Bignon Agathe, Renouf Mathieu, Sicard Roland, Azéma Emilien
LMGC, Université de Montpellier, CNRD, 34090 Montpellier, Herault, France.
Thess Corporate, 34090 Montpellier, Herault, France.
Phys Rev E. 2023 Nov;108(5-1):054901. doi: 10.1103/PhysRevE.108.054901.
By means of two-dimensional numerical simulations based on contact dynamics, we present a systematic analysis of the joint effects of grain shape (i.e., grain elongation) and system size on silo discharge for increasing orifice sizes D. Grains are rounded-cap rectangles whose aspect ratio are varied from 1 (disks) to 7. In order to clearly isolate the effect of grain shape, the mass of the grains is keeping constant as well as the condition of the discharge by reintroducing the exiting grains at the top of the silo. In order to quantify the possible size effects, the thickness W of the silos is varied from 7 to 70 grains diameter, while keeping the silos aspect ratio always equal to 2. We find that, as long as size effects are negligible, the flow rate Q increases as a Beverloo-like function with D, also for the most elongated grains. In contrast, the effects of grain elongation on the flow rate depend on orifice size. For small normalized orifice sizes, the flow rate is nearly independent with grain elongation. For intermediate normalized orifice sizes the flow rate first increases with grain elongation up to a maximum value that depends on the normalized size of the orifice and saturates as the grains become more elongated. For larger normalized orifice size, the flow rate is an increasing function of grains' aspect ratio. Velocity profiles and packing fraction profiles close to the orifice turn out to be self-similar for all grain shapes and for the whole range of orifice and system sizes studied. Following the methodology introduced by Janda et al. [Phys. Rev. Lett. 108, 248001 (2012)PRLTAO0031-900710.1103/PhysRevLett.108.248001], we explain the nonlinear variation of Q with grain elongation, and for all orifice sizes, from compensation mechanisms between the velocity and packing fraction measured at the center of the orifice. Finally, an equation to predict the evolution of Q as a function of the aspect ratio of the grains is deduced.
通过基于接触动力学的二维数值模拟，我们对颗粒形状（即颗粒伸长率）和系统尺寸对筒仓卸料的联合影响进行了系统分析，其中卸料口尺寸D不断增大。颗粒为圆帽形矩形，其长宽比从1（圆盘）变化到7。为了清晰地分离颗粒形状的影响，通过在筒仓顶部重新引入排出的颗粒，使颗粒质量以及卸料条件保持不变。为了量化可能的尺寸效应，筒仓厚度W从7个颗粒直径变化到70个颗粒直径，同时保持筒仓长宽比始终等于2。我们发现，只要尺寸效应可忽略不计，对于最细长的颗粒，流量Q也会随着D以类似贝弗洛的函数形式增加。相比之下，颗粒伸长对流量的影响取决于卸料口尺寸。对于较小的归一化卸料口尺寸，流量几乎与颗粒伸长无关。对于中等归一化卸料口尺寸，流量首先随着颗粒伸长而增加，直至达到一个取决于卸料口归一化尺寸的最大值，并且随着颗粒变得更加细长而趋于饱和。对于较大的归一化卸料口尺寸，流量是颗粒长宽比的增函数。对于所有颗粒形状以及所研究的整个卸料口和系统尺寸范围，靠近卸料口的速度分布和堆积分数分布结果是自相似的。遵循扬达等人[《物理评论快报》108, 248001 (2012)PRLTAO0031 - 900710.1103/PhysRevLett.108.248001]引入的方法，我们从卸料口中心测量的速度和堆积分数之间的补偿机制出发，解释了Q随颗粒伸长的非线性变化，以及对于所有卸料口尺寸的情况。最后，推导了一个预测Q随颗粒长宽比变化的方程。
