We present a verification study of three simulation techniques for fluid–particle flows, including an Euler–Lagrange approach (EL) inspired by Jackson's seminal work on fluidized particles, a quadrature–based moment method based on the anisotropic Gaussian closure (AG), and the traditional two-fluid model. We perform simulations of two problems: particles in frozen homogeneous isotropic turbulence (HIT) and cluster-induced turbulence (CIT). For verification, we evaluate various techniques for extracting statistics from EL and study the convergence properties of the three methods under grid refinement. The convergence is found to depend on the simulation method and on the problem, with CIT simulations posing fewer difficulties than HIT. Specifically, EL converges under refinement for both HIT and CIT, but statistics exhibit dependence on the postprocessing parameters. For CIT, AG produces similar results to EL. For HIT, converging both TFM and AG poses challenges. Overall, extracting converged, parameter-independent Eulerian statistics remains a challenge for all methods. © 2017 American Institute of Chemical Engineers AIChE J, 2017

中文翻译：

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验证湍流-颗粒流的欧拉-欧拉和欧拉-拉格朗日模拟

我们提供了对三种流体-颗粒流动模拟技术的验证研究，其中包括受杰克逊关于流化颗粒的开创性工作启发的欧拉-拉格朗日方法（EL），基于各向异性高斯封闭（AG）的基于矩的矩量法，以及传统的两流体模型。我们执行两个问题的模拟：冻结均质各向同性湍流（HIT）和团簇诱导湍流（CIT）中的粒子。为了进行验证，我们评估了从EL中提取统计数据的各种技术，并研究了网格细化下这三种方法的收敛性。发现收敛取决于仿真方法和问题，CIT仿真的难度比HIT小。具体来说，EL在HIT和CIT的优化下都趋于收敛，但是统计数据显示出对后处理参数的依赖性。对于CIT，AG产生的结果与EL相似。对于HIT，融合TFM和AG带来了挑战。总体而言，提取收敛的，与参数无关的欧拉统计量仍然是所有方法的挑战。©2017美国化学工程师学会AIChE的Ĵ，2017年