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罗志强,黄玉萍.水槽涡的变化规律数值模拟
Numerical simulation of vortex evolution in a tank[J].计算力学学报,2017,34(6):793~799
水槽涡的变化规律数值模拟
Numerical simulation of vortex evolution in a tank
Numerical simulation of vortex evolution in a tank
投稿时间:2016-09-30  修订日期:2017-08-16
DOI:10.7511/jslx201706017
中文关键词:  不可压缩Naver-Stokes方程  Crank-Nicolson隐格式  有限差分方法    数值模拟
英文关键词:Navier Stokes equations  Crank-Nicolson implicit scheme  finite difference method  vortex  numerical simulation
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)资助项目.
作者单位E-mail
罗志强 昆明理工大学 理学院数学系, 昆明 650500 zql1009@126.com 
黄玉萍 昆明理工大学 理学院数学系, 昆明 650500  
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中文摘要:
      建立了不可压缩Navier-Stokes方程的Crank-Nicolson有限差分方法,数值模拟水槽晃动中流场及其涡流的数值变化规律。将数值解与解析解和前人的数值解进行比较,数值验证了不可压缩Naver-Stokes方程有限差分方法的有效性。通过数值模拟得到水槽在不同程度的倾斜激励晃动下流场及涡流的数值变换规律,当倾斜激励晃动的频率接近或远离共振频率时,水槽涡场的变化逐步由双涡变成单涡,再到不规则的涡场。当倾斜激励晃动的频率靠近共振频率ωp=0.95ω1附近时,水槽流场上部形成一个小涡,然后小涡扩大成整个水槽中的大涡,大涡下沉分裂成两个单涡,最后在底部消失;当倾斜激励晃动的频率在ωp=0.75ω1附近时,水槽底部形成一个小涡,然后扩大成大的单涡,最后在自由面消失;当倾斜激励晃动的频率在ωp=0.55ω1附近时,水槽底部出现小涡,然后扩大成大的单涡,大涡在自由面消失,继而出现不规则的大涡和不规则的小涡。
英文摘要:
      The Crank-Nicolson finite difference method for incompressible Navier-Stokes equations is developed in this paper,and the evolution regular of the vortexes and flow field are simulated under forced pitching oscillation.The numerical results are compared with the linearized analytical solution and the previous reported numerical calculation to validate the effectiveness of the present numerical method.From the numerical results,we find the evolution process of the flow field and the vortex under different degrees of pitching excitation in a tank.When the excited frequency approaches to or goes far away the oscillation frequency,the vortex field appears double vortexes,then the double vortexes convert into a single vortex and the single vortex vanishes finally in complex flow fields.When the excited frequency is ωp=0.95ω1,the profile of vortex near the free surface appears a small vortex and the vortex becomes a large vortex along the tank and splits into two vortexes,finally the vortexes disappear near the base wall.When the excited frequency is ωp=0.75ω1,the profile of vortex near the base wall appear a small vortex,then become a large vortex,then the vortex diminishes near the free surface.When the excited frequency is ωp=0.55ω1,the profile of little vortex appear on the base wall,then becomes a large vortexes,finally the large vortex diminishes near the free surface,the flow field exists big irregular vortexes and small vortexes.
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