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Direct numerical simulation and statistical analysis of stress-driven turbulent Couette flow with a free-slip boundary

机译：具有自由滑动边界的应力驱动湍流耦合流的直接数值模拟及统计分析

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摘要

The effects of free-slip boundary on shear turbulence are studied numerically using the direct numerical simulation (DNS) approach. The flow considered in this study is a stress-driven turbulent Couette flow between two flat boundaries. The top boundary has an imposed shear stress in the streamwise direction and a free-slip condition for the streamwise velocity fluctuation and the spanwise velocity, and the bottom boundary satisfies the no-slip condition. This type of flow has a mean flow pattern similar to the turbulent plane Couette flow between a stationary flat plate and a moving flat plate but exhibits considerable differences in turbulence statistics due to the effects of the free-slip boundary. Statistical analysis based on the DNS data and theoretical derivation based on Taylor series expansion show that near the free-slip surface the turbulence variances of the three velocity components vary as quadratic functions of the vertical distance from the boundary while the Reynolds shear stress exhibits a linear behavior, which are very different from the counterparts near the no-slip boundary. The free-slip surface condition also leads to zero horizontal vorticities at the surface but allows nonzero vertical vorticity in the meantime, leading to considerable differences in the near-boundary statistics of vorticities and coherent vortex structures. Comparison of three DNS runs with different grid resolutions shows that smoothly resolving the more energetic turbulent flow structures near the free-slip boundary requires a higher horizontal grid resolution than that used for resolving the structures near the no-slip boundary.
机译：使用直接数值模拟（DNS）方法在数值上进行了对剪切湍流对剪切湍流的影响。在本研究中考虑的流动是两个平边之间的应力驱动的湍流耦合。顶边界在流动方向上具有施加的剪切应力和用于流速速度波动和翼展速度的自由滑动条件，并且底部边界满足无滑移条件。这种类型的流具有类似于固定平板和移动平板之间的湍流平面沟槽流的平均流动模式，而是由于自由滑动边界的效果，由于自由滑动边界的效果，在湍流统计中表现出相当大的差异。基于DNS数据的统计分析和基于泰勒序列的展开的理论推导，显示了三个速度分量的湍流方差随着距边界的垂直距离的二次函数而变化，而雷诺剪切应力呈现线性行为，与无滑动边界附近的对应物非常不同。自由滑动表面条件也导致表面处的零水平涡流，而是允许非零垂直涡度在此期间导致涡流和连贯的涡流结构的近边界统计存在相当大的差异。三个DNS采用不同网格分辨率的比较表明，平稳地解析了自由滑动边界附近的更精力湍流结构，需要更高的水平网格分辨率，而不是用于解析无滑边界附近的结构。

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  • 来源
    《Physics of fluids》 |2019年第8期|共19页
  • 作者

    Li Meng; Yang Di;

  • 作者单位

    Univ Houston Dept Mech Engn Houston TX 77004 USA;

    Univ Houston Dept Mech Engn Houston TX 77004 USA;

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  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 流体力学;
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