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基于FTM方法的二维Kelvin-Helmholtz不稳定性数值模拟*
Numerical simulation of two-dimensional Kelvin-Helmholtz instabilities using a front tracking method*
投稿时间:2017-05-12  修订日期:2017-07-28
DOI:
中文关键词:  Kelvin-Helmholtz不稳定性  速度梯度层厚度  Neumann边界条件  Dirichlet边界条件  界面跟踪法
英文关键词:Kelvin-Helmholtz instability  The thickness of velocity gradient layers  Neumann boundary condition  Dirichlet boundary condition  Front tracking method
基金项目:国家自然科学基金(11562011)、江西省自然科学基金(20151BAB202002)
作者单位E-mail
张莹 南昌大学机电学院 yzhan2033@163.com 
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中文摘要:
      使用界面跟踪法(Front Tracking Method,FTM)对二维不混溶、不可压缩流体的K-H(Kelvin-Helmholtz)不稳定性进行数值模拟。研究表明,速度梯度层越厚,界面在水平分量中移动越快,卷起越少。还发现初始水平速度差越大,界面卷起越多,内扰动增长速度越快,K-H不稳定性的特征形式变得更加明显。此外,我们还观察到在Neumann边界条件(即无滑移边界条件)下的界面的扰动发展得比Dirichlet边界条件(即对称边界条件)下的扰动快。由于Dirichlet边界中的边界层,在开始时刻涡量开始扩展到两侧,其影响了K-H不稳定性的生长速率。而在Neumann边界条件下涡量由于初始水平速度差在界面中心聚集。最后,我们研究了不同边界条件下各种理查德森数对K-H不稳定性的影响。
英文摘要:
      The two-dimensional Kelvin-Helmholtz (K-H) instability of immiscible and incompressible fluids is performed using a front tracking method. It is shown that the thicker the velocity gradient layer, the faster the interface moves in horizontal component and roll up less. It is also found that the initial horizontal velocity differences gets larger, the interface roll-up more as well as the inward disturbance growth rate gets faster, and the characteristics form of K-H instability becomes much more obvious. Besides, we also observe that the disturbance of interface in Neumann boundary condition(that is no slip boundary condition) develops faster than the disturbance in Dirichlet boundary condition(that is symmetrical boundary condition). Due to the existence of boundary layer in Dirichlet boundary, vorticity has begun to spread to both sides at initial moment, affecting the growth rate of the K-H instability. While vorticity gather in center of interface due to initial horizontal velocity differences in Neumann boundary condition. Finally we investigate the effect of a variety of Richardson number in different boundary conditions on the K-H instability.
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