Chen Pengfei, Ottino Julio M, Lueptow Richard M
Department of Chemical and Biological Engineering, Northwestern University, Evanston, Illinois 60208, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Aug;78(2 Pt 1):021303. doi: 10.1103/PhysRevE.78.021303. Epub 2008 Aug 14.
To better understand the subsurface velocity field and flowing layer structure, we have performed a detailed numerical study using the discrete element method for the flow of monodisperse particles in half-full three-dimensional (3D) and quasi-2D rotating tumblers. Consistent with prior measurements at the surface, a region of high speed flow with axial components of velocity occurs near each endwall in long tumblers. This region can be eliminated by computationally omitting the friction at the endwalls, confirming that a mass balance argument based on the slowing of particles immediately adjacent to the frictional endwalls explains this phenomenon. The high speed region with the associated axial flow near frictional endwalls persists through the depth of the flowing layer, though the regions of high velocity shift in position and the velocity is lower compared to the surface. The axial flow near the endwalls is localized and independent with the length of the tumbler for tumblers longer than one tumbler diameter, but these regions interact for shorter tumblers. In quasi-2D tumblers, the high speed regions near the endwalls merge resulting in a higher velocity than occurs in a long tumbler, but with a flowing layer that is not as deep. Velocity fluctuations are altered near the endwalls. Particle velocity fluctuations are greatest just below the surface and diminish through the depth of the flowing layer.
为了更好地理解地下速度场和流动层结构，我们使用离散元方法对单分散颗粒在半满三维（3D）和准二维旋转转鼓中的流动进行了详细的数值研究。与先前在表面的测量结果一致，在长转鼓的每个端壁附近会出现一个具有轴向速度分量的高速流动区域。通过在计算中忽略端壁处的摩擦力，可以消除该区域，这证实了基于紧邻摩擦端壁的颗粒减速的质量平衡论点可以解释这一现象。尽管高速区域的位置会发生移动且速度比表面处低，但在摩擦端壁附近具有相关轴向流动的高速区域会贯穿流动层的深度。对于长度超过一个转鼓直径的转鼓，端壁附近的轴向流动是局部化的，并且与转鼓长度无关，但对于较短的转鼓，这些区域会相互作用。在准二维转鼓中，端壁附近的高速区域会合并，导致速度比长转鼓中的速度更高，但流动层没有那么深。端壁附近的速度波动会发生变化。颗粒速度波动在表面下方最大，并在流动层深度范围内逐渐减小。
