Scaling relations for granular flow in quasi-two-dimensional rotating cylinders.
Scaling relations for granular flow in quasi-two-dimensional rotating cylinders.
复制标题
DOI：
10.1103/physreve.64.031302
复制
发表时间：
2001-08
期刊：
影响因子：
--
通讯作者：
A. V. Orpe;D. Khakhar
中科院分区：
文献类型：
--
作者：
A. V. Orpe;D. Khakhar
利用流动显示技术对不同材料（钢球、玻璃珠和沙子）在准二维旋转圆柱中的流动进行了实验研究。旋转圆筒中的流动由薄流动表面层和作为固定床旋转的剩余颗粒组成。实验结果表明，缩放层厚度随着弗劳德数（Fr= ω（2）R/g，其中ω是角速度，R是圆柱体半径，g是重力加速度）和尺寸比（s=d/R，其中d是颗粒直径）的增加而增加。自由表面轮廓，在低Fr下几乎是平坦的，并且随着Fr的增加而变得越来越S形。在低Fr下对称的层厚度轮廓在高Fr值和小s下变得偏斜。所有研究材料的动态休止角随转速（Ω）呈近线性增加。实验数据的缩放分析表明，缩放的表面轮廓和缩放层厚度轮廓的形状几乎是相同的，当弗劳德数和尺寸比保持恒定时，对于每种材料。表面轮廓和层厚度轮廓也被发现是几乎独立的所使用的材料。然而，动态休止角（β）不与Fr和s成比例，而是取决于颗粒性质。实验结果进行了比较，在层中的流动的连续模型。Elperin和Vikhansky [Europhys. Lett. 42，619（1998）]和Makse [Phys. Rev. Lett. 83，3186（1999）]在低Fr下显示出良好的一致性，而Khakhar等人[Phys. Fluids，9，31（1997）]在所考虑的整个参数范围内给出了良好的预测。对实验数据的分析表明，在低Fr时，沿层的速度梯度（gamma）几乎是沿着恒定的，在层中点处的计算值随gamma（0）~[gsin（beta（0）-beta（s））/dcos beta（s）]（1/2）而变化，其中beta（s）是静止角，beta（0）是层中点处的界面角。“堆”模型（BCRE，BRdG）的扩展被用来预测的界面角的配置文件，这是在合理的协议与实验测量。
An experimental study of the flow of different materials (steel balls, glass beads, and sand) in quasi-two-dimensional rotating cylinders is carried out using flow visualization. The flow in the rotating cylinder comprises of a thin-flowing surface layer with the remaining particles rotating as a fixed bed. Experimental results indicate that the scaled layer thickness increases with increasing Froude number (Fr=omega(2)R/g, where omega is the angular speed, R is the cylinder radius, and g the acceleration due to gravity) and with increase in size ratio (s=d/R, where d is the particle diameter). The free surface profile, is nearly flat at low Fr and becomes increasingly S shaped with increasing Fr. The layer thickness profiles, which are symmetric at low Fr become skewed at high values of Fr and small s. The dynamic angles of repose for all the materials studied show a near-linear increase with rotational speed (omega). Scaling analysis of the experimental data shows that the shape of the scaled surface profiles and the scaled layer thickness profiles are nearly identical when Froude number and size ratio are held constant, for each material. The surface profiles and layer thickness profiles are also found to be nearly independent of the material used. The dynamic angle of repose (beta), however, does not scale with Fr and s and depends on the particle properties. The experimental results are compared to continuum models for flow in the layer. The models of Elperin and Vikhansky [Europhys. Lett. 42, 619 (1998)] and Makse [Phys. Rev. Lett. 83, 3186 (1999)] show good agreement at low Fr while that of Khakhar et al. [Phys. Fluids, 9, 31 (1997)] gives good predictions over the entire range of parameters considered. An analysis of the data indicate that the velocity gradient (gamma;) is nearly constant along the layer at low Fr, and the value calculated at the layer midpoint varies as gamma;(0)~[g sin(beta(0)-beta(s))/d cos beta(s)](1/2) for all the experimental data, where beta(s) is the static angle of repose and beta(0) is the interface angle at the layer midpoint. An extension of "heap" models (BCRE, BRdG) is used to predict the interface angle profiles, which are in reasonable agreement with experimental measurements.