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arXiv 2104.14201cond-mat.softphysics.flu-dyn
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旋转剪切作用下筒仓内颗粒流率

Particle flow rate in silos under rotational shear

D. Hernández-Delfin, T. Pongó, K. To, T. Börzsönyi, R. C. Hidalgo

摘要:

最近,To et al.~实验研究了圆筒形筒仓中的颗粒流,筒仓底壁相对于侧壁\cite{Kiwing2019}水平旋转。在这里,我们数值重现他们的实验结果,特别是,作为旋转频率的函数的质量流率$Q$的特殊行为$f$。也就是说,我们发现,对于小的出口直径$D$的流量增加与$f$,而对于较大的$D$的非单调行为得到证实。此外,使用粗粒化技术,我们计算的宏观密度,动量和应力张量场。这些结果最终表明,放电过程中的变化直接关系到从漏斗流到质量流的流动模式的变化。此外,通过将小孔处的质量流(线动量场)分解为宏观速度场和密度场两个主要因素,我们得到了线动量的非单调行为是由密度变化引起的,而不是由宏观速度的变化引起的.此外,通过分析动应力的空间分布,发现对于小孔,增大旋转剪切力可以提高平均动压$\langle p^k \rangle$,提高系统的流动性。这降低了拱的稳定性,因此,体积流量单调增加。然而,对于大的孔口,我们检测到$\langle p^k \rangle$非单调地变化,这可以解释当改变旋转剪切时$Q$的非单调行为。

英文摘要:

Very recently, To et al.~have experimentally explored granular flow in a cylindrical silo, with a bottom wall that rotates horizontally with respect to the lateral wall \cite{Kiwing2019}. Here, we numerically reproduce their experimental findings, in particular, the peculiar behavior of the mass flow rate $Q$ as a function of the frequency of rotation $f$. Namely, we find that for small outlet diameters $D$ the flow rate increased with $f$, while for larger $D$ a non-monotonic behavior is confirmed. Furthermore, using a coarse-graining technique, we compute the macroscopic density, momentum, and the stress tensor fields. These results show conclusively that changes in the discharge process are directly related to changes in the flow pattern from funnel flow to mass flow. Moreover, by decomposing the mass flux (linear momentum field) at the orifice into two main factors: macroscopic velocity and density fields, we obtain that the non-monotonic behavior of the linear momentum is caused by density changes rather than by changes in the macroscopic velocity. In addition, by analyzing the spatial distribution of the kinetic stress, we find that for small orifices increasing rotational shear enhances the mean kinetic pressure $\langle p^k \rangle$ and the system dilatancy. This reduces the stability of the arches, and, consequently, the volumetric flow rate increases monotonically. For large orifices, however, we detected that $\langle p^k \rangle$ changes non-monotonically, which might explain the non-monotonic behavior of $Q$ when varying the rotational shear.

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