Abstract Simulations of granular flow assume a consistent flowing layer profile observed in circular tumblers that were half full. While the constant shear rate model predicts mixing kinematics adequately, the model has not been empirically tested in systems where the erosion from the solid body has inertial velocity components along the dynamic angle of repose. This paper explores experiments that analyze the relationship between tumbler fill fraction and the kinematics of the erosion boundary transition into the flowing layer. Tumblers greater than 50% full have inertial velocity along the angle of repose whereas fill conditions less than 50% enter with velocity opposite the free surface angle. Results confirm that flowing layer chord length alone properly scales flowing layer depth only when fill fraction is near 50% – otherwise fill fraction must be considered. This is due to the streamwise velocity of particles at the erosion boundary affecting the energy balance of the system. In addition, the asymmetric velocity profile derived from the non-dimensional momentum equation is confirmed for non-half full systems. Lastly, linear and exponential shear models are explored and shown to be qualitatively similar and variation is only exhibited at extreme fill and far ends of the flowing layer.

中文翻译：

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由于准二维颗粒滚筒内填充率变化引起的侵蚀边界效应

摘要 颗粒流模拟假设在半满的圆形滚筒中观察到一致的流动层轮廓。虽然恒定剪切速率模型充分预测了混合运动，但该模型尚未在固体侵蚀具有沿动态休止角的惯性速度分量的系统中进行经验测试。本文探讨了分析滚筒填充率与侵蚀​​边界过渡到流动层的运动学之间关系的实验。大于 50% 的不倒翁沿静止角具有惯性速度，而小于 50% 的填充条件以与自由表面角相反的速度进入。结果证实，仅当填充率接近 50% 时，单独的流动层弦长才能正确调整流动层深度——否则必须考虑填充率。这是由于侵蚀边界处粒子的流向速度影响了系统的能量平衡。此外，从无量纲动量方程导出的非对称速度剖面在非半满系统中得到证实。最后，探索了线性和指数剪切模型，并表明它们在性质上是相似的，并且变化仅在流动层的极端填充和远端出现。由无量纲动量方程导出的非对称速度分布在非半满系统中得到证实。最后，探索了线性和指数剪切模型，并表明它们在性质上是相似的，并且变化仅在流动层的极端填充和远端出现。由无量纲动量方程导出的非对称速度分布在非半满系统中得到证实。最后，探索了线性和指数剪切模型，并表明它们在性质上是相似的，并且变化仅在流动层的极端填充和远端出现。