Extended kinetic theory applied to inclined granular flows: role of boundaries
Extended kinetic theory applied to inclined granular flows: role of boundaries
复制标题
DOI：
10.1007/s10035-017-0738-1
复制
发表时间：
2017-07
期刊：
影响因子：
2.4
通讯作者：
D. Gollin;D. Berzi;E. Bowman
中科院分区：
文献类型：
--
作者：
D. Gollin;D. Berzi;E. Bowman
我们比较扩展动力学理论（EKT）的预测，其中的表面摩擦和相关性的波动速度的作用被考虑在内，与离散元模拟的稳定，充分发展，倾斜流动的相同的球体颠簸的基础上，在存在和不存在的平坦，摩擦侧壁。我们表明，EKT的压力的本构关系必须修改的边界附近，因为排除体积和屏蔽与粒子的碰撞与边界本身的影响。我们还注意到，目前可用的边界条件的流动在颠簸的飞机在动力学理论低估了能量耗散。这两个观测结果解释了EKT与模拟结果不一致的原因，即在最大倾斜角方面，稳定、充分发展的流动是可能的。也就是说，对于一些高角度的倾斜，EKT没有解决方案，而稳定的流动在DEM中预测。然而，只要一个解决方案的微分方程系统的EKT确实存在，预测的速度，固体体积分数和颗粒温度的分布令人满意地匹配的数值测量。不可压缩的，代数近似的EKT，它忽略了能量平衡中的能量传导，承认解决方案的倾斜角的范围更广，在模拟中，但未能再现的定量和定性行为的固体体积分数和颗粒温度在两个导电层的顶部和底部的流动。当摩擦侧壁添加到域中，我们表明，展向比的剪切应力压力是线性分布在致密的核心区域的流，确认侧壁施加，平均而言，库仑阻力的流动与有效的摩擦系数，这是小于一半的实际颗粒壁摩擦。
We compare the predictions of extended kinetic theory (EKT), where the roles of surface friction and correlation in fluctuation velocities are taken into account, with discrete element simulations of steady, fully-developed, inclined flows of identical spheres over bumpy bases, in the presence and absence of flat, frictional sidewalls. We show that the constitutive relation for the pressure of EKT must be modified in the proximity of the boundary, because of the influence of excluded volume and shielding associated with collisions of particles with the boundary itself. We also note that currently available boundary conditions for flows over bumpy planes in kinetic theory underestimate the energy dissipation. These two observations explain the lack of agreement of EKT with the simulations, in terms of the maximum angles of inclination for which steady, fully-developed flows are possible. That is, for some high angles of inclination, EKT does not have solutions, while steady flows are predicted in DEM. However, whenever a solution to the system of differential equations of EKT does exist, the predicted distributions of velocity, solid volume fraction and granular temperature satisfactorily match the numerical measurements. The incompressible, algebraic approximation of EKT, which ignores the conduction of energy in the energy balance, admits solutions for a wider range of angles of inclination, as in the simulations, but fails to reproduce the quantitative and qualitative behaviour of solid volume fraction and granular temperature in the two conductive layers at the top and bottom of the flow. When frictional sidewalls are added to the domain, we show that the spanwise ratio of shear stress to pressure is linearly distributed in the dense core region of the flow, confirming that the sidewalls exert, on average, a Coulomb-like resistance to the flow with an effective friction coefficient which is less than half the actual particle-wall friction.