Stochastic model for the hydrodynamic force in Euler–Lagrange simulations of particle-laden flows
Stochastic model for the hydrodynamic force in Euler–Lagrange simulations of particle-laden flows
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DOI：
10.1103/physrevfluids.7.014301
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发表时间：
2021-03
影响因子：
2.7
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
标准欧拉-拉格朗日（EL）方法通常采用仅表示作用在载有颗粒的悬浮液上的平均流体动力的拖曳力模型。因此，高阶阻力统计，所产生的邻居引起的流扰动，不占;与颗粒速度方差和分散的预测的影响。我们开发了一个力朗之万（FL）模型，把邻居引起的阻力波动作为一个随机力EL框架内。随机阻力遵循Ornstein-Uhlenbeck过程，并且需要闭合脉动水动力和阻力标准差的积分时间尺度。前者是封闭的，使用连续碰撞之间的平均自由时间，来自非均匀气体的动力学理论。对于后者，粒子分辨直接数值模拟（PR-DNS）的固定粒子组件被用来开发的相关性。随机EL框架指定未解决的阻力统计，导致正确的演变和维持粒子速度方差在很宽的范围内的雷诺数和固体体积分数相比，PR-DNS的自由发展的均匀悬浮液。相比之下，标准EL推断阻力统计数据的变化，在解决流，从而低估了均匀悬浮液中的增长和稳定的颗粒速度变化。从标准EL方法的速度统计被发现依赖于用于双向动量耦合的投影函数的带宽，而从随机EL方法获得的结果是不敏感的投影带宽。
Standard Eulerian–Lagrangian (EL) methods generally employ drag force models that only represent the mean hydrodynamic force acting upon a particle-laden suspension. Consequently, higherorder drag force statistics, arising from neighbor-induced flow perturbations, are not accounted for; with implications on predictions for particle velocity variance and dispersion. We develop a force Langevin (FL) model that treats neighbor-induced drag fluctuations as a stochastic force within an EL framework. The stochastic drag force follows an Ornstein-Uhlenbeck process and requires closure of the integral time scale for the fluctuating hydrodynamic force and the standard deviation in drag. The former is closed using the mean-free time between successive collisions, derived from the kinetic theory of non-uniform gases. For the latter, particle-resolved direct numerical simulation (PR–DNS) of fixed particle assemblies is utilized to develop a correlation. The stochastic EL framework specifies unresolved drag force statistics, leading to the correct evolution and sustainment of particle velocity variance over a wide range of Reynolds numbers and solids volume fractions when compared to PR–DNS of freely-evolving homogeneous suspensions. By contrast, standard EL infers drag statistics from variations in the resolved flow and thus under-predicts the growth and steady particle velocity variance in homogeneous suspensions. Velocity statistics from standard EL approaches are found to depend on the bandwidth of the projection function used for two-way momentum coupling, while results obtained from the stochastic EL approach are insensitive to the projection bandwidth.