Stochastic models for capturing dispersion in particle-laden flows
Stochastic models for capturing dispersion in particle-laden flows
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DOI：
10.1017/jfm.2020.625
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发表时间：
2020-09
影响因子：
3.7
通讯作者：
A. Lattanzi;Vahid Tavanashad;S. Subramaniam;J. Capecelatro
中科院分区：
文献类型：
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作者：
A. Lattanzi;Vahid Tavanashad;S. Subramaniam;J. Capecelatro
摘要本研究提供了一种可用于欧拉-拉格朗日模拟的随机方法的详细说明，以解释邻近诱导的阻力波动。这里研究的框架对应于粒子位置（PL）、粒子速度（VL）和波动阻力（FL）的朗格万方程。给出了每种方法所产生的粒子速度方差（颗粒温度）和分散的严格推导。所得解为与粒子解析直接数值模拟进行比较提供了依据。FL方法允许最复杂的行为，能够控制颗粒温度和分散。对于将力的积分时间尺度与斯托克斯响应时间联系起来的波动力，定义了斯托克斯数St_F。对于St_F \gg 1$，给出了FL格式对VL格式的形式收敛性。在相反的极限$St_F \ll 1$中，波动阻力是高度惯性的，FL格式与VL格式明显不同。
Abstract This study provides a detailed account of stochastic approaches that may be utilized in Eulerian–Lagrangian simulations to account for neighbour-induced drag force fluctuations. The frameworks examined here correspond to Langevin equations for the particle position (PL), particle velocity (VL) and fluctuating drag force (FL). Rigorous derivations of the particle velocity variance (granular temperature) and dispersion resulting from each method are presented. The solutions derived herein provide a basis for comparison with particle-resolved direct numerical simulation. The FL method allows for the most complex behaviour, enabling control of both the granular temperature and dispersion. A Stokes number $St_F$ is defined for the fluctuating force that relates the integral time scale of the force to the Stokes response time. Formal convergence of the FL scheme to the VL scheme is shown for $St_F \gg 1$. In the opposite limit, $St_F \ll 1$, the fluctuating drag forces are highly inertial and the FL scheme departs significantly from the VL scheme.