Numerical simulation of vortex evolution in a tank
Received:September 30, 2016  Revised:August 16, 2017
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KeyWord:Navier Stokes equations  Crank-Nicolson implicit scheme  finite difference method  vortex  numerical simulation
罗志强 昆明理工大学 理学院数学系, 昆明
黄玉萍 昆明理工大学 理学院数学系, 昆明
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      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.