Abstract The objective of this study is to understand the dynamics of freely evolving particle suspensions over a wide range of particle-to-fluid density ratios. The dynamics of particle suspensions are characterized by the average momentum equation, where the dominant contribution to the average momentum transfer between particles and fluid is the average drag force. In this study, the average drag force is quantified using particle-resolved direct numerical simulation in a canonical problem: a statistically homogeneous suspension where an imposed mean pressure gradient establishes a steady mean slip velocity between the phases. The effects of particle velocity fluctuations, particle clustering, and mobility of particles are studied separately. It is shown that the competing effects of these factors could decrease, increase, or keep constant the drag of freely evolving suspensions in comparison to fixed beds at different flow conditions. It is also shown that the effects of particle clustering and particle velocity fluctuations are not independent. Finally, a correlation for interphase drag force in terms of volume fraction, Reynolds number, and density ratio is proposed. Two different approaches (symbolic regression and predefined functional forms) are used to develop the drag correlation. Since this drag correlation has been inferred from simulations of particle suspensions, it includes the effect of the motion of the particles. This drag correlation can be used in computational fluid dynamics simulations of particle-laden flows that solve the average two-fluid equations where the accuracy of the drag law affects the prediction of overall flow behavior.

中文翻译：

---

自由演化粒子悬浮液的粒子分辨模拟：流动物理和建模

摘要 本研究的目的是了解在广泛的颗粒与流体密度比范围内自由演化的颗粒悬浮液的动力学。粒子悬浮的动力学特征是平均动量方程，其中对粒子和流体之间平均动量传递的主要贡献是平均阻力。在这项研究中，平均阻力是在一个典型问题中使用粒子解析直接数值模拟来量化的：统计均匀的悬浮液，其中施加的平均压力梯度在相之间建立了稳定的平均滑动速度。分别研究了粒子速度波动、粒子聚类和粒子迁移率的影响。结果表明，这些因素的竞争效应可能会减少、增加、或与不同流动条件下的固定床相比，保持自由演化的悬浮液的阻力恒定。还表明粒子聚类和粒子速度波动的影响不是独立的。最后，提出了相间阻力在体积分数、雷诺数和密度比方面的相关性。两种不同的方法（符号回归和预定义的函数形式）用于开发阻力相关性。由于这种阻力相关性是从粒子悬浮的模拟中推断出来的，因此它包括粒子运动的影响。这种阻力相关性可用于含颗粒流的计算流体动力学模拟，该模拟求解平均双流体方程，其中阻力定律的准确性影响整体流动行为的预测。