Spatial and velocity statistics of inertial particles in turbulent flows
Spatial and velocity statistics of inertial particles in turbulent flows
复制标题
湍流中惯性粒子的空间和速度统计
DOI：
10.1088/1742-6596/333/1/012003
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
F. Toschi
中科院分区：
文献类型：
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作者：
J. Bec;Luca Biferale;M. Cencini;A. Lanotte;F. Toschi
采用直接数值模拟方法，在泰勒尺度雷诺数Reλ <$200和Reλ <$400两个数值条件下，分别对应于5123和20483个网格点，研究了不可压、均质、各向同性三维湍流中点状重粒子的空间和速度统计特性。粒子斯托克斯数值范围从St = 0.2到70。静止的小尺度颗粒分布显示一个奇异的多重分形测量，其特征在于由一组广义分形维数与斯托克斯数和一个可能的，小雷诺数的依赖性具有很强的敏感性。两个惯性粒子之间的速度增量取决于平滑事件之间的相对权重-其中粒子速度与流体速度大致相同-以及焦散贡献-当两个接近的粒子具有非常不同的速度时。后者的事件导致一个不可微的小尺度行为的相对速度。这两个贡献的相对权重随着惯性重要性的变化而变化。结果表明，速度差的矩具有准双分形性质，并且在Stokes数不太小的情况下，速度增量的标度性质与K. Gustavsson和B. Mehlig arXiv：1012.1789v1 [physics.flu-dyn]，将速度标度指数的饱和度与颗粒聚集的分形维数联系起来。
Spatial and velocity statistics of heavy point-like particles in incompressible, homogeneous, and isotropic three-dimensional turbulence is studied by means of direct numerical simulations at two values of the Taylor-scale Reynolds number Reλ ∼ 200 and Reλ ∼ 400, corresponding to resolutions of 5123 and 20483 grid points, respectively. Particles Stokes number values range from St ≈ 0.2 to 70. Stationary small-scale particle distribution is shown to display a singular –multifractal– measure, characterized by a set of generalized fractal dimensions with a strong sensitivity on the Stokes number and a possible, small Reynolds number dependency. Velocity increments between two inertial particles depend on the relative weight between smooth events - where particle velocity is approximately the same of the fluid velocity-, and caustic contributions - when two close particles have very different velocities. The latter events lead to a non-differentiable small-scale behaviour for the relative velocity. The relative weight of these two contributions changes at varying the importance of inertia. We show that moments of the velocity difference display a quasi bi-fractal-behavior and that the scaling properties of velocity increments for not too small Stokes number are in good agreement with a recent theoretical prediction made by K. Gustavsson and B. Mehlig arXiv: 1012.1789v1 [physics.flu-dyn], connecting the saturation of velocity scaling exponents with the fractal dimension of particle clustering.