论文标题
在湍流中重力下沉降的颗粒相对速度的统计
Statistics of relative velocity for particles settling under gravity in a turbulent flow
论文作者
论文摘要
我们研究了相对速度的分离，$ r $和径向分量的联合概率分布，$ v _ {\ rm rm r} $是在湍流中重力下降的粒子的粒子。我们还获得了这些分布的时刻，并使用球形谐波分析了它们的各向异性。我们发现，联合分布的定性性质与无重力案例相同。 $ v _ {\ rm rm}的分布$ r $的固定值显示power-v _ {\ rm rm r} $的powerlaw依赖性，对于$ v _ {\ rm rm r} $的范围，powerlaw的指数依赖于重力。重力的影响也以以下方式表现出来：（a）分布的力矩是各向异性的；各向异性的程度取决于粒子的stokes数字，但不取决于$ r $ $ r $的$ r $。 （b）对于具有相等的stokes数量的粒子，两个颗粒之间碰撞之间的碰撞速度降低，但对于具有不同stokes数量的颗粒而增加。对于后来，碰撞速度是通过其沉降速度的差异来设定的。
We study the joint probability distributions of separation, $R$, and radial component of the relative velocity, $V_{\rm R}$, of particles settling under gravity in a turbulent flow. We also obtain the moments of these distributions and analyze their anisotropy using spherical harmonics. We find that the qualitative nature of the joint distributions remains the same as no gravity case. Distributions of $V_{\rm R}$ for fixed values of $R$ show a power-law dependence on $V_{\rm R}$ for a range of $V_{\rm R}$, exponent of the power-law depends on the gravity. Effects of gravity are also manifested in the following ways: (a) moments of the distributions are anisotropic; the degree of anisotropy depends on particle's Stokes number, but does not depend on $R$ for small values of $R$. (b) mean velocity of collision between two particles is decreased for particles having equal Stokes numbers but increased for particles having different Stokes numbers. For the later, collision velocity is set by the difference in their settling velocities.
