满足要求的方法,最后与现有试验资料进行对比校核,验证了该方法的实用性。
Large amplitude sloshing is an active research field in CFD.The truncation error due to dispersion of partial differentiation equation is the main error origin and is a close relative of gird dimension.The similarity function in CFD between truncation error and physical viscous parameter are introduced from the view of process of dispersion of partial differentiation equation.Based on that conception,together with the characteristics of dynamic responses of fluid sloshing,the method that how to estimate the effect range of truncation error by sensitivity analysis of physical viscous parameters to satisfy the computational precision is promoted.The practicability of the method is verified by the comparison with existing experimental data.
Large amplitude sloshing is an active research field in CFD.The truncation error due to dispersion of partial differentiation equation is the main error origin and is a close relative of gird dimension.The similarity function in CFD between truncation error and physical viscous parameter are introduced from the view of process of dispersion of partial differentiation equation.Based on that conception,together with the characteristics of dynamic responses of fluid sloshing,the method that how to estimate the effect range of truncation error by sensitivity analysis of physical viscous parameters to satisfy the computational precision is promoted.The practicability of the method is verified by the comparison with existing experimental data.
引文
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[15]Anderson,John D,Jr.Computational Fluid Dynam-ics:The Basics with Applications[M].McGraw HillCopyright,1995.
[16]居荣初.弹性结构与液体的耦联振动理论[M].北京:地震出版社,1983.(J Rong-chu.The coupled Vi-bration Theory of Elastic Structure and Fluid[M].Beijing:Earthquake Publisher,1983.(in Chinese))
[2]刘云贺,陈厚群.大型渡槽铅销橡胶支座减震机理的数值模拟[J].水利学报,2003,12:98-103.(LI U Yun-he,CHEN Hou-qun.Aseismic effect of lead rubberbearing for large scaled aqueduct[J].Journal of Hy-draulic Engineering,2003,12:98-103.(in Chinese))
[3]庄中华,李敏霞,陈厚群.渡槽结构隔震与耗能减振控制机理的研究[J].噪声与振动控制,2002,2:10-12.(ZHUANG Zhong-hua,LI Min-xia,CHEN Hou-qun.Basic theory on aqueduct bridge vibration con-trolusing lsolation and energy dissipation hybrid sis-tem[J].Noise and Vibration Control,2002,2:10-12.(in Chinese))
[4]Nie Li-ying,Chu Jia-yi,Zhang Liao-jun.The charac-teristics of dynamic response of water in aqueductbridge under large amplitude sloshing[A].The 14thWorld Conference on Earthquake Engineering[C].Paper No.06-0157,2008
[5]Okamoto T,Kawahara M.Two-di mension sloshinganalysis by Lagrangian finite element method[J].In-ternational Journal for Numerical Methods in Flu-ids,1990,11:453-477.
[6]Ramaswamy B,Kawahara M.Arbitrary Lagrangian-Eulerian finite element method for unsteady,conv-etive,incompressible viscous free surface flow[J].International Journal for Numerical Methods inFluids,1987,7:1053-1075.
[7]吴轶,莫海鸿,杨春.U形渡槽水体大幅晃动的ALE有限元模拟[J].华南理工大学学报,2003,31(9):90-93.(Wu Yi,Mo Hai-hong,Yang Chun.ALEsi mulation of large sloshing of water in U-shaped aq-ueduct[J].Journal of South China University ofTechnology,2003,31(9):90-93.(in Chinese))
[8]Nakayama T,Washizu K.The boundary elementmethod applied to the analysis of two-di mensionalnonlinear sloshing problems[J].International Jour-nal for Numerical Methods in Engineering,1981,17(11):1631-1646.
[9]李遇春,楼梦麟.渡槽中流体非线性晃动的边界元模拟[J].地震工程与工程振动,2000,20(2):51-56.(LIYu-chun,LOU Meng-lin.BEMsi mulation of nonlin-ear sloshing for aqueduct fluid[J].Earthquake Engi-neering and Engineering Vibration,2000,20(2):51-56.(in Chinese))
[10]Hakan Akyildiz M,Serdar C Eleb.Numerical compu-tation of hydrodynamic loads on walls of a rigid rec-tangular tank due to large amplitude liquid sloshing[J].Turkish J Eng Env Sci,2002,26:429-445.
[11]Cho J R,Lee H W.Numerical study on liquid slos-hing in baffled tank by nonlinear finite element meth-od[J].Comput.Methods Appl Mech Engrg,2004,193:2581-2598.
[12]昌普,苏万华.计算网格与湍流模型对柴油喷雾多维数值模拟结果的影响[J].天津大学学报,2004,37(11):965-969.(ZHAO Chang-pu,SU Wan-hua.Effects of the computation mesh and turbulence mod-el on multi-di mensional numerical si mulation resultsof a diesel spray[J].Journal of Tianjin University,2004,37(11):965-969.(in Chinese))
[13]方斌,朱锡,张振华,等.水下爆炸冲击波数值模拟中的参数影响[J].哈尔滨工程大学学报,2005,26(4):419-424.(FANG Bin,ZHU Xi,ZHANG Zhen-hua,et al.Effect of parameters in numerical si mula-tionof underwater shock wave[J].Journal of HarbinEngineering University,2005,26(4):419-424.(inChinese))
[14]张涵信,呙超,宗文刚.网格与高精度差分计算问题[J].力学学报,1999,31(4):398-405.(ZHANG Han-xin,WO Chao,ZONG Wen-gang.Problems about girdand high order schemes[J].Chinese Journal of Theo-retical and Applied Mechanics,1999,31(4):398-405.(in Chinese))
[15]Anderson,John D,Jr.Computational Fluid Dynam-ics:The Basics with Applications[M].McGraw HillCopyright,1995.
[16]居荣初.弹性结构与液体的耦联振动理论[M].北京:地震出版社,1983.(J Rong-chu.The coupled Vi-bration Theory of Elastic Structure and Fluid[M].Beijing:Earthquake Publisher,1983.(in Chinese))
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